Side channels to improve navigability on the river Waal

November 2005

Author: Corstiaan van Dam

Side channels to improve navigability on the river Waal November 2005

Preface

This document is the final report for the MSc. thesis work of Corstiaan van Dam, student at Delft University of Technology, Faculty of Civil Engineering & Geosciences. The work was carried out between February 2005 and October 2005, partly at WL | Delft Hydraulics and partly at RIZA, Arnhem.

The work was commissioned by the Ministry of Transport, Public Works and Water Management. It concerns a possible solution to the problem of a fast growing pointbar in the inner bend of the river Waal at Hulhuizen, The Netherlands.

I would like to use this opportunity to thank Rijkswaterstaat, Oost-Nederland for the financial support and the supervision by ir. R.H. Smedes, which I also gratefully acknowledge. WL | Delft Hydraulics for the facilities and assistance during my stay there. Especially the advice of dr.ir. H.R.A. Jagers and dr.ir.C.J. Sloff has been indispensable.

Dr.ir. E. Mosselman was the supervisor of this study. His encouraging support and guidance are acknowledged with gratitude.

Furthermore, I would like to thank prof. dr. ir. H.J. de Vriend (Chairman) and drs. R. Booij for being members of my graduation committee and dr.ir. A. Sieben for being my supervisor at RIZA.

Delft, November 2005

Corstiaan van Dam

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Summary

Rivers in the Netherlands are not only meant to safely discharge; water, ice and sediment, they also have an important role in the National economy. Due to the favourable position of the Netherlands on the North Sea, the rivers form important fairways to the hinterland. In the past, this location already gave rise to significant activity in the sea harbours and on the inland waterways. To maintain this favourable position, the economical processes in the harbours and on the rivers should be optimised. With respect to inland navigation, obstacles should be removed as much as possible, to maximise the efficiency of the navigation routes. One of the principle limiting factors for navigation in the Dutch rivers is the limited navigable width in bends. Every year, during flood period, the bed level in the inner bends increases rapidly and limits the width for navigation in the subsequent low-water period. Several studies have been performed on how to reduce this so-called pointbar formation. This report investigates the possibility of a certain type of floodplain intervention to reduce the effect of pointbar formation on the navigable width. Via Multi Criteria Analysis and a rough qualitative assessment, it was decided to study the applicability of side channel for this purpose. Side channels are applied nowadays to increase flood conveyance and biodiversity, but never with the intention to reduce pointbar formation.

First, an analytical model (from De Vriend and Stuiksma [1983]) predicting bed deformation in curved alluvial channels was used to get an impression of the morphological activity in the Hulhuizen bend. In order to understand the morphological activity, it is necessary to consider not only the bed topography, but also the water and sediment motion in a channel of transient curvature. The bed level deformation is a combination of the following two phenomena:

1. tilting of the transverse bed slope (axi-symmetrical solution) 2. overshoot phenomenon

The analytical model showed that the overshoot phenomenon is likely to occur only at relatively small discharges (sufficiently high width-to-depth ratio). At these low discharges, the damping lengths become negative, which corresponds to exponential growth of the bed level. The corresponding morphological time scale during the actual low-water season (more than nine months), however, is too long to allow this bed evolution to take place. This indicates that the observed navigable width problems directly after flood a period cannot be ascribed to the overshoot phenomenon.

At higher discharges, the damping length becomes positive, which implies rapidly decaying amplitude of the overshoot. The model showed that the bed level tends to develop rapidly towards the axi-symmetric solution, without overshooting it. The morphological time scale corresponding to this phenomenon is relatively small compared to the time scale for the overshoot phenomenon. The conclusion from the analytical model is therefore that the tilting of the transverse bed slope, which is the predominant morphological activity during flood, is the most propable cause of the observed navigable width problem.

In order to determine the influence of side channel application, the Delft3D SED-online (2D depth-averaged) program was used, in which an existing model of the Waal at Hulhuizen was adjusted to the present conditions.

The general morphological phenomenon, caused by withdrawing water from the main channel is a one-dimensional sedimentation wave. This tends to increase the bed level, which is

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unfavourable to navigation. On the other hand, the analytical model showed that when the discharge through the main channel is reduced, the pointbar tends to be less pronounced. Furthermore, the analytical model showed that a decrease of discharge coincides with an increase of the morphological time scale. It is the combination of both the one-dimensional sedimentation wave and the tilting of the transverse bed slope, that determines the actual bed level.

A number of computations have been made, most of them with constant discharges of 3500 m3/s or 4500 m 3/s. First, a reference computation was made, in which no water is extracted. Subsequently, a computation was made, in which only water was abstracted. Finally, computations were made in which both water and sediment were abstracted

Four side channels alignments were taken into account. By a lack of time, however, most computations were executed with the same side channel alignment. The following conclusions are derived from the computations for this side channel:

• The offtake location should be located such, that the one-dimensional bed level wave, which starts at the offtake and gradually expands downstream cannot reach the critical cross-section. The results showed a propagation length of 900 m for a simulation period of one year.

• The bed level in the inner bend increases less fast if the side channel transports only water.

• Lateral withdrawal of water only has not only a positive effect on the rate of pointbar accretion, but it is also able to reduce its maximum height. To reduce the pointbar height at higher discharges, relatively more water needs to be withdrawn than at lower discharge discharges.

• Lateral withdrawal of both water and sediment decreases the pointbar height and accretion rate even more than when only water is abstracted.

• Yet, the results of this study did not show a significant increase of navigable width within a time span of one year.

The computations in this study were mainly executed with a constant discharge and only for a period of one year. It is recommendable to extend the simulation time and execute the computations with a varying discharge, because this corresponds more to reality. It is also recommended and to include the bed level legacy from the previous flood periods. Furthermore, Delft3D-SEDonline should be adjusted to simulate the spilling process over the summer dikes, which makes the modelling of the exchange between floodplain and summer bed possible. Therefore, the computational model should be extended with the floodplain area. These two adjustments will constitute another step forward towards more accurate simulation.

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Contents

PREFACE ...... I

SUMMARY...... II

LIST OF FIGURES ...... VI

LIST OF TABLES ...... VIII

NOTATION ...... IX

1. INTRODUCTION...... 1

1.1. MOTIVE ...... 1 1.2. PROBLEM ANALYSIS ...... 4 1.3. RESEARCH QUESTION ...... 6 1.4. OBJECTIVE ...... 6 1.5. APPROACH ...... 6

2. STATE OF ART ...... 7

2.1. RIVER MORPHOLOGY ...... 7 2.1.1. QUALITATIVE ANALYSIS ...... 7 2.1.2. SPIRAL MOTION ...... 9 2.1.3. THEORETICAL MODEL ...... 10 2.2. EFFECTS OF FLOOD PLAIN LOWERING ...... 12 2.3. SIDE CHANNELS ...... 14 2.3.1. BIFURCATION ...... 16 2.3.2. CONFLUENCES ...... 18 2.3.3. NUMERICAL MODELLING ...... 22 2.3.4. RIVER MORPHOLOGY DUE TO SIDE CHANNEL APPLICATION ...... 22

3. IDENTIFICATION OF SUITABLE MEASURES...... 25

3.1. TIME SCALES OF GENERAL BED LEVEL DEVELOPMENT ...... 25 3.2. MORPHOLOGY AT HULHUIZEN ...... 25 3.3. ANALYTICAL MODEL ...... 27 3.3.1. BOTTOM TOPOGRAPHY ...... 27 3.3.2. INPUT PARAMETERS ...... 29 3.3.3. RESULTS OF THE ANALYTICAL MODEL ...... 31 3.3.4. SENSITIVITY ANALYSIS ...... 36 3.4. EVALUATION OF THE DREDGING TEST AT HULHUIZEN IN 1992 ...... 41 3.5. ANALYTICAL MODEL VS . D REDGING TEST ...... 42 3.6. GENERATION OF ALTERNATIVES ...... 45 3.6.1. INTRODUCTION ...... 45 3.6.2. ALTERNATIVES ...... 45 3.7. SELECTION OF ALTERNATIVES ...... 54

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4. NUMERICAL MODELLING ...... 59

4.1. RIVER GEOMETRY ...... 60 4.2. MODEL INPUT ...... 61 4.2.1. MODEL PARAMETERS ...... 61 4.2.2. INITIAL CONDITIONS ...... 61 4.2.3. BOUNDARY CONDITIONS ...... 62 4.3. CALIBRATION ...... 63 4.4. SENSITIVITY ANALYSIS ...... 65 4.4.1. INTRODUCTION ...... 65 4.4.2. CONCLUSION ...... 65 4.5. SIDE CHANNEL MODELLING...... 66 4.6. SIDE CHANNEL ALIGNMENT ...... 67

5. RESULTS ...... 70

5.1. INTRODUCTION ...... 70 5.2. REFERENCE SITUATION ...... 70 3 5.3. DISCHARGE WITHDRAWAL AT A CONSTANT DISCHARGE OF 3500 M /S...... 71 3 5.3.1. RESULTS DISCHARGE WITHDRAWAL OF 500 M /S ...... 71 5.3.2. RESULTS DISCHARGE WITHDRAWAL OF 250 M3/S ...... 74 5.3.3. RESULTS DISCHARGE AND SEDIMENT WITHDRAWAL OF 500 M3/S ...... 75 5.4. DISCHARGE WITHDRAWAL AT A CONSTANT DISCHARGE OF Q = 4500 M3/S...... 77 5.4.1. RESULTS DISCHARGE WITHDRAWAL OF 250 M3/S ...... 77 3 5.4.2. RESULTS DISCHARGE WITHDRAWAL OF 500 M /S ...... 78 3 5.4.3. RESULTS DISCHARGE AND SEDIMENT WITHDRAWAL OF 500 M /S ...... 78 5.5. RESULTS FLOOD COMPUTATIONS ...... 80 5.6. MORPHOLOGICAL ANALYSIS ...... 82 5.6.1. 1-D MORPHOLOGICAL PHENOMENA ...... 82 5.6.2. 2-D MORPHOLOGICAL PHENOMENON ...... 83 5.7. NAVIGABLE WIDTH ...... 83 5.8. SIDE CHANNEL DIMENSIONS ...... 90

6. CONCLUSIONS...... 91

7. RECOMMENDATIONS...... 93

REFERENCES...... 94

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List of figures

Figure 1-1: Rivers of major economic value ...... 2 Figure 1-2: Runoff area of the river Rhine...... 2 Figure 1-3: River Waal at Hulhuizen ...... 3 Figure 1-4: Discharges Rivers Rhine and Waal...... 4 Figure 2-1: Schematic profile of a crossing...... 7 Figure 2-2: Principle of secondary flow...... 9 Figure 2-3: Spiral motion in a river bend (illustration by K. Nuyten) ...... 10 Figure 2-4: Theoretical vertical distribution of transverse velocities in river bends. Jansen [1979] ...... 11 Figure 2-5: Spiral water motion in offtaking channel ...... 17 Figure 2-6: Length ratio, offtake angles and orientation angle...... 17 Figure 2-7: Scour formation in laboratory flumes depending on the orientation angles...... 18 Figure 2-8: Relation between maximum scour depth, ds, and confluence angle α, compiled from four studies ...... 20 Figure 2-9: Morphological reaction in the main channel ...... 23 Figure 3-1: 1-D Time scale...... 31 Figure 3-2: 2-D Morphological time scale ...... 31 Figure 3-3: 1-D Bed celerity...... 31 Figure 3-4: 2-D Bed celerity...... 31 Figure 3-5: Bed level due to the axi-symmetrical solution plus overshoot (m)...... 32 Figure 3-6: Damping length as a function of IP and b ...... 33 Figure 3-7: Wave length as a function of IP and b ...... 33 Figure 3-8: Wave and damping length of periodic solutions...... 33 Figure 3-9: Bed level (m) ...... 35 Figure 3-10: Axi-symmetrical bed level (m), maximum bed level (m) and relative influence of overshoot (-)...... 35 Figure 3-11: Bed level due to axi-symmetric solution and overshoot phenomenon...... 44 Figure 3-12: Possible solutions of the first type ...... 46 Figure 3-13: Normal secondary flow in a river bend ...... 46 Figure 3-14: Adjusted secondary flow ...... 46 Figure 3-15: Alternative 1: Side channel alignment ...... 47 Figure 3-16: Overview dike set back and groyne extension...... 48 Figure 3-17: Principle of dike setback and groyne extension...... 48 Figure 3-18: Alternative 3a; side channel layout ...... 49 Figure 3-19: Alternative 3b; side channel layout...... 49 Figure 3-20: Alternative 4; Bend cut-off...... 50 Figure 3-21: Alternative 4b: Radical Bend cut-off ...... 50 Figure 3-22: Alternative 5: Groyne extension downstream of Pannerdensche Kop ...... 51 Figure 3-23: Alternative 6: Submerged vanes parallel along river axis ...... 52 Figure 3-24: Alternative 7; Side channel to blow away pointbar ...... 53 Figure 4-1: Initial computational grid Hulhuizen ...... 60 Figure 4-2: Example Discrete upstream boundary condition ...... 62 Figure 4-3: Final overall computational grid...... 64 Figure 4-4: Computational grid, bend Hulhuizen ...... 64 Figure 4-5: Bed level N=2,15 T 750 days Engelund-Hansen, Q = 1600 m 3/s...... 66 Figure 4-6: Adapted morphological grid Side channel ...... 67 Figure 4-7: Side channel 1...... 67 Figure 4-8: Side channel 2...... 68 Figure 4-9: Side channel 3...... 68 Figure 4-10: Side channel 4...... 69 Figure 5-1: Bed level difference between Channel 1 and Reference situation [m]...... 71

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Figure 5-2: Bed level difference between Channel 2 and Reference situation [m]...... 72 Figure 5-3: Bed level difference between Channel 3 and Reference situation [m]...... 72 Figure 5-4: Bed level difference between Channel 4 and Reference situation [m]...... 73 Figure 5-5: Water level difference between Channel 3 and reference situation ...... 74 Figure 5-6: Bed level change in the bend it self of side channel 3 (blown-up)...... 75 Figure 5-7: Bed level difference due to the abstraction of water and sediment...... 76 Figure 5-8: Bed development borderline as a function of time for Q = 3500 m 3/s ...... 77 Figure 5-9: Bed level change between channel 1 and reference situation at T= 42 days ...... 78 Figure 5-10: Bed development borderline as a function of time for Q = 4500 m 3/s ...... 79 Figure 5-11: Bed level difference at the end of flood period...... 80 Figure 5-12: Bed development borderline as a function of time for flood period...... 81 Figure 5-13: Pointbar height as a function of time [m] ...... 81 Figure 5-14: Bed level difference between reference situation and side channel 1...... 83 Figure 5-15: Initial situation ...... 84 Figure 5-16: Result after flood period ...... 84 Figure 5-17: Location critical cross-section...... 85 Figure 5-18: Critical cross-section Q = 3500 m 3/s ...... 86 Figure 5-19: Critical cross-section Q = 4500 m 3/s ...... 86 Figure 5-20: Cross-section HW computation ...... 87 Figure 5-21: (Bed level - OLR) development in critical cross-section after low water season...... 88 Figure 5-22: Overview navigable width after low water period ...... 89 Figure 5-23: (Bed level - OLR) in new critical cross-section development after low water season...... 89 Figure 5-24: Side channel 1 alignment...... 90

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List of tables

Table 1-1: River characteristics ...... 1 Table 3-1: Input parameters analytical model ...... 30 Table 3-2: Input parameters for overshoot calculation and results (m)...... 34 Table 3-3: Original values of the input parameters for Engelund-Hansen power law calculation...... 37 Table 3-4: Input parameters for Meyer-Peter-Müller transport formula...... 39 Table 3-5: Morphological time scales according to dredging test 1992 (days) ...... 42 Table 3-6: Comparison table (days), Taal (’94) and analytical model...... 43 Table 3-7: Criteria and variables used in the MCA ...... 54 Table 3-8: Qualitative Multi Criteria Analysis ...... 55 Table 4-1: Model parameters for Delft 3D...... 61 Table 5-1: Reference pointbar heights for Q = 3500 m 3/s and Q= 4500 m 3/s ...... 70 Table 5-2: Pointbar height comparison ...... 73 Table 5-3: Pointbar height at a withdrawal of 250 m3/s...... 74 Table 5-4: Pointbar heights due to water and sediment abstraction at Q =3500 m 3/s...... 76 Table 5-5: Maximum pointbar heights due to water (500 m 3/s) abstraction at after 42 days .. 77 Table 5-6: Maximum pointbar heights due to water (500 m 3/s) abstraction at after 42 days .. 78 Table 5-7: Maximum pointbar heights due to water and sediment abstraction at Q =4500 m 3/s ...... 79 Table 6-1: Pointbar height (m) difference due to extraction of 500 m 3/s...... 92

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Notation

A spiral motion coefficient depending on hydraulic roughness (Waal A ≈ 10) [-] b power of the velocity term in the transport formula [-] B width (summer bed) m C Chézy coefficient m1/2 /s cb 1-D bed propagation velocity m/s cr 2-D bed propagation velocity m/s D grain size diameter (Waal D ≈ 1 mm) mm EP pore volume coefficient [-] f( θ0) cross-slope effect [-] Fc centripetal force N Fr o (undisturbed) Froude number [-] g acceleration due to gravity m/s 2 h water depth m h0 water depth at the river axis m h(0) water depth on T = 0 m h(t) water depth on T = t m h( ∞) equilibrium water depth m heq equilibrium water depth m H bed level due to axi-symmetrical solution and overshoot m H0 amplitude of axi-symmetrical cross-profile m Hmax maximum bed level due to axi-symmetrical solution and overshoot m I spiral flow intensity m/s ieq equilibrium bed slope [-] IP interaction parameter [-] LD damping length scale m Lp wave length of steady alternate bar m Q discharge m3/s 3 Q0 initial discharge m /s ∆Q abstracted discharge m3/s R radius of channel curvature m s,n local coordinate system [-] S total sediment transport m3/s 3 S0 initial sediment transport m /s 2 s0 undisturbed sediment transport m /s ∆S abstracted sediment m3/s T0 1-D morphological time scale s T 2-D morphological time scale s Te effective time scale according to analytical recovery relation s t time s u velocity component along x or s axis m/s U depth average velocity m/s v velocity component along y or n axis m/s x,y,z global coordinate system m Zb bed level m β cross-slope [-] ∆ relative sediment density [-] θ0 Shields parameter [-] θcr critical Shields value [-] -1 Γˆ curvature m ρ density of water kg/m 3

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3 ρs density of sediment kg/m µ ripple factor [-] λs relaxation length of the sediment motion m λw relaxation length of the water motion m

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1. Introduction

1.1. Motive The Netherlands has a favourable position in Northwest Europe, due to its location near the North Sea and its main thoroughfares, the rivers Rhine and Meuse. In the past, this location has led already to large economical activity in the sea harbours and on the inland waterways. Rotterdam is one of the world’s largest sea harbours and has therefore a pivot position in Europe. The many commodities that are transhipped into inland vessels in Rotterdam and transported further into Europe confirm this. Many countries are connected to Rotterdam by inland waterways. Transport by inland vessels is an important and increasing way of transportation, especially in 1993, as the Rhein-Main-Donau-Canal was put into operation, which made even more countries accessible. Nowadays the river Rhine is still one of the most important links between mainport Rotterdam and most European countries.

To give an indication how important the waterways are for Dutch economy; about 22% of the total freight traffic of The Netherlands is transported by inland navigation. Translated into tonnage, this percentage corresponds to 280 million tons. It is expected that this amount will reach 300 million tons within the next five years. Table 1-1 gives a brief overview of some characteristics of the most important Dutch inland fairways. The numbers hold for the year 2002.

Table 1-1: River characteristics

Rivier CEMT Class Intensiteit Tonnage (x100 ships per year) (Mton per year)

IJssel Va 20 - 40 5 - 15 Pannerdensch Kanaal Va 20 - 40 5 - 15 Maas Va 25 - 50 5 - 15 Waal Vic >125 >50 Nederijn Va <25 <5

Nowadays, (river)flood protection and inland navigation are the most important issues in river engineering in The Netherlands. This is associated with the economic value described above, but also with the floods of 1993 and 1995, which caused substantial damage in the southeast of the country. The floods triggered more attention to flood risk and flood protection, both upstream and downstream of the country’s border. In the past, Dutch river authorities were mainly focussed on the navigability of their rivers and the safe discharge of water, ice and sediment, thus ignoring the other functions of a river. Rivers also have a variety of socio- economic functions: agriculture, sand/ gravel/ clay mining, carrier of landscape, natural and cultural values, recreation, discharge of pollutants etc.

The Netherlands has a number of important rivers, which are depicted in Figure 1-1.

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Figure 1-1: Rivers of major economic value

The river Waal is one of the Rhine branches in The Netherlands. The river Rhine is about 1320 km long and springs in the mountains of Switzerland, see Figure 1-2. The river is not only fed by rain, but also by snowmelt. Therefore, the upper part of the river has a discharge curve, that peaks in the early summer months, whereas the discharge at Lobith peaks generally during the winter period. The evaporation is relatively small then and the Rhine discharges mainly rainwater. As shown in Figure 1-1, the river Rhine enters The Netherlands at Lobith and bifurcates into the rivers Waal and Nederrijn at the Pannerdensche Kop bifurcation. The Nederrijn takes tabout ⅓ of Rhine discharge in the direction of Arnhem, where the river IJssel branches off and takes about ⅓ to the Lake IJssel. Passing the weirs at Driel, Amerongen and Hagenstein, the water flows via the rivers Lek and Maas also to Rotterdam and finally ends up in the North Sea.

The river Waal is a Rhine branch on which multiple river-improvement works have been carried out to increase the wet cross-section. By nature and due to the river-improvements, roughly ⅔ of the Rhine discharge is transported via the river Waal to Rotterdam, the largest harbour of Europe, and ends up in the North Sea. The Waal is a relatively wide river (as compared to other rivers in The Netherlands) and has a run off. Furthermore, clay and sand mining have lowered most of the floodplains and therefore the floodplains are flooded once or twice a year( Middelkoop [1998]).

Figure 1-2: Runoff area of the river Rhine

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For this project, the river Waal directly downstream of the bifurcation Pannerdensche Kop is of special interest (between river marks 867.200 km - 872.000 km). The river is surrounded by the floodplains of the Klompenwaard and the Millingerwaard at the north and south side, respectively. This area is depicted in Figure 1-3. Both floodplains have large environmental values. The Millingerwaard, for instance, is characterised by several quiet spots reserved for a variety of animals, meadowland, swamp spots and the Colenbrandersbos (riparian forest) in the most Northernmost part of the floodplain. These characteristics are highly valued and therefore no interference is allowed which might harm them. The Millingerwaard has recently been given back to the river, which means that during the highest discharges the floodplain is filled with water, which causes a water level reduction of 10 cm in the main channel.

Figure 1-3 shows that some river-improvement works have been carried out. The bifurcation is artificially adapted to a preferred water and sediment distribution between the river Waal and the Pannerdensch Kanaal. The figure also shows, that, except for the inner bend, there are groynes either side of the main channel, which guarantees a minimum navigable depth during low discharges. On average, the river width is about 260 m, and the radius of the second bend(at Hulhuizen) is about 1150 m. The total area of the Millingerwaard is about 7.000.000 m 2.

Figure 1-3: River Waal at Hulhuizen

The discharge in the river Waal is continuously changing, due to the fluctuating runoff in the upstream parts of the basin in Germany, France and Switzerland. Figure 1-4 gives an impression of the discharge fluctuations through a year.

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Discharge 2004 (m3/s)

6500 5500 4500 Rhine 3500 Waal 2500 1500 500 1-jan 2-mrt 2-mei 2-jul 1-sep 1-nov 1-jan Date

Figure 1-4: Discharges Rivers Rhine and Waal

Not only the discharge and water level fluctuates in the river Waal, but also the sediment transport capacity. At high discharges (flood season) the river is able to transport significantly more sediment than during the low-water season. Morphologically speaking, the river is more active in winter. A changing overall sediment transport capacity of the river does not necessarily imply that the bed topography of the river changes, since it is primarily the gradient in the sediment transport capacity that causes morphological changes. By definition, sedimentation leads to a bed level increase and erosion to the opposite. These changes in bathymetry may cause conflicts with river usage. For example: shallow bars in the inner bend (pointbars) of the river or crossings in the transition area between consecutive bends tend to restrict the maximum draught of the inland vessels.

It is exactly this pointbar phenomenon that , which will be of major interest in this report, because every year during the flood season (November- February) a pointbar appears in the inner bend of the river Waal at Hulhuizen, The Netherlands.

1.2. Problem analysis Since 1947 an international treaty on the river Waal guarantees an effective navigable width of 150 m at a level of OLR -2.50 m. OLR (Overeengekomen Lage Rivierenwaterstand) is a sloping reference level, equivalent to the water surface along the river at a discharge that is exceeded during 95% of the time (on average). A navigation optimization study by Rijkswaterstaat [1993] resulted in a future norm for the minimum navigable width on the river Waal: 170 m at a level of OLR -2.80 m. This norm will take effect in 2012. The river Waal does not meet this norm in its bends and, as a consequence, safety for navigation is threatened. Ships are forced to reduce their draught during the low water season, thus becoming less cost efficient. Rijkswaterstaat estimated that this leads to an increase of the annual transportation costs by €25 to €100 million.

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Rijkswaterstaat has made an inventory of the most important problems on the river Waal concerning the currently available navigable width. The river bends upstream of Nijmegen at Hulhuizen, Erlecom and Haalderen turned out to be important bottlenecks, besides stretches between Nijmegen and Haalderen and near IJzendoorn. Some improvement works have been carried out: fixed layer, were implemented in the bends near Nijmegen and St. Andries, and underwater groynes were built in the bend neart Erlecom.

As stated in the previous section, the river Waal does have a bottleneck near Hulhuizen. Therefore, Rijkswaterstaat is developing plans to resolve the width/depth problem in the bend near Hulhuizen. As can be seen in Figure 1-3, close to the Pannerdensche Kop, the river Waal curves gently to the right and two kilometres downstream a left-hand bend creates the main navigation bottleneck. The minimum radius of this bend is 1100 m, whereas the currently available width at OLR -2.80 m is 115 m only. It should be stated that the problem originates from the high water season, when a pointbar forms in the inner bend and causes depth/ width restrictions to navigation during low-water season. The pointbar is therefore removed directly after the yearly flood period.

Rijkswaterstaat [1992] describes the investigation of several solutions to solve navigable width problems, particularly in river bends. The initially most promising options are: • fixed layer in the deep outside bend • channel constrictions with groynes • underwater groynes in the outer bend • submerged vanes in the outer bend • periodic dredging of the shallow inner bend

The effects of the first three options are predominantly due to a reduction of the cross sectional area of the river. This increases the flow velocity in the inner bend, causing the bed level to erode there. However, it also leads to an increased flow resistance and consequently the upstream water level will rise. This water level rise influences the discharge distribution at an upstream bifurcation and is highly unfavourable in case of peak discharges. Therefore, Dutch law requires compensating measures, which may lead to a significant increase of the projects costs. Furthermore, the available space to realize these measures is often limited. Another disadvantage when a fixed layer in the outer bends is applied is that it causes a scour hole directly downstream of the layer and thereby affects the stability and thus then lifetime of the layer itself.

Submerged vanes and periodic dredging were considered the most promising options to solve navigable width problems, since their influence on the upstream water level is expected to be small. Because of the depth restrictions, however, collisions between ships and the vanes are theoretically conceivable. Therefore, a test project with submerged vanes was cancelled. Also the desired effect of influencing the secondary flow is doubted. Because of the doubts, the application of submerged vanes has ceased to be an option in the Netherlands. On the other hand, periodic dredging introduces a discontinuity in sediment transport, with possibly large-scale and long-term effects on the riverbed. Furthermore, periodic dredging could also be a hindrance to navigation. Despite these disadvantages, every year in the inner part of the bend (pointbar location), a significant amount of bottom material is dredged and is relocated at several outer bends on the river Waal. The expenses for maintenance dredging are quite substantial so alternatives for pointbar removal are welcome. It is also interesting to know whether intervention in the formation itself is possible in order to reduce the influence of the pointbar to navigation. Two aspects play an important role, the pointbar dimensions (height and length) and the morphological time scale. If these aspects can be influenced the frequency of dredging and/ or the amount of sediment to be dredged can be reduced.

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In the past research has been done on the morphological phenomena in the river Waal, e.g.: Taal [1994], Klaassen & Sloff [2000]. These reports describe the evaluation of a dredging test and give a methodology to realize a dredging strategy, respectively. An important issue in both documents is the morphological time scale. This topic is treated extensively in the next chapters of this thesis, because it gives an indication of the river’s morphological activity. By investigating the mechanisms underlying pointbar formation, insight into important aspects like the bar height and morphological time scale can be gained. This is actually one of the most important issues of this thesis, because once the underlying mechanisms are known, effective intervention can be designed to keep the pointbar from becoming to be an obstacle to navigation. The Institute for Inland Water Management and Wastewater Treatment (RIZA), and Oost- Nederland, both divisions of the Ministry of Transport, Public Works and Water Management, have shown specific interest in the application of side channels to reduce of pointbar formation. Therefore, special attention will be paid to this kind of floodplain intervention.

1.3. Research question The main question of this thesis project is therefore: How and to what extent can floodplain measures be used to reduce pointbar formation in the inner bend of a river, so as to reduce the hindrance to navigation.

1.4. Objective The objective of this thesis project is actually twofold:

1. To identify the factors that affect height and recovery time of the pointbar after dredging. 2. To evaluate possible interventions to reduce pointbar height or to prolong the recovery time after dredging.

1.5. Approach To answer the research question and to achieve the objectives, the following consecutive steps will be taken:

• Theoretical analysis of all processes in a river bend • Identification of suitable measures • Theoretical determination of the morphological time scale and the pointbar height • Sensitivity analysis of both the pointbar height and morphological time scale, so as to make the dependencies on several parameters explicit • Development of alternatives to extend the morphological time scale and to reduce the height • Delft3D model of the river Waal at Hulhuizen to simulate the water and sediment motions • Testing of alternatives to prolong morphological time scale and to reduce the pointbar height

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2. State of art RIZA and Rijkswaterstaat’s Oost-Nederland have shown specific interest in the application of side channels to reduce the impact of pointbar formation. Therefore, this chapter is a small enumeration of literature related to interventions in flood plains and specifically aspects about side channels. From the studies or projects below, the most relevant information, concerning the present study is listed.

2.1. River morphology

2.1.1. Qualitative analysis In order to know how to deal with this depth/ width problem and preliminary to a quantitative analysis a qualitative analysis has to be made. Therefore, a small summary is made to get an idea of which phenomena are present in a river.

Generally, morphological phenomena can be divided in two ways: 1. phenomena that are encouraged or forced by the geometry of the river and therefore are not able to propagate through the river 2. phenomena that are not encouraged or forced by the geometry of the river and are therefore free to propagate along the river (mostly downstream) (like for example: alternating bars and bed perturbations.

Before focusing on the pointbar in the inner bend, some examples will be given to clarify the upper standing phenomena;

Examples for geometry-forced phenomena are: • Natural bends: In bends, which are forced by the specific geometry of the summer bed, a cross-slope exists due to spiral motion in the bend (see next sections).

• Crossings between two consecutive bends: In the downstream bend of two consecutive bends, the water flow distribution is a mirror image of the distribution in the upstream bend. In the transition area, between the two bends the maximum water velocity shifts from one side to the other, resulting in a bar across the river, see Figure 2-1. During the flood season, these bars will decrease in height, but these bars will still form an obstacle to navigation in the low water period.

Figure 2-1: Schematic profile of a crossing

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• Bends with a fixed layer in the outer part of the bend: Distribution of water and sediment differs from those in bends without a fixed layer. The cross-slope will be less steep, and most of the sediment will be transported in the inner part of the bend. Downstream of the bend two morphological phenomena occur, sedimentation downstream of the inner bend and a scour hole on the opposite site.

• Sedimentation during floods: During floods, a part of the discharge flows via the floodplain. The contribution of the winter bed is not uniform along the flow and therefore velocity variations exist in the main channel, causing erosion and sedimentation. In principle, these sedimentation patterns are determined by the geometry of the winter bed, in which the roughness is an important parameter. When the winter bed does not contribute to the discharge anymore (flood peak has past), the geometry of the winter bed does not play a significant role anymore and the high water sedimentation patterns become free propagating morphological phenomena, which make them actually a phenomena, which belongs to the first type. So, the sedimentation patterns as described above belong during the flood period to the second type and when the patterns become free, they belong to the first type.

• Scour holes near the tip of a groyne: Due to the 3D flow round the tip of the groynes, an extra turbulence is created near the groynes, creating large scour holes.

Examples for non geometry forced phenomena are: • Sediment, which is accreted during high water: It will propagate freely downstream when the water level is falling. The height of these irregularities will decrease.

• Free alternate bars: In relatively straight rivers, with a large ratio between width and depth, alternating bars might be formed. The growth of these bars is suppressed by large curvatures of a river, see Struiksma [1985], Lambeek and Mosselman [1998], Schoor and Sorber [1998] or Schoor et al [1999].

• Bed forms: The bed forms in the river Waal are build up by relatively small dunes added up on large dunes. Dunes are positively correlated with the water depth, which means that a decrease of water depth leads to a decreasing dune height.

• Inland navigation The influence of ships on the morphology of a river cannot be ignored, especially the next three aspects: 1. Return current under the ships, this current presumably has a tendency to level bed irregularities. 2. Propeller race, which has a similar effect as the return current. 3. Water movement in and out of the groyne fields. Leading to erosion between two groynes. It is expected that the influence of navigation on the bottom will increase as the discharge decreases, although this is not certain for the erosion pattern between two groynes. The influence of navigation is a function of the ship path, which is on its turn depending on the geometry of the river, so the geometry is indirectly responsible for the influence of navigation on the bottom.

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2.1.2. Spiral motion Presumably, the pointbar grows due to the increased secondary flow and therefore the increased amount of transported sediment during flood condition. Due to the curvature of the bend, the water particles will be ‘forced’ to move to the outer bend by the centripetal force F c.

mu 2 F = 2.1 c R

Due to this force a lateral slope of the water level exists, which increases from the inner part of the bend to the outer part. When a water particle is considered, a difference of hydraulic pressure on the particle, causes a resultant pressure gradient uniform distributed over the depth will occur. From equation 16, it is clear that the centripetal force is a function of the water velocity (u 2) and the position on the radius (R). The value of (R) is larger in the outer bend than in the inner part of the bend. Together with the logarithmic velocity profile over the vertical (due to bottom friction), the value of the centripetal force changes in both lateral and vertical direction in the bend, see Figure 2-2

Inner bend Outer bend Inner bend Outer bend

Inner bend Outer bend

Water slope and Resultant of the hydraulic pressure difference hydraulic pressure difference

Resultant: Secondary flow

Centripetal force Figure 2-2: Principle of secondary flow

Fc has its maximum in the inner bend, in the upper part of the water column (water level). Both the resultant hydraulic pressure and the value of the centripetal force induce the secondary flow. When the discharge increases, the water depth and velocity increase. Due to this velocity increase, the centripetal force will be stronger and therefore the later slope of the water level is steeper. Both the steeper slope of the water level and the increase of the water velocity will cause a more intense secondary flow and therefore lateral sediment transport capacity. This increase of secondary flow will be balanced by an increase of the lateral bed level slope and therefore the height of the pointbar in the inner bend increases when the discharge increases. This is quite a simple but realistic theory of pointbar formation. In order to reduce the pointbar formation in time and height, reduction of the transverse sediment transport by discharge adjustments through the summer bed, seems an adequate intervention at the source itself. The transverse circulation of the water (from Figure 2-2) superimposed on the main flow following the river bend, yielding a spiral motion, as is depicted in Figure 2-3.

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Figure 2-3: Spiral motion in a river bend (illustration by K. Nuyten)

The combination of most sediment being present in the lower part of the water column and the velocity distribution in the vertical, results in a net transport of sediment from the outer bend towards the inner bend. This transport is balanced by the transport resulting from the gravity acting downwards along the lateral bed slope towards the outer bend.

2.1.3. Theoretical model In order to get an idea of the morphological response of a river in terms of 2-D-time-scales, propagation velocities and bed level changes, complementarily to 1-D phenomena, estimation methods are needed. Since the end of the seventies, interesting studies have been executed about 2-D morphology with help of linear and perturbation analysis of 2-D equations. Despite the simplifications, more understanding about the term 2-D morphology has been accomplished. In the same period, computer-programs have been developed, based on complete systems of 2-D equations, with which numerical models can be designed. These numerical models are a more powerful and complementary tool to the simple estimation methods used so far to estimate the complex morphological changes in a river.

In order to estimate the morphological time scale and dimensions of a pointbar, an analytical model should be derived. This derivation is described in the first three Appendices. In Appendix 1 a small summary is given from Jansen et al [1979] about the basic theory of the water motion on rivers and in Appendix 2, the flow theory in river bends is described. This last theory is based on a scalar eddy viscosity model for the turbulence and a corresponding power law profile for the downstream velocity. One of the results approximates the vertical distribution of the transverse velocity (see Figure 2-4).

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Figure 2-4: Theoretical vertical distribution of transverse velocities in river bends. Jansen [1979]

In the paper of Struiksma, Olesen et al [1985], it is shown that on the assumption that the lateral bed slope is determined by local parameters such as water depth, bed shear stress, bend curvature and sediment properties, i.e. by the balance between the upslope drag force induced by the spiral flow in a bend and the downslope gravitational force, both acting on the grains moving along the bed, is often a too simple approach. The non-local effects due to the redistribution of flow and sediment motion can give rise to an important increase of the lateral bed slope. The flow in a river is essentially three-dimensional, especially when there are bends that induce the spiral motion. Computation of such a flow using a 3D mathematical mode, as required for time-dependent morphological computations, will lead to excessively high computer costs. For this reason, depth-averaged equations are used here for the description of the flow. These equations are often applied to shallow flows (see Appendix 3). In this third Appendix the derivation of the morphological time scale in a river is shown. Essential are the longitudinal adaptation length scales of the main flow λw, the spiral flow λss , the bed perturbation λs and the ratio of λs and λw, the interaction parameter. This last parameter highly influences the bed topography of a river. The important parameters are calculated in the following way:

C2 h λ = 2.2 w 2g

  2 h0 B λs= 2   f s () θ 2.3 π h0 

Ch λ= β 2.4 ss g in which C = Chézy roughness coefficient (m 1/2 /s) h = water depth (m) g = gravitational acceleration (m/s 2) h0 = water depth at the river axis (m) θ = Shields parameter (-) β = coefficient (-)

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2.2. Effects of flood plain lowering In the MSc-thesis of Van Breen [2002], the morphological effect due to large-scale floodplain lowering along the river Waal, using a stochastic approach is analysed. She used the 1-D morphological program Sobek Rijntakken model, which covers all the Rhine branches, but since the emphasis of this study was on the river Waal, the model was adjusted. Different alternatives of floodplain lowering between Nijmegen and St.Andries are modelled with help of the Beslissing Ondersteunend Systeem Rijntakken.

First the various uncertainties related to modelling of river morphology and their effect on the morphological response are determined in the sensitivity analysis, resulting in the selection of the variables that will be randomly generated. The sensitivity analysis showed that the uncertainty in the discharge upstream, at Ruhrort was dominating the morphological activities; see also Van Vuren en Van Breen [2003]. Therefore, Van Breen chose to vary the discharge only. At the schematisation of the model and specification of the model input, like initial and boundaries conditions and other model parameters, the uncertainties were introduced. The objective of her research was to get more insight into the effects of large-scale floodplain lowering along the river Waal, thereby using the Monte Carlo simulations. Before a simulation a sequence of discharges was determined at random, based on a prescribed probability distribution. This distribution takes into account the seasonal variation of the discharge and the correlation of the discharge between two consecutive periods. Based on 500 simulations the statistical characteristics of the bed level changes are analysed (averaged value and 90% confidence band interval). The 90% confidence band interval comprises 90% of the results. The were three types of situations taken into account on the river Waal: • Reference situation • Situation with lowered floodplains • Situation with lowered floodplains in combination with removed summer dikes

The conclusion of the research was that various morphological reactions are possible, which are heavily influenced by the river geometry. At the location of a significant constriction or widening, the morphological response results in erosion or sedimentation, and an increase in the confidence band. This is due to the gradients in the current velocity, which are caused by these differences in cross-sections. Areas, which show a big difference in river geometry with their neighbouring cross-sections, are more susceptible to measures and will show more morphological response, both in mean value as in size of the confidence band. The results made clear that when the floodplain are lowered while the summer dikes are maintained, the morphological response differs little from the unchanged reference situation. For the lowering of the floodplain and removal of the summer dikes the mean value showed a slight increase and a larger variability in the confidence band.

Not only the varying discharge causes a variation in the morphological response, but the seasonal variation in the annual variation is recognisable in the morphological variation as well. Both the mean value and the size of the confidence band vary in time. The mean value has a slight variability, wheras the size confidence varies considerably. An asymmetry in the seasonal variation was observed between the 5% and the 95% percentile. At certain locations the 5% percentile fluctuates while the 95% percentile remains constant and vice versa. This asymmetry is explained by the river geometry. At the transition point between a narrow and a wide flow area in the cross-section, sedimentation (bed) waves will be initiated during high discharges. These sedimentation waves are enhanced by the sedimentation waves resulting from the reduced discharge through the main channel, due to the flooding of the floodplains. At the transition point from a wide to a narrow flow area in the cross-section the opposite can be found. During high discharges the constriction leads to erosion waves. These erosion

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waves are partly counteracted by the sedimentation waves resulting from the reduced discharge due to the flooding of the floodplains.

One of the new approaches to river management is Dynamic River Management (DRM). One of the key aspects of DRM is to implement preferably only measures, which are reversible with no distant response. However when more influential measures should be applied, first the measures should be tested on a small scale. The results of Van Breen’s study show that certain areas are more suitable for pilot areas than others, because these areas showed a greater resilience to measures. When measures are applied in these areas, the morphological response will be very small. Consequently, some areas are not suitable as a test area, because the slightest change in the river geometry will lead to a great morphological response, which could have great consequences. The results of her study show some areas to have not only a great morphological response, but also a great variance in this morphological response. This means that in these areas extra care should be taken by extensive monitoring. Especially the areas mentioned above, the areas with a change in river geometry, show a great variance in the morphological response. Furthermore, this study emphasises the need for more research to uncertainties connected with the modelling of the river morphology and the need for stochastic modelling. In this study only the discharge is varied, and already a large variability can be found. This means that the results with a deterministic model should be observed carefully, because the prediction is only one possible solution. As the comparison of deterministic run with the Monte Carlo simulation pointed out, the deterministic run is only one of the possible realisations, and is not necessarily the mean morphological response.

Another project concerning the morphological effects by lowering the summer dikes was given in Sieben [1999]. This project was divided into two parts. First, in order to study the hydraulic effects, a numerical analysis was executed with the WAQUA two-dimensional modelling program. Secondly, to analyze the morphological effects the SOBEK one-dimensional model was used.

A summer dike in the outer bend was lowered, which implied an increase of discharge through the winter bed. Some interesting (one-dimensional) morphological effects were discovered, and the most interesting ones are described next. For a full description of the project, reference is made to Sieben [1999].

Due to the hydraulic changes, the river can be divided into 5 zones: 1. Upstream of the withdrawal 2. Part of the river at the bifurcation 3. Zone between bifurcation and confluence 4. Part of the river at the confluence 5. Downstream of the confluence

Zone 1: Due to the water abstraction, the water level in this zone dropped and therefore the water velocity slightly increased. This increase in velocity and sediment transport capacity coincided with bed erosion upstream of the abstraction zone.

Zone 2: In the area where water is withdrawn from the river, a redistribution of the velocity is observed. Due to the withdrawal, the average velocity in the outer bend increased and the opposite occurred in the inner bend. This implies an increase of flow curvature, which leads to a local intensified secondary flow. Whether this effect influences the pointbar formation depends on the relaxation length of velocity changes. The velocity changes depend on their turn on the amount of abstracted water trough the winter bed.

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The local deceleration and acceleration of the flow results into sedimentation in the inner bend and erosion in the outer bend, respectively. So, it ultimately leads to an increase of lateral slope of the bed level. This is exactly the effect which forms the obstacle to navigation and is therefore undesirable.

Zone 3: In the river, between the in- and outlets of the parallel channel, where less water is transported than it usually did, both the hydraulic and morphological response to the changed discharge, depends on the ratio between the actual length of the river and the relaxation length scales of both the water and sediment movement. If the river Waal would be straight and the bend at Haalderen would not have had a fixed layer, it would be expected that the discharge distribution from upstream would approach to the uniform distribution. The bend and the fixed layer influence the local morphology seriously. Furthermore, due to the decreased transport capacity, in this third zone sedimentation must be expected.

Zone 4: In the fourth zone, the water from the side channel returns to the river again, where actually the flow converges, the local discharge increase coincides with an increase of sediment transport capacity and therefore scour formation will occur. Depending on the location of the outlet (inner/ or outer bend), an erosion and sedimentation pattern develops.

Zone 5: In this last zone, downstream of the confluence, the hydraulic and morphological response from the disturbed discharge distribution damps out (depending on the relaxation lengths.

Concluding from above, sideways abstraction of water in an outer bend will not have the desirable effect of decreasing the pointbar formation in the inner bend. Furthermore, the abstraction does not only affect the hydraulics and morphology locally, but has a global effect as well. The effects on the upstream area are very important concerning the situation at Hulhuizen, due to the presence of the bifurcation.

As state in the introduction of this project, the hydraulic computation was executed with a 2-D depth averaged model (Waqua). Question marks should be placed by the applicability of such a model, realizing that the streamlines are heavily curved (3D) and therefore the water movement is actually complex three-dimensional.

2.3. Side channels This section is a small enumeration of literature related to side channels and some special characteristics of them. • Nevengeulen: Haas de, A.W. [1991] The report offers an overall survey of the research that was being carried out by the Institute for Inland Water Management and Waste Water Treatment (RIZA) into the hydraulic, morphological and ecological consequences of the construction of a side channel. Since the normalizations of the large river, side channels and their specific flora and fauna are not found anymore in The Netherlands. The re-creation of side channels will enhance ecological diversity in the water systems. A couple of aspects playing an important role;

One channel bank in the side channel should have at least a slope of (1:30) for ecological requirements.

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The desired discharge in the side channel is 5-8 % of the total discharge, with a flow velocity smaller than 0.50 m/s (also for ecological requirements).

Both the horizontal and vertical dimensions of the side channel influence the bed development of the side channel itself and of the main channel. The construction of a side channel does not have detrimental consequences to the main channel bottom level, if the width and depth of the side channel are limited and the sediment supply can be guided entirely through the main channel. Under these conditions, a quick silting-up of the side channel can be prevented as well.

In the morphological research, a study of literature has been carried out, concerning side channel design with regard to the degree of stability required from the hydraulic, morphological as well as from the ecological point of view. Subjects that arise are; channel alignment, slope, transverse profile, meandering and the in- and outlet design. Designing a stable channel by virtue of empirical formulae appears to have many uncertainties. These among others spring from the heterogeneity of the bed material. It is attempted to arrive at unambiguous statements with the help of so-called regime equations. To guarantee a reasonable degree of stability, it is recommended to apply a side channel in cohesive material. It is clear that cohesive material is more resistant against erosion than non-cohesive material. So larger flow velocities are needed to erode the channel banks. Erosion on a larger scale leads to a fast changing layout of a side channel. This is undesirable, because of the possible threats to the stability of flood defences and groynes. The wider or deeper the side channel, the faster the percentage of the discharge through the side channel increases and the faster the sedimentation process in the main channel occurs. When about 10%, or less, of the total discharge is guided through the side channel, a morphologically stable side channel can be expected. At small discharges through a side channel, both the water level and width are limited.

• Geulen in uiterwaarden: WL | Delft Hydraulics [1990] This project is actually a literature research about channels in the floodplain, executed by WL | Delft Hydraulics in September (1990). A meandering channel is morphologically more stable than a braided one. Whether a channel is categorised as braided or meandering depends on the erosive character of the channel bank and bottom. It is better to have a stable side channel than one, with a layout that changes continuously. Therefore, a meandering channel is preferable. In case of undesirable erosion of the banks, the erosion rate can be reduced by means of bank protection or streamlining. Bank protection by vegetation is preferable, because of its natural character. Guidance of the flow is possible with bars of gravel, which can be dug in at the location of the outlet.

Also the discharge through the channel influences the meandering character of it. The ‘normal’ daily discharge seems to be responsible for the erosion and sedimentation, which leads to the shifting bends in the cross-section.

The ‘bankfull’ discharge is responsible for the overall layout of the channel. At high discharges, when the floodplains are flooded, the flow in the floodplains dominates. The channel is nothing more then an extra resistance for the flow. At these high discharges, the meander pattern migrates downstream.

The empirical regime equations give relations between the discharge, the bottom and bank material and the bank vegetation on the one side and the cross-sectional area and the bottom slope of a channel on the other side. These regime equations are derived from field measurements within certain areas. Outside these areas, the regime equations are probably not valid.

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• Nevengeulen, Verkenning naar de ecologische betekenis van inrichtingsvarianten: Duel, During, Specken [1994] Sedimentation in the side channel can be reduced by using a sand trap directly downstream of the bifurcation point in the side channel.

2.3.1. Bifurcation • Morphological development of side channels: Mosselman [2001] Side channels are defined as floodplain channels which convey water during at least 180 days per year.

In theory, the morphological development of side channels can be computed with two or three-dimensional morphological models, but the required data and computational effort are still too demanding for an evaluation of CFR (Cyclic Flood Rejuvenation) strategies. Moreover, there is even a lack of good submodels for some of the key processes, because application of two- or three-dimensional models to floodplain morphodynamics is only a recent development. Applications in the past were traditionally limited to river engineering problems in the main channel. The following relevant processes are still poorly known: exchange processes between main channel and floodplains, interactions between vegetation and sediment and the transport of sediment over obstacles and upward slopes (e.g. into a shallower side channel or over a weir at the entrance of the side channel).

Ship passages contribute substantially to the morphological development of side channels as they counteract sedimentation in the side channels.

No side channels should be excavated within a distance of 100 m from the river dikes, to avoid geotechnical instability of dikes. A limit of 50 m from the dikes is applied when the floodplain contains a sufficiently thick layer of stiff clay.

For natural bend cut-offs, Joglekar (1956) introduces a “cut-off ratio” as a critical value for the ratio between the lengths of a deep river bend and a shallow shortcut channel. The bend is cut off by erosion of the shallow channel when the length ratio exceeds the cut-off ratio. These cut-off ratios vary from river to river.

The bifurcation angle between the side channel and the main channel determine the sediment distribution. This can be understood from flow inertia and the Bulle effect, see Bulle [1926]. The latter results from the spiral water motion, which is generated in curved flows, Figure 2-5. This spiral motion deflects the water near the surface towards the outer part of the curve and deflects the water near the bed towards the inner part. As most sediment is transported on or close to the bed, a disproportionate part of the sediment transport is directed into the offtaking channel with the largest bifurcation angle. The resulting sedimentation forms initially a spit or sand arrow, and hence increases the angle between the offtaking channel and the approach flow. This enhances the flow curvature and the Bulle effect. Further development may cause bank erosion at the nose of the floodplain wedge between the side channel and the main channel.

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Figure 2-5: Spiral water motion in offtaking channel

The transport of the sediment close to the bed into the offtaking channel with the largest bifurcation angle implies also that the sediment in this offtaking channel is coarser then the sediment with the smallest angle.

A side channel should not be silted up within 15 or 20 years. The speed of siltation depends on the sediment supply, the length ratio between main- and side channel, bottom level difference between the channels at the intake and orientation angle. Sedimentation in the side channel is unlikely to happen when there is a small suspended bottom sediment concentration, or a large bottom level height difference, or when the water depth in the main channel is small.

The distinction between slowly, moderately and fast aggrading side channels is based also on the orientation angle, which is defined as the angle between the side channel and the floodplain flow lines during a flood, see Figure 2-6.

A reduction of the sedimentation process in the side channel can be realised when the intake of the side channel in situated in the outer bend of the main channel, or when the offtake angle between the channels at the bifurcation point is more or less 60 degrees.

For definitions of the above-mentioned parameters, see Figure 2-6

Figure 2-6: Length ratio, offtake angles and orientation angle Most side channels in the Rhine branches are assumed to be moderately aggrading, so they are expected to be closed after about 15 years of sedimentation. Slowly aggrading side channels are characterized by length ratios below 1 and offtake angle smaller than 10 o.

As a first guideline, the geometry of a side channel is considered to be (un)favourable, with respect to sedimentation, if two or three of the following conditions are met: • The length ratio is larger than 1.5 • The offtake angle is 90 o or larger • The orientation angle is 45 o or larger (maximum of 90 o) • The side channel takes off from the inner bend of the main channel.

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• Rivierdynamiek in nevengeulen: Barneveld, Pedroli & Sweerts [1994] The layout of the bifurcation point should be designed to minimize the sediment intake into the side channel. This has a positive effect on the interval of maintenance dredging. The target is to dredge once per 10 years.

By gradually decreasing the length of the groynes upstream of the bifurcation point, the unfavourable flow between two successively groynes is removed. Therefore, less sediment will be transferred into the side channel.

By increasing the length of the groyne directly downstream of the bifurcation point, the width will be reduces, so the flow velocities increase and less sedimentation will occur. This is only a local solution, because the actual problem (sedimentation) is transferred downstream.

Another way to reduce the amount of sediment in the side channel is by applying a movable intake. This movable intake allows only water particles in the upper part of the water depth to flow into the side channel. Since most of the sediment is bottom material and located in the lower parts of the vertical, this intake construction saves the side channel from quick siltation.

2.3.2. Confluences • The morphology of river channel confluences, Best, J.L. [1986] The bed morphology at a river channel confluence can be divided into three elements:

1. Distinct and commonly steep avalanche faces that form at the mouth of each of the confluent channels. 2. A region of pronounced scour within the centre of the junction. 3. Bars of sediment which are formed downstream of the confluence, where the large-scale separation zone is situated.

The location of the elements depends on the layout of the confluence. The following figure shows where the characteristic phenomena occur. (from Ashmore, 1982)

Figure 2-7: Scour formation in laboratory flumes depending on the orientation angles

Avalanche faces Within ‘Y’ shaped planforms confluences (Figure 2-7), the avalanche faces and scour maintain a similar position, but a bar is formed midstream in the post confluence channel. In both cases above, there may be noticeable channel widening around these bars (Mosley,

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1976). In addition, smaller bars may be present below the downstream junction corners in ‘Y’ planform junctions

The height of the avalanches is a direct reflection of the scour depth into which they dip. The exact position of the faces in the confluence is controlled not only by the junction angle, but

Qt also by the discharge ratio between the two confluent channels, Q r, where: Qr = Qm in which Q t and Q m are the discharges from the tributary and main channels, respectively. Discharge ratio is acceptable as a control variable where the channel widths of both main and tributary channels are identical. In The Netherlands, side channels have significantly different dimensions from the main channel, which off course does not mean the discharge ratio is not a control variable, because the discharge through a channel depends also on other parameters. At small confluence angles and small discharge ratios, the avalanche face of the mainstream penetrates well into the confluence. However, as both junction angle and discharge ratio increase and the deflection of the mainstream flow and its sediment load by the entry becomes greater, the face propagates upstream (avalanche slope becomes flatter). At discharge ratio above unity, the tributary avalanche face begins to migrate into the confluence.

In both asymmetrical and symmetrical planform confluences, the scour originates at the upstream corner of the junction and stretches downstream. The axis of the scour approximately changes the junction angle with a factor 0.5. Just like the avalanche slope, the orientation of the scour varies also with the confluence angle and the discharge ratio. Changes in these parameters will change the cross-channel sediment distribution and therefore the position of the avalanche slope and orientation of the scour. For example: as the contribution of flow from the tributary channel (in this project side channel) increases at any confluence angle, the scour shifts to align with this side channel.

The confluence scour The origin of scour is complex. It involves both initial erosion and distinctive sediment transport pathways within the confluence. Erosion of the bed occurs along the turbulent shear layer between two flows. This generates vertical vortices within the flow which are responsible for the bottom erosion. Bed erosion is also aided by high shear stresses along the reattachment line of the flow which separates over the avalanche faces. The formation of flow separation zones in the lee of each avalanche face provides an explanation for the origin of the counter rotating helicoidal flow cells (see Figure 2-7). These two erosional mechanisms together scour the bed and the hollow aligns itself along the shear layer between the flows. However, the form of the scour is significantly influenced by the nature of sediment transport within the confluence. Sediment movement at the centre of the scour is almost non-existent. Transport is concentrated in two zones on the flanks of the scour. This creates an area of higher bed elevation on both sides of the scour. Where the concentration of sediment transport in two pathways is less distinct, such as at lower angle junctions, the scour depth decreases as more sediment is transported through the centre of the confluence.

Several studies have sought to express scour depths at channel confluences as a function of junction angle. The relationships found in four studies are compiled in the figure below. The scour dept is defined as the height from the water surface to bed surface and is made dimensionless by using the mean flow depth of the upstream channels. All the studies give values in the same order of magnitude, especially for confluence angles of 90 o. Variation is introduced by several factors, discharge ratios are taken into account, symmetrical and asymmetrical planforms are combined. The study of Kjerfve (1979) concerns scour at tidal creek junctions. Both Mosley (1976) and Best (1985) indicate that there is no noticeable scour up to confluence angles of approximately 15 o. After this, a rapid increase in scour depth is present. Best and Reid (1984) give one reason for this pattern by showing that as confluence angles

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increases, the postconfluence separation zone increases at the expense of the combined flows. The result of this is an increase in fluid velocity in the confluence, which causes greater bed erosion.

Figure 2-8: Relation between maximum scour depth, ds, and confluence angle α, compiled from four studies Bars within the confluence Figure 2-8 shows that the bars at the channel confluences vary in position and form between asymmetrical and symmetrical planform junctions. These bars owe their existence to the sediment transport pathways within the junction which are, in turn, controlled by the flow. At asymmetrical planform junctions, the most frequently occurring bar is the one formed just below the downstream junction corner. The origin of this bar is linked to the formation of a large zone of separated flow (Best and Reid, 1984). Flow separation occurs at the downstream junction corner where fluid of the tributary channel cannot remain attached to the channel wall. This creates a zone of low velocity, recirculating flow, which provides a favourable site for sediment deposition. Sediment, mainly from the side channels, is concentrated along a distinct pathway and is carried into this zone, where it sinks. An indication for the low flow velocities in those areas is the presence of fine grained sediment. The size of the bar is related to the size of the separation zone which grows both at higher confluence angles and higher discharge ratios. Erosion of the far bank may cause channel widening opposite this bar because of the constriction of the effective channel width through which the combined discharge must flow.

At symmetrical planform confluences (Figure 2-8) the pattern of bar formation is slightly more complex, bars being present in the midstream region of the postconfluence channel as well as near the downstream junction corners and against the channel banks as in the asymmetrical case. The midchannel bar is formed through downstream accumulation of material eroded from the scour and the convergence of flows as well as the sediment pathways. The formation of this midchannel bar and subsequent channel widening around it, was especially pronounced at junction angles greater than 60 o. Figure 4b shows the two distinct sediment transport pathways. At higher confluence angles, these pathways lie on the flanks of separation zone bars, which form just below the downstream junction corners. The transport pathways are not of simple linear nature. While the gross movement of the sediment is heading downstream, secondary currents are responsible for transporting the grains crosswise onto the bars. This happens more or less also

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at the asymmetrical planform confluence, these bars may be expected to grow at higher junction angles, as their sediment load from each confluent channel is concentrated into narrower transport pathways and influenced by larger separation zones.

• Confluence effects in rivers: Interactions of basin scale, network geometry and disturbance regimes, Benda, L. Andas, K. Miller, D. Bigelow, P . [2004] Data obtained by several studies in the USA, covering 167 confluences and spanning seven orders of magnitude drainage area, determined that the probability that a tributary channel will locally alter main stem morphology scales with the size of the tributary relative to the main stem. This scaling relationship links confluence effects to basin shape, network patterns, drainage density, and local network geometry and hence to the spatial distribution of fluvial geomorphic processes and forms.

• Investigation of controls on secondary circulation in a simple confluence geometry using a three-dimensional numerical model, Bradbrook, K.F. Biron, P.M. Lane, S.N. Richards, K.S. Roy, A.G. [1998]. Recent research into river channel confluences has identified confluence geometry and particularly bed discordance as a control on confluence flow structures and mixing processes. This has been illustrated using both field measurements in natural confluences and laboratory measurements of simplified confluences. Generalization of the results obtained from these experiments is limited by the number of confluence geometries that can be examined in a reasonable amount of time. Numerical models, in which confluence geometry is more readily varied, may overcome this limitation and data is acquired more rapidly.

The velocity ratio is the prime parameter of the cross-stream pressure gradient that initiates cross-stream velocities. However, for significant secondary circulation to form, cross-stream velocities must lead to significant transfer of fluid in the cross-stream direction. This depends on the vertical extent of the cross-stream pressure gradient, which is controlled by the depth ratio. In this study, strong secondary circulation occurred for a depth differential of 25% or more, as long as the velocity in the shallower tributary was at least as great as that in the deeper channel. This provides an important context for interpretation of previous work and for the design of new experiments in both the field and the laboratory.

Previous field and laboratory investigations have concentrated on examining flow structures consequent from two main controls: • Planform streamline curvature, which depends on junction angle and discharge ratio and tends to promote `back to back' helical cells that maintain segregated sediment transport patterns (e.g. Mosley, 1976; Best, 1987, 1988; Ashmore et al., 1992; Rhoads and Kenworthy, 1995; Rhoads, 1996) • Vertical separation owing to bed level difference (depth ratio) at the junction, which can lead to shear layer distortion and thus enhanced mixing (e.g. Best and Roy, 1991; Gaudet and Roy, 1995; Biron et al., 1996a,b). There is a wide range of variables associated with these geometries and flow structures, and laboratory investigations have been used to provide better experimental design to assess their effects than is possible in the field.

However, even though laboratory experiments allow researchers to test systematically the effects of the main controls on flow structure, this is time-consuming and there remain many possible combinations of boundary condition values that need consideration. The limited number of experimental set-ups that have been examined leaves large gaps in our knowledge and impinges on the intercomparison of different types of experiment.

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At confluences, where streamline curvature may play an important role, significant superelevation of the water surface can occur and representing the effects of spatial variation of water surface elevation is necessary for confluence flow modelling. In the present application, surface depression at the mixing layer is likely, and a method of approximating the free surface displacement is required.

A high cross-stream pressure gradient will entrain large cross-stream velocities towards the recirculation zone below a small step, but the cross-stream momentum transfer is limited by the small height of this zone. This configuration does not lead to the development of strong secondary circulation, upwelling or greatly enhanced mixing. However, when the step height and velocity ratio are both large enough that cross-stream momentum transfer leads to significant fluid impingement on the sidewall, some fluid will be forced upwards, with the associated flow being re-entrained into the downstream direction in the horizontal shear layer that begins at the step. In such a case, cross-stream velocities will also persist downstream of the reattachment zone, leading to upwelling along the sidewall and the associated secondary circulation cell. The stronger the entrainment and subsequent distortion of the mixing layer and secondary circulation, the greater the intensity of mixing of fluid between the two channels. The rate of cross-stream momentum transfer can also explain the deviation of the separation zone length from that predicted for two-dimensional vertical separation: the entrainment of cross-stream fluid near the bed acts to delay the vertical reattachment, and reattachment occurs slightly further downstream than predicted for two-dimensional separation. However, for the smallest depth ratios with a velocity ratio of at least 1.0, the cross-stream flow is sufficient to force earlier reattachment along the sidewall, and the separation zone length is shorter than would occur with two-dimensional vertical separation. In this case, the recirculation zone has a strongly three-dimensional shape.

2.3.3. Numerical modelling • Tweedimensionale bodemveranderingen in de vaarweg van de Waal, Sloff, C.J. [2004] A curved calculation grid is used to follow the normal lines of the summer bed, because a normal rectangular grid lead to ‘stair case’ boundaries and therefore to oscillations downstream which influenced the outcomes dramatically. The grid-width and length used are respectively: 22-27 m and 90-110 m. When the change of (summer) bed level is of interest, a smaller grid size is recommended. The morphological effects, due to the side channel, in the main river are slowly propagating downstream with a relatively small damping rate.

According to De Haas [1991], the accuracy of the flow simulation increases when a finer computational grid is used in the side channel than in the main channel.

2.3.4. River morphology due to side channel application A first impression of the morphological reactions due to the presence of a side channel is provided by using the following empirical relations:

Q= Buh 2.5

u= C hi 2.6

s= mu n 2.7

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S= Bs 2.8 1 − S  n Q h =   2.9 eq Bm  B

3 S  n B i =   2.10 eq Bm  CQ2

Starting point for the indication is the assumption of the equilibrium situation in river before the side channel is applied. As the side channel extracts water, the discharge though the main channel decreases, this will cause sedimentation in the main channel. Initially, upstream of the inlet erosion will occur and upstream of the outlet sedimentation, see Figure 2-9. It should be stated, that this theoretical morphological development is only applicable in a straight river with a constant width and with constant discharge.

Figure 2-9: Morphological reaction in the main channel

After a sufficient time, there will be a new equilibrium situation, where the bed level in the main channel (upstream of the outlet) will be higher than in the “old” equilibrium situation. The new bed slope will be steeper than in the reference situation. An approach to describe this new equilibrium is provided by the following formulae:

∆Q  heqnew=1 −  h eqold 2.11 Q0    Q0 ieqnew=   i eqold 2.12 Q0 − ∆ Q 

For a non-constant river discharge, the river will continuously adapt to the changing discharge. New bed waves will occur when the discharge changes. The last two formulae are only applicable when there is only water abstracted from the river.

When only sediment is abstracted, the following formulae are applicable:

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−1 ∆S  n heqnew=1 −  h eqold 2.13 S0  3 ∆S  n ieqnew=1 −  i eqold 2.14 S0 

When not only the water is abstracted, but sediment as well, the new equilibrium water depth and bed slope are calculated with the formulae 2.9 and 2.10, but a first indication might be provided by superimposing the two individual bed level changes.

A measure for the bed level change is pre scribed by:

∂Z ∂s  ∂ u b = −   2.15 ∂t ∂ u  ∂ x

In case of the sediment transport formula of Engelund-Hansen:

∂Z ∂u b = − ()5mu 4 2.16 ∂t ∂ x

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3. Identification of suitable measures This chapter describes the identification of suitable measures for the pointbar formation in the inner bend at Hulhuizen. The aims identified for this chapter therefore are: • to analyse the morphological situation at Hulhuizen. • to analyse the mechanisms and parameters, which control the growth of the pointbar. • to indicate the effect from changes of important parameters on the height and morphological time scale of the bar. • to determine alternatives, which prolong the morphological time scale (during flood period) and / or alternatives, which reduce the pointbar height.

3.1. Time scales of general bed level development Before the morphology at Hulhuizen is treated, an overview is given about the bed level developments , which takes place on several time scales: • Long term time scale (more than a year) The largest time scale is a trend in the annual average bed elevation. • Seasonal time scale (a year) The seasonal variation of discharge will cause a seasonal variation in bed level. • Intermediate time scale (several weeks) The variation in river discharge influences the present local reaction of the bed. • Short term time scale (day) De smallest time scale is a time scale of bed forms.

The problem analysis indicates that the bed developments in this project belong to a category on the boundary of the seasonal and the intermediate time scale.

3.2. Morphology at Hulhuizen In section 2.1.1 the morphological phenomena is rivers is described. Before actual measures are undertaken to intervene in the morphological activities in the river Waal at Hulhuizen, it should be determined which phenomenon is responsible for the excessive bed level rise during flood period.

As stated in section 2.1.1, the morphological phenomena in rivers can be divided in two ways: 1. Phenomena that are encouraged or forced by the geometry of the river and therefore are not able to propagate through the river 2. Phenomena that are not encouraged or forced by the geometry of the river and are therefore free to propagate along the river (mostly downstream) (like for example: alternating bars and bed perturbations.

Due to the river-improvements (groynes) in the past, the width-to-depth ratio has been artificially changed and therefore the determined bed level rise in the inner bend at Hulhuizen can not be explained by the phenomenon of free alternate bars. Besides, alternate bars are only likely to occur at low discharges, which is actually the opposite regime at which the bed level rises. The influence of ships passing groynes is still hard to determine. It is known that there is water and sediment exchange between the fairway and groyne fields, there are no models, which are able to accurately determine the actual exchange. It is still a delicate matter, and more research is needed. Due to a lack of time, it is impossible to take the influence of ships into account in the determination of the bed level change in this thesis project.

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Side channels to improve navigability on the river Waal November 2005

So, the morphological phenomena, which are not encouraged or forced by the geometry of the river and are therefore free to propagate along the river of the second type will not be considered in this project.

In section 2.1.1 a number of examples were given to clarify the geometry-forced phenomenon: • Natural bends • Crossings • Fixed layers • Sedimentation during floods • Scour holes • Groynes

The only examples, which might influence the determined bed level rise are the morphological activities due to the presence of a bend, groynes and the sedimentation during floods. The problem description makes clear that the problem at Hulhuizen does not concern the morphological activity at crossings (which occur between two consecutive bends).

Furthermore, according to the problem analysis, it is very unlikely that the bed level change during floods can totally be ascribed to the presence of groynes. It is known that deceleration of the flow exists between two consecutive groynes, due to the widening of the local flow line. The decreases of flow velocity causes a gradient in the longitudinal sediment transport capacity, which will lead to sedimentation. Considered like this, the morphological activity is actually one-dimensional, which is too simplistic approach. From Sieben [2005], the information was obtained that the presence of groynes do not haven a significant role in the navigable width problem. Therefore, in the morphological analysis, the presence of groynes will not be taken into account.

The description of sedimentation during floods in the same section makes clear that the morphological activity is mainly 1-D. Due to the discharge capacity of the flood plain, during flood period, the potential sediment transport capacity drops in the summer bed, which causes a gradient in the in longitudinal direction and will ultimately lead to sedimentation. This is actually one possibility, because the actual sediment and water distribution over the flood plain and summer bed determines the morphological behaviour. This 1-D phenomenon is likely to occur at the bend of Hulhuizen and will be intensified when a side channel is applied. Therefore, the one-dimensional morphological approach will form a pivot role in the succeeding phases of this project.

Due to the presence of the bend, streamlines are curved and cause a specific behaviour of both the water and sediment motion. In reality this motion is three-dimensional (see next section), especially the water motion. The assumption of a two-dimensional sediment motion is based on two facts: 1. That the sediment motion takes place mainly in the relative small zone near the bed. 2. The fact that the nominal grain size on the upper part of the Waal is about 2 mm (according to RIZA and WL | Delft Hydraulics), which is quite coarse, justifies the idea that sediment is transported mainly by bed load and to a lesser extend by suspension transport.

Concluded from above: 1. In order to analyse the situation at Hulhuizen, one should take into account the complex water and sediment motion in bends (3-D and 2-D, respectively). 2. Due to the water and sediment exchange between the summer bed and flood plain, bed waves will occur, which are mainly 1-D dominant.

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3.3. Analytical model

3.3.1. Bottom topography In Appendix 3, the derivation of the theoretical formulas of pointbar formation is treated. These formulas give an idea of the different time and length scales, which will be used in this chapter. It should be emphasized that these formulas give only an idea of the value of the parameters, because the formulas are based on several simplifications. This does not mean that the outcomes should the ignored beforehand, but should be used rather to get an idea whether a parameter is dominant or not.

In natural bends, which are forced by the geometry of the summer bed, a cross slope exists due to spiral motion in the bend. This spiral motion redistributes water and sediment along the width and therefore a pointbar in the inner bend is formed. When it is a long bend or when there is a strongly damped system, the axi-symmetrical situation will be established. The way the cross-slope adapts depends, for example, on the water depth. If the water depth decreases, the cross-slope will be gentler and the dimensions of the pointbar changes. This is known as the respiration of a bend. The cross-slope for the axi-symmetrical situation is given by:

h tan β= A f () θ 0 3.17 o R in which the cross-slope ( β) depends on a function of the Shields parameter, water depth, grain size, bend radius and a coefficient for the spiral motion. The function of the Shields parameter reads:

0.3 D  f ()θ0 = 9  θ o 3.18 ho 

h i with a Shields parameter via: θ = 0 , and ∆ ( relative sediment density) (-), defined by ∆ 0 ∆ D

= ( ρs-ρ)/ ρ Presumed value for ∆ is 1.65

When a cosine-shape for the bed level is assumed in a cross section, formula 0.4 changes to:

HA 0 =f()θ h Γ ˆ 3.19 B π o 0 in which Γˆ represents the curvature. Considering both Eq. 3.18 and 3.19 for a given geometry, bed material, bottom roughness (R, D and C are known), the axi-symmetrical solution exclusively depends on the water depth 1.2 (h 0 ). This means the cross-slope will get milder when the discharge decreases. In the river Waal not only the axi-symmetrical solution of the cross-section is important, but also the impact of the non-uniform curvature should be taken into account. These variations will cause a bar pattern which should be added to the solution of the axi-symmetrical solution. In the context of this report, these extra bars will be known by overshoot bars, although this term in the geomorphologic tradition is known as the be at the inner part of the bend.

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The extra increase of the bed level is called ‘overshoot’. When the axial-symmetrical solution is added to overshoot phenomenon, the theoretical bed level due to both phenomena is:

x   2π  H=−− H0 1 exp   cos () x + φ  3.20 LD   L P 

The dimensions of this pointbar are influenced by the interaction of the damping length scales of the water motion and the sediment motion. Two parameters are therefore important; the wave length and the damping length of the pointbar, L P and L D respectively. Concluding from the axi-symmetrical solution, the height of the pointbar is highly influenced by the value of the damping length. When it is negative, the height of the bar will be higher than the maximum amplitude (overshoot). The actual value of these parameters can be derived from the next two equations;

λ 1b − 3  2 2π w =()b + 1 IP−1 −− IP − 2   3.21 Lp 2 2 

λ 1b − 3  w =IP −1 −  3.22 LD 2 2  in which; IP = interaction parameter (-), defined by the ratio of λs and λw, see;

 2  0.3 λs g B D IP = ≈ 2 2    θo 3.23 λwC h o  h o 

Concluded from this last equation, the width/depth ratio mainly determines the formation of the pointbar. This means an increase of discharge leads to a decrease of the interaction parameter and eventually to a decrease of the pointbar formation as well. In case of a lower discharge, the interaction parameter will tend to grow and therefore the overshoot phenomena might occur. This might neutralize the milder transverse slope of the axi-symmetrical solution. Although the topography of the bend is determined by the geometry of the main channel and will therefore not propagate downstream, there is a typical 2-D time scale for the adaptation of the bed level (see also Appendix 3). The linear analysis of free bars leads to the following expression;

−1 1 ()b−1 k ' 2  T= − T0 1 − 2 IP  3.24 2 1+ k '  in which: T0 is the 1-D morphological time scale for a distance λs (see equation 3.25) and T the 2-D morphological time scale.

hλs T0 = 3.25 s0 b the (constant) exponent in the sediment transport formula, k ′= 2 π/L P.

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In the previous chapter, sedimentation during high water is described as sedimentation, which occurs when the winter bed transports a part of the total discharge. When the water level drops below the height of the summer dikes, the winter bed does not contribute to the discharge. Depending on the 2-D shape and sequence along the river of the accretions, the accretions (perturbations) propagate downstream with the 1-D or 2-D propagation velocity. A lot of knowledge has been gathered in the previous century about the propagation velocity, resulting for example from a linear analysis, which gives pretty good insight in the morphological processes, but still its is a delicate matter. It is still hard to describe the complex 2-D morphology and to catch the matter in manageable mathematical relations. For completeness, the 1-D and 2-D propagation velocities are calculated in the following way:

b s 0 1-D: cb = 2 3.26 h0(1− Fr 0 )

b − 3  k '2 −  s0 2  2-D: cr = 2 3.27 ho k '+ 1

3.3.2. Input parameters In order to quantify the analysis of pointbar formation, some calculations are made, based on the linearized model described in Appendix 3. As stated in previous sections, the parameters of interest should give an indication of the properties of the pointbar or the properties of the environment in which the pointbar is able to develop. Therefore the parameters of interest are:

• T0: 1-D morphological time scale • T: 2-D morphological time scale • λs: relaxation length of sediment motion • λw: relaxation length of water motion • IP: interaction parameter • H0: amplitude axi-symmetrical cross-profile

The above parameters are determined as a function of the discharge of the river Waal. The required input to calculate the parameters of interest is deduced from the next sources: • Klaassen and Sloff [2000] • Waterbase [internet] • Taal [1994] • 1-D Sobek Rijntakken model

From the several sources above input parameters are derived for the period November 1992 - March 1993 (high water season from Nov-Feb). In this period the low and high discharges were both represented, which gives a good indication of the variation of the output parameters and therefore a good idea of the pointbar formation. In Taal [1994] an evaluation of dredging tests in 1992 is described. In these tests, profile measurements were made, which shows the bed level changes throughout the year. Furthermore, calculation of the morphological time scale and the bed level were made. Both the computation and the profile measurements of these tests can be of great help to compare with the theoretical outcomes of the analytical model, used in this project.

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The Sobek Rijntakken model was used in previous projects as a simulation tool for the most important rivers of The Netherlands. In this thesis project, the results of this 1-D model is used to compare values of several parameters.

In Table 3-1, the input parameters for the theoretical model are depicted. To get an impression of the actual discharge as a function of the time, reference is made to Appendix 4.

Table 3-1: Input parameters analytical model

Parameter Value Unit

3 Discharge 1000 - 6000 m /s Width 260 m Acceleration of Gravity 9.81 m/s 2 Bend radius 1150 m Exponent in sed. transport formula 5 [-] 1/2 Ch ézy Coefficient 45 m /s Nominal Diameter 0.002 m Equilibrium slope 0.00011 [-] Delta 1.65 [-]

As it is impossible to derive the values of the parameters of interest directly from the input parameters, the next parameters have to be determined first: • water depth (h) • velocity (u) • shields parameter ( θ) • damping length scale (L D) • wave length pointbar (L P) • undisturbed sediment transport (s 0)

These parameters are calculated under the following assumptions: • Stationary equilibrium situation is applicable • Rectangular cross section • A power law formula is used( s= m ⋅ u b ), which approaches the transport formula of Engelund-Hansen • fixed width • Constant hydraulic roughness along the bend (independent of water level) • One fixed representative nominal diameter is taken into account • Sediment transport is evenly distributed over the river width • Winter bed does not contribute to the total discharge, because in the Sobek model a contribution of the winter bed (from 1 – 6 %) was noticeable between discharges on the Waal from 3300 to 5200 m 3/s. To get an impression of the river system, the calculations are made for discharges up to 6000 m 3/s, assuming all the discharge flows through the summer bed.

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3.3.3. Results of the analytical model Before comparing the theoretical results with the results of the dredging evaluation and drawing the conclusions, the results of the theoretical model are depicted in the following figures. It should be stated, that the comparison will be based on only two different discharges, (1663 m 3/s and 1750 m 3/s). Only these two discharges were taken into account in the dredging test. Despite of the limited comparison data and the bankfull discharge of 2700 m3/s (according to the Sobek Rijntakken mode), all actual measured discharges smaller than 5000 m 3/s (of 1992) are used in the analytical model, to give an impression of the values of parameters of interest as a function of the discharge.

The results are depicted in Appendix 6. The most relevant figures are depicted below as well.

700 700

600 600

500 500

400 400

300 300

200 200 2D Time 2D scale (days) 1D Time 1D (days) scale 100 100

0 0 0 1000 2000 3000 4000 5000 6000 1500 2500 3500 4500 5500 Discharge (m^3/s) Discharge (m^3/s)

Figure 3-1: 1-D Time scale Figure 3-2: 2-D Morphological time scale

30,00 2,00

25,00 1,00

20,00 0,00 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 15,00 -1,00 -2,00 10,00 -3,00 5,00 1D bed1D celerity [m/day]

2D bed2D celerity [m/day] -4,00 0,00 0 1000 2000 3000 4000 5000 6000 7000 -5,00 Discharge [m^3/s] Discharge [m^3/s]

Figure 3-3: 1-D Bed celerity Figure 3-4: 2-D Bed celerity

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4,00

3,50

3,00 2,50 Q = 1000 Q = 2000 2,00 Q = 3000 1,50 Q = 4000

Bed level Bed (m) 1,00 Q = 5000 0,50

0,00 0 1000 2000 3000 4000 5000 6000 -0,50 Longitudinal position (m)

Figure 3-5: Bed level due to the axi-symmetrical solution plus overshoot (m)

From Figure 3-1, the conclusion can be drawn that the 1-D morphological time scale increases when the discharge decreases. This was expected, concerning equation 3.25 for the 1-D time scale and equation 3.26 of the bed celerity. Figure 3-2 shows only the morphological time scale from 1500 < Q > 6000 m 3/s, because an asymptotic behaviour is noticeable in this 2-D time scale and therefore the time scale reaches (+ and -) infinity, see Figure 6-2 of Appendix 6. This implies the factor, which links the 1-D time scale with the 2-D time scale explodes. The asymptote appears at a discharge of 1300 m3/s. At this discharge, a couple of interesting transitions occur: • The 2-D morphological time scale is negative for Q < 1300 m 3/s and positive for Q > 1300 m 3/s. • The interaction parameter becomes smaller than one, which implies that the adaptation length scale for water motion is larger than the morphological adaptation length scale. Therefore, the water motion adapts more slowly to a perturbation than the sediment motion. • The sign of the damping length changes, indicating whether the axi-symmetrical solution tends to grow or decay.

How do these, on first hand strange results, match with the theory used? As stated in the previous sections, the value of the actual bed level depends on the amplitude of the axi-symmetrical solution and the value of the damping length and wave length (L P and LD)(overshoot phenomena). In Figure 3-8 the relative damping coefficient and the wave number, λw/L D and 2 πλ w/L P, are given as functions of the interaction parameter ( λs/λw) for b = 5 ( Engelund and Hansen [1967]). The factor b indicates how the sediment transport depends on the main velocity; bottom shear stress plays an important part in L P and L D. For other values of b, the lines in Figure 3-8 will be different. In general, they tend to keep their shapes, but shift upwards as b becomes smaller, which implies that a decrease of b leads to considerable increase of damping (see also Figure 3-6). In principle, Figure 3-8 can also be used to obtain a first indication of the equilibrium bottom configuration in a curved alluvial channel, even though the underlying model is strongly simplified. An extensive linear analysis of the system of equations for river bend morphology has show that the present conceptual model includes the essential processes and that the conclusions drawn from it are relevant to river bends, qualitatively and, with certain constraints, for L P and L D even quantitatively. This is corroborated by the results of

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preliminary computations with a complete non-linear mathematical model in De Vriend & Struiksma [1983]. The limits of the linear analysis are perfectly shown in Figure 3-4. At a discharge larger than 4200 m 3/s the value of the interaction parameter drops below 0.2 where the linear theory is not valid anymore.

Figure 3-6: Damping length as a function of IP and b Figure 3-7: Wave length as a function of IP and b

Figure 3-8: Wave and damping length of periodic solutions

From Figure 3-6, Figure 3-7 and Figure 3-8, it is observed that the tendency to form steady alternate bars is present in the range 0.2 ≤ λs/λw ≤ 5, approximately. For IP < 1 the oscillation will decay whereas for IP > 1, it will grow. As seen from Figure 6-4 from Appendix 6, the value of the interaction parameter in the model ranges from 0.3 to 1.6, when 1000 ≤ Q ≤ 1300 (m 3/s) the IP drops from 1.6 to 1.0. For discharges larger than 1300 m 3/s the interaction parameter becomes even smaller than 1.0. Together with the drop of the interaction parameter below 1.0, the damping length becomes positive, which means, the amplitude of the damped, oscillatory solution decays as a function of longitudinal distance along the river axis, (see equation 3.20). As the discharge increases, the damping length becomes smaller (still positive), which implies that a bar might appear with dimensions which might be predicted by the combination of L P and L D as a function of the discharge.

Now that the results of the parameters are known individually and the calculations have been proved to be consistent with the theory, it is worthwhile to show what these outcomes mean to pointbar formation.

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As explained in the sections above, the amplitude in a lateral cross-section is actually a summation of the axi-symmetrical solution and the possible appearance of the overshoot phenomenon. The amplitude of the bed level, due to the axial symmetrical solution and the overshoot phenomenon is already calculated and shown in Figure 3-5. To give an indication how the amplitude is changed by the value of L P and L D, see equation 3.20, which is repeated here:

x   2π  H=−− H0 1 exp   cos () x + φ  3.28 LD   L P 

Keeping φ zero, which implies the amplitude is a function of the position (x,y) and the local values of L P and L D, which are indirectly depended on the discharge. In the following calculation, the bed level is determined, as a function of: the discharge, longitudinal position along the river axis (x) and the input parameters of the first three columns of Table 3-2. Both the damping length and the wavelength are a function of the discharge. The maximum bed level, ratio of overshoot to the axi-symmetrical solution and the position of the maximum value are depicted in the fourth, fifth and sixth column, respectively. The computation is made to for eight different discharges, two of them are smaller than 1300 m3/s and the others are larger and up to 5500 m 3/s. For discharges larger than 4250 m 3/s, the results are questionable, because the interaction parameter (IP) drops below 0.25 and the linear derivation is not applicable anymore. Despite this limited applicability, still the results are given up to a discharge of 5500 m 3/s.

Table 3-2: Input parameters for overshoot calculation and results (m)

Q (m 3/s) H0 Lp Ld Hmax Hmax/H0 x (Hmax)

1000 0.98 3.104 -3.137 2.43 2.47 1.675 1250 1.17 3.113 -23.536 2.61 2.23 1.725 1500 1.36 3.163 5.668 2.39 1.76 1.625 2000 1.71 3.329 1.936 2.46 1.44 1.600 3000 2.36 3.879 998 2.77 1.17 1.650 4000 2.98 4.919 734 3.15 1.06 1.825 5000 3.56 7.926 602 3.58 1.01 2.250 5500 3.84 17.736 557 3.84 1.00 2.850

The results of the computations and the values of Table 3-2 are depicted in the following two figures.

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6,00

4,00 Q = 1000 Q = 1250 2,00 Q = 1500 Q = 2000 0,00 Q = 3000 0 1000 2000 3000 4000 5000 6000 Q = 4000 Bed Bed level (m) -2,00 Q = 5000 Q = 5500 -4,00

-6,00 Longitudinal position (m)

Figure 3-9: Bed level (m)

4,00

3,50

3,00

2,50 Hmax [m] Hmax/H0 [-] 2,00 H0 [m]

1,50

1,00

0,50 500 1500 2500 3500 4500 5500 6500 Discharge [m^3/s]

Figure 3-10: Axi-symmetrical bed level (m), maximum bed level (m) and relative influence of overshoot (-)

In both figures above, the position of x = 0, is located where the bend starts (river mark 869 km). In this computation, the bend is simulated to be 6 km long, which is in fact not realistic. The bend at Hulhuizen is about 2.5 - 3.0 km long.

According to Figure 3-9, at the smallest discharges, the maximum bed level increases as the position along the river axis increases. Actually, the solution becomes unstable for lager x- values. On the contrary, at discharges between 1300 and 5500 m 3/s, the solution oscillates to H0 and thereby overshoots the H0-value.

However, both Table 3-2 and the figures above indicate that the relative influence of the overshoot phenomenon decreases as both the discharge (Q > 5500 m 3/s) and position in the bend increases. As the longitudinal position in the bend increases, the bed level asymptotically reaches to the H0-value, due to the small (positive) damping lengths, at the higher discharges. The oscillating motion and the overshoot pointbar is hardly noticeable, this implies that the overshoot phenomenon is of minor importance at higher discharges.

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So, the observations above lead to the conclusion, that during the low water period (Average Q ≈ 1200 m 3/s), the overshoot phenomenon is of dominant influence on the bed level. As the discharge increases during the flood season (November – February), the theoretical pointbar height approaches to H0, which is actually the results of the secondary flow exclusively.

Now this behaviour has been identified, the question arises, whether the behaviour will actually appear within a period of both high and low discharges. To answer this question, reference is made to the celerity and time scale figures in first part of this section. According to Figure 3-1 and Figure 3-2, both the morphological time scales, for the smallest discharges, are actually larger than the (eight months) low water season. From this, it is concluded that the solutions of Figure 3-5 and Figure 3-9 will not be reached. Secondly, for the flood season (November – February), the morphological time scales are much shorter and the bed celerity’s are much faster, therefore it is more likely to assume that the ultimate solution of Figure 3-5 and Figure 3-9 will actually be reached. In this last case, the overshoot phenomenon is of minor importance compared to the lateral change of slope due to the secondary flow.

The Delft3D modelling phase will ultimately show whether the above conclusions are right and in what matter the bed level correspond to the calculated theoretical levels.

3.3.4. Sensitivity analysis In reality, the input parameters do not have a constant value. In order to know how the results of the analytical model depend on the various values of the input parameters a sensitivity analysis has been executed.

This sensitivity analysis is actually divided into two parts:

1. calculations based on Engelund-Hansen power law sediment transport formula 2. calculations based on Meyer-Peter-Müller sediment transport formula

Appendix 5 gives an impression of the several sediment transport formulas and shows how these are used. The basic assumption was to use the Engelund-Hansen formula, because at the start of this thesis, in most reports, this transport formula was used. Later on, other reports showed that a number of projects were also executed with the Meyer-Peter-Müller sediment transport formula. To give an indication of how these two difference approaches (total transport versus bed load) for both transport formulas, a sensitivity analysis is made, but due to a lack of time, the sensitivity analysis of the Meyer-Peter-Müller approach is less extensive

Part one: Engelund-Hansen The previous section has proven that the pointbar in the inner part of a bend is built up by two mechanisms:

1. the lateral change of the bottom slope, due to the secondary flow 2. the overshoot phenomenon

The most important parameters for these two mechanisms are the amplitude of the axi- symmetrical cross-profile (H 0), the damping length (L D) and wavelength (L P). In order to get an idea of the values of these parameters, a sensitivity analysis has been executed in a

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spreadsheet program. Furthermore, the 1-D and 2-D morphological time scales are closely related the morphological activity in a river as well. The input parameters for this sensitivity analysis are the discharge (Q), Chézy coefficient (C), river width (B), radius of the bend (r), and the slope of the water/bed level (assuming steady state situation)(I w). The original values of these parameters and other (assumed) representative constant values, for the river Waal are depicted in Table 3-3. Although, the exponent of the power law formula is constant (Engelund-Hansen theory), it will be varied as well to give an indication how the results changes (Appendix 8). It is impossible to make a computation for graded sediment with the theory used in this chapter, but in this sensitivity analysis, the nominal diameter is varied as well to show the influence of the diameter to the morphology of the river Waal.

Table 3-3: Original values of the input parameters for Engelund-Hansen power law calculation

Parameter Value Unit

3 Discharge 1000 - 6000 m /s Width 260 m Bend radius 1150 m Exponent in sed. transport formula 5 [-] 1/2 Ch ézy Coefficient 45 m /s Nominal Diameter 0.002 m Equilibrium slope 0.00011 [-]

The reference values of T 0, T (2-D), H 0 and L D, L P and IP are shown, as a function of the discharge, in the first column at the right side of the tables in Appendix 7, respectively. According to the tables and the figures in Appendix 7, the following can be observed:

When the roughness decreases (C → 47 m 1/2 /s): • Both the T 0 and T (2-D) morphological timescales decrease, especially for the smaller discharges. The timescales remain almost unaffected for the larger discharges. • The amplitude of the axi-symmetric solution increases, over the full range of discharges. • The damping length remains negative for the smallest discharges, but becomes already positive at a discharge of 1300 m 3/s. This implies, the overshoot phenomenon is more likely to occur at the smallest discharges compared to the reference situation, Table 6 of Appendix 6 confirms this. • The wavelength increases, which implies that the possible bars are longer than in the reference case. • The actual bed level height decreases (6% – 4%, as the discharge increases) (both the axi- symmetrical solution and overshoot are taken into account). • The overshoot phenomenon becomes less dominant compared to H0.

When the width increases (B → 300 m): • The morphological timescale increases, both T 0 and T (2-D), at all discharges. • The amplitude of the axi-symmetrical solution increases. • The interaction parameter becomes smaller than one at a higher discharge, therefore the asymptotic behaviour in the 2-D time scale graph shifts to a higher discharge. • The bed level increases over the full range of discharges, especially for the smallest discharge (unstable computations), bed level increases with 60%, up to 100%. This is not

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surprising, because the B/h ratio is a dominant term in the derivation of the overshoot phenomenon. • For the higher discharges (Q > 3000 m 3/s) the bed level increases from 25% - 9%. • The overshoot phenomenon becomes significantly important, which is confirmed by the relative increase of the ratio Hmax/H0. The ratio increases from 21% - 7% for 3000 m 3/s < Q > 5000 m 3/s. • At the highest discharges, the value of the interaction parameter (IP) drops below 0.25, which forms a limit to the applicability of the linear model

Although in this sensitivity analysis the propagation velocities are not extensively treated, a number of observations are described here: • The width enlargement reduces the propagation velocities (1-D and 2-D), the growing bars will eventually propagate more slowly and therefore it will take more time for the bars to develop. • The amount of potential sediment transport (through the whole river) decreases as well.

The radius only affects the lateral slope. Therefore as the radius becomes smaller (more curvature, R → 1100 m): • The morphological timescales, propagation velocity and the relaxation lengths will not be affected (according to this linear model). • H0 will increase. • Bed level will increases by 4.5% over the full range of discharges. • The ratio Hmax/H0 will be constant, which implies the ratio between overshoot and axi- symmetrical solution remains the same.

-4 As the bottom slope becomes steeper (I w=I b → 1.0*10 ): • The morphological time scales (1-D and 2-D) decreases. • The propagation velocities 1-D and 2-D both increases. • The axi-symmetrical solution (H0) slightly increases and the actual bed level increases about 10% for the lower discharges. As Q ↑, the bed level increases from 6% to 2% for the highest discharges. • At the highest discharges, the value of IP drops below 0.25, which forms a limit to the applicability

The sensitivity of the results, due to a variable value for the nominal grain size is not extensively tested. But when the nominal diameter increases from 2 mm to 2.5 mm (D 50 ↑ with 25%): • The morphological time scales (1-D and 2-D) increase. • The propagation velocities 1-D and 2-D both decrease. • H0 decreases. • The bed level decreases about 5% over the full range of discharges. • The overshoot phenomenon becomes less dominant, because the Hmax/H0 ratio drops about 4% for the lower discharges Q < 1300 m 3/s and 1% for the higher discharges.

In the analysis above, the value of the exponent in the power law formula of Engelund- Hansen is kept constant (b=5). Although this value is always five for the Engelund-Hansen method, it is important to know how this value affects the computation. Therefore, the calculations are repeated for b= 3 and b=7.

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The results of the computation with b= 3 were compared with the ones from b= 5, which leaded to the following observations, see also Appendix 8: • The one-dimensional time scale is always larger from Q > 1150 m 3/s than with b = 5. This is not surprising, because the equilibrium flow velocity is larger than 1,00 m/s for Q > 1150 m 3/s. Therefore, the amount of sediment transport is always larger, which affects eventually the 1-D time scale. • The 2-D time scale is smaller for b = 3, because the factor, which links the 1-D time scale with the 2-D time scale, is affected by the value of b as well. • The applicable range of the linear theory is smaller Q < 4000 m 3/s at higher discharges, the interaction parameter becomes smaller than 0.25. • Both the maximum bed level due to the axial-symmetric solution and the overshoot phenomenon is smaller for b = 3. • The overshoot phenomenon is relatively less important for the b = 3.

When the results of the computation with b= 7 and b= 5 are compared: • The 1-D time scale is always smaller from Q > 1150 m 3/s and the 2-D time scale as well. • Due to the significant change of the wave length (LP), the factor, which influences the 2-D time scale is remarkable changed as well. Therefore, the 2-D time scale is smaller for b = 7. • For b = 7, the applicable range of the linear theory is smaller 2000 m 3/s < Q < 6900 m 3/s. • In this range both the maximum bed level due to overshoot and the axi-symmetrical solution is larger, compared to the other values of b. • The overshoot phenomenon is more dominant for higher discharges.

Part 2: Meyer-Peter-Müller As explained before in this section, in order to compare the results to various values of the input parameters, it is recommendable to test the several approaches themselves as well. Therefore, a number of computations were repeated with the Meyer-Peter-Müller transport formula and compared with the results from the Engelund-Hansen method. The calculations were executed with the following set of parameters:

Table 3-4: Input parameters for Meyer-Peter-Müller transport formula

Parameter Value Unit

1/2 Ch ézy Coefficient 45 m /s Width 260 m relative sediment density 1.65 [-] Bend radius 1150 m Equilibrium slope 0.00011 [-] Nominal Diameter 0.002 m Ripplefactor 0.7 [-] Critical Shields value 0.047 [-]

This leaded to the following observations, see also Appendix 9: • The amount of sediment transport is smaller for Q > 3000 m 3/s than with the Engelund- Hansen approach. The difference becomes larger as the discharge increases. This is not

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surprising, because, the Meyer-Peter-Müller (M-P-M) transport formula considers only bed load. • According to the figures in Appendix 9, the applicable range of this method is Q < 4000 m3/s, which is smaller than with Engelund-Hansen. • Due to this different transport formula, the 2-D behaviour is different as well. This behaviour is not only influenced by the amount of sediment transport, but by the value of b as well. This parameter is a function of the discharge; see Figure 49 of Appendix 9. For the smallest discharges, the value of b is larger than 4. • For Q > 2900 m 3/s, b < 4. The non-constant value of b influences the damping length and wavelength, see formulas A3.64 and A3.65. As L D and L P changes, the 2-D behaviour changes as well, which is depicted in Appendix 9. • Compared to the E-H computation, the maximum bed level due to overshoot and axi- symmetrical solution is with the Meyer-Peter-Muller approach is over the entire range of discharges about 5 - 10 % smaller, according to figure 7 in Appendix 9.

• The damping length (L D) is smaller and therefore the overshoot is less dominant over the full range of discharges. • For Q > 2000 m 3/s the 1-D bed celerity for the Meyer-Peter-Muller approach becomes smaller than the bed celerity of Engelund-Hansen • For the smallest discharges (Q < 1300 m 3/s) both the approaches cause a negative 2-D bed celerity, in which the absolute bed celerity of the Meyer-Peter-Muller approach is about 7% larger. • For 1300 < Q < 4000 m 3/s, both the 2-D bed celerities are positive, but the bed celerity of the Meyer-Peter-Muller approach is larger (on average about 10%).

When the width (B) is increased from 260 m to 300 m, the following observations are made: • The value of b is for all discharges larger, about 6%. • Both the 1-D and 2-D time scales are always larger for B = 300 m. • The amplitude of the axi-symmetric solution is always 3% larger 3 • The damping length (L D) for B=300 is for Q > 1800 m /s 50% larger. • The maximum bed level is for all Q larger when B = 300 m • The overshoot phenomenon is for all Q more dominant than when B = 300 m.

Conclusion of the sensitivity analysis: This sensitivity analysis made clear that, to reduce the bed level in the inner bend, it is worthwhile to reduce the discharge through the main channel. Another way is to increase the width of the channel (reduce discharge per meter width), but attention should be paid to the overshoot phenomenon, which becomes relative more dominant as the width increases.

In the analysis above, two different transport formulas are used. Both have there own characteristics and in theory the ratio between the velocity of fall (W s) and the shear stress velocity (u *), suggested which transport formula should be used. In this thesis, the ratio is larger than one and therefore the Meyer-Peter-Muller theory should be applied. However, in the numerical modelling phase of this thesis, the Delft3D model will be used and depending on the results with both theories a choice will be made, which transport formula will be used.

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3.4. Evaluation of the dredging test at Hulhuizen in 1992 In the period September- November 1992, an amount of 129.000 m 3 of sediment was withdrawn from the downstream bend and 93.000 m 3 from the upstream bend at Hulhuizen. All the material was relocated in the outer part of the same bends and in the groyne fields as well. The total costs of this project were about € 370.000. After this dredging operation, an evaluation project started, in which the cross-sections were monitored in a measurement program. Later on, the measured morphological developments were compared with the results of a numerical morphological model (Sedredge) and the outcomes of an analytical recovery process. Survey ships made depth measurements of the cross-sections, every twenty-five metres, between the banks. The measurement programme showed that the bed topography in February 1993 had the same shape as it had a year earlier. Apparently, the dredging operation during the high water period did not have the desired effect of enlarging the navigable width. The morphological activity was so strong during this period that the full amount of withdrawn sediment returned to the inner side of the bends. In order to guarantee a specific minimum navigational width during low water season, it is better to plan a dredging operation after the high water period. The most important bottleneck appeared to be the second bend downstream of the bifurcation Pannerdensche Kop. The measurements programme showed that the largest cross-slopes were situated at the left bank (inner bend). This corresponds to the pointbar formation after the high water period every year.

The results of the depth measurements, from the monitoring program, were translated into bar heights near the bank. Due to the draft of the ships, the ships were not able to determine the actual bed level near the bank. Via mathematical conservation laws and the assumption of a sinus profile in both lateral and longitudinal direction, the actual bank height was calculated. The wave length in longitudinal direction is, with the help of maps and longitudinal profiles determined, on 5500 m, the lateral wave length was 260 m (width of the river). The results of the depth measurements and computations before and after the high water period were compared and showed a bed level change of 0.25 m in 68 days (December ’92 – February ’93). This value served as input parameter for the recovery process, with the analytical recovery relation, which was used to calculate the morphological time scale, see equation 15.

t − HtH()= () ∞+ [ H (0) − H ()]* ∞ e Te 3.29

When the river discharge or geometry changes, the bottom will not immediately adapt to the new situation. It will take the river time (days, months or even years) to reach the new equilibrium profile, depending on the present discharge, sediment transport etc. In the first computations, a yearly sediment transport was determined with the Engelund & Hansen transport formula. The calculated volume of sediment was changed with a factor 0.47, which leads to an amount of 300.000 m 3 per year, at a (dominant) discharge of 1663 m3/s. The factor resulted from the previous Sedredge calculation. When these values were used, a recovery of 0.07 m was calculated after 68 days. Subsequently, a computation was done with the actual measured discharge of 1750 m 3/s. The outcome of the calculation was a change of 0.09 m of bed level. This number did still not agree with the measured change of 0.25 m. In order to reach a recovery of 25 cm in 68 days, the amount of transported sediment was increased with a factor 2.94 to 887.000 m 3 per year. The results of the computations are depicted in the following table.

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Table 3-5: Morphological time scales according to dredging test 1992 (days)

Q (m 3/s) To Te S (m 3/yr)

1663 722 1.140 300.000 1663 244 386 887.000 1750 673 1.077 300.000 1750 227 365 887.000

Some remarks should be made about the method to estimate the morphological time scale in this evaluation of the dredging test; • The recovery process is strongly simplified. • The formula (analytical recovery relation) should only be used in cases where all the dredged material from the inner bend is dumped in the outer part of the same bend. Together with the conservation of mass in a cross-section, a relocation of sediment in a cross-section immediately results in a changing transverse slope and therefore a changing height of the pointbar. • There is some obscurity about the chosen discharge. The morphological time scale depends on the discharge, but the discharge is not constant throughout a long period. Therefore, to determine the morphological time scale (T e), a discharge is chosen, which is representative for a longer period.

According to the conclusions and discussion point of Taal [1994]: • The recovery relation used seems applicable to the second bend downstream of the Pannerdensche Kop on the river Waal, when the amount of transported sediment is increased. • By assuming a sinusoidal shape in both longitudinal and transverse direction, the bottom shape is too much spread out. Nevertheless, this assumption leads to quit accurate results. • Comparison of the measurements with the results of the recovery relation, suggests that the three-dimensional effects are not taken into account in the recovery relation, which is quite important to determine the navigational width.

The sensitivity analysis showed that: • An (artificial) increase of sediment transport does not influence the height of the pointbar. • An increase of the spiral flow influence does not change the morphological time scale (no influence on the propagation speed of the morphological processes), but it does increase the equilibrium bank height. • An increase of the radius does not influence the morphological time scale, but the bed level in the inner bend will decrease.

3.5. Analytical model vs. Dredging test In order to make the comparison, Table 3-6 shows the results of the computation with two discharges. In this table both the 1-D and 2-D time scales of the analytical model are shown.

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Table 3-6: Comparison table (days), Taal (’94) and analytical model

Q (m 3/s) To T 2D Te S (m 3/yr) Remark

1663 722 1.140 300.000 Taal ('94) 1663 244 386 887.000 Taal ('94) 1663 295 1.876 793.152 An. Model 1750 673 1.077 300.000 Taal ('94) 1750 227 365 887.000 Taal ('94) 1750 273 1.436 863.508 An. Model

According to Table 3-6, the results of the model do not correspond with the values of the dredging test. Before a conclusion is drawn from Table 3-6, it should be taken into account that the following aspects are only included in the dredging test, due to the fact that the test is based on actual depth measurements:

• Both the 1-D and 2-D erosion/ sedimentation processes • The influence of navigation (propeller) to the morphology • The influence of the groynes to the morphology • Local obstacles, which influence the flow and therefore also the morphology

In addition, an important difference between the methods above, are the input parameters. In the dredging test, a hydraulic roughness of 44 m 1/2 /s (Chézy) and a nominal diameter of 1/2 0.0025 m (D n50 ) were used. In the analytical model, the following values are used: 45 m /s, 0.002 m, respectively. Therefore, the difference that exist in the 1-D morphological time scale, shall be ascribed to the different input values of the roughness and the nominal grain diameter. What remains is the difference of the Te and the 2-D morphological time scale. Take into account that in the dredging test computation, the actual mechanisms or influences themselves are not quantified, but the results of all these influences together. It is therefore hard to compare Te with the theoretical 2-D morphological time scale. Both computations do have their pros and cons. The method used in the dredging evaluation seems to give quite accurate results when the amount of transported sediment is increased artificially. Despite this adjustment and the restrictions, see section 2.2, this method gives quit a good indication of the morphological time scale and the pointbar height.

The linear method used in the analytical model should not be rejected, despite the differences with the results of the recovery relation, because it gives a good indication of the importance of the overshoot phenomenon on the river Waal and both the 1-D and 2-D behaviour as a function of the discharge.

According to the results of the spreadsheet calculations (and Figure 3-11), the overshoot phenomenon is only likely to occur at relative small discharges (sufficiently high width-to- depth ratio). At the higher discharges, the damping length becomes positive, which implies a rapid decaying amplitude of the overshoot. This implies that the bed level tends to grow faster to the axi-symmetrical solution, without overshooting it.

At the lowest discharges, the overshoot phenomenon dominates the height of the bed level, but this height is still smaller than at the higher discharges, where the axi-symmetrical

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solution determines the height mostly. This should implied that when the discharges becomes smaller after a flood period, the bed level in the inner bend should be decreasing as well, see bed level difference in Figure 3-11 between Q = 5000 m 3/s and Q = 2000 m 3/s. However, the large morphological time scale, at the smallest discharges implies that the morphological activity is limited and therefore a decrease in bed level will take a long period in which the circumstances should not vary. Due to this relative slow morphological activity after the flood period, the pointbar height causes an obstacle to the navigable norm.

4.00

3.50

3.00

2.50 Q = 1000 Q = 2000 2.00 Q = 3000 1.50 Q = 4000

Bed level Bed (m) 1.00 Q = 5000 0.50

0.00 0 1000 2000 3000 4000 5000 6000 -0.50 Longitudinal position (m)

Figure 3-11: Bed level due to axi-symmetric solution and overshoot phenomenon.

Therefore, the conclusion of the analytical model should be that the pointbar formation is not caused by the overshoot phenomenon in the bends of the river Waal, but it is caused by a difference in morphological activity between flood and low water season.

In order to handle this problem, two different approaches can be used: • Reduce morphological activity during flood season • Increase morphological activity during low water season

The model of the overshoot phenomenon is derived from a mathematical model, in which the river is modelled as two straight parallel channels. Although in history this modelled has proved to give sufficient good results, both in laboratories and in reality (see De Vriend & Struiksma [1983]), in this project the pointbar existence can not be explained by the 2-D (overshoot) model.

From the results of section 2.1.3 and the Appendices 7, 8 and 9 can be concluded that the 1-D processes (time scale) is always (over the whole discharge range) significant smaller than the 2-D time scale. In addition, the bed celerity of the two-dimensional motion is always smaller compared to the one-dimensional motion. This justifies the conclusion that the 1-D process in rivers bends is far more dominant than the 2-D processes.

Although it is not known, whether the 1-D or the 2-D mechanism is in particularly fully responsible for the pointbar formation, (in reality it will be caused by a combination of the two processes), it is clear that the morphological activity increases as the discharge increases. A constructive method to decrease the morphological activity could therefore be to artificially decrease the discharge (per meter width) through the summer bed during high run offs (high water season). Adjustments will lead to a less favourite condition for morphological activity and therefore it will take the bottom more time to rise.

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3.6. Generation of alternatives

3.6.1. Introduction Keeping the objectives of this project in mind; to prolong the morphological time scale and decrease the height of the pointbar at the inner bend on the River Waal at Hulhuizen, this section will discuss a number of possible solutions to reach these objectives. When the alternatives have been described, a selection will be made of the most promising alternatives, in the next section.

Depth measurements show that the bed level (in the inner bend) increases mainly at the highest discharges the year. Therefore, it seams reasonable to guide more water through the floodplain instead of the summer bed. Actually, this means that a wet cross-section enlargement might help to reduce the pointbar formation.

There are several ways to achieve this objective, for example: 1. Removal of obstacles in the floodplain, with increases the roughness (trees, dikes, constrictions, higher grounds .etc) 2. Summer dike lowering 3. Floodplain lowering 4. Controlled discharge withdrawal, (combination of option two and three)

As stated in the area description in the first chapter, it is not allowed to start activities, which change the environmental values in the floodplain. The trees, for example, form a pivot element in the local environment. Furthermore, the amount of small dikes (obstacles) in the Millingerwaard is such small and therefore, the first option drops out.

In section 2.2, the results are described from Van Breen’s thesis [2002]. She studied the effect of the last three options, mentioned above. Her results descend from a straight 1-D model, which does not correspond to the situation at the bend of Hulhuizen. Both the hydraulic and sediment motion in a bend differs significantly from a straight channel (3-D instead of 1-D), that her findings are not directly applicable to this study. It is therefore recommendable to use a multi-dimensional approach. The fourth option is actual a combination of the second and third option. In reality, this option can be translated into the appliance of a side channel.

In this section special attention will be paid to the enlargement of the wet cross-section, keeping the results of previous research in mind.

3.6.2. Alternatives In a meeting with representatives from TU Delft, WL | Delft Hydraulics and the Rijkswaterstaat’s Oost-Nederland (Part of the Ministry of Transport, Public works and Water Management), several ideas or approaches were launched, which might explain the pointbar formation and could perhaps be helpful to reduce the influence or growth of the pointbar in inner bends. The alternatives are categorized in two different types of solutions:

1. Solutions, which deals with the direct cause of pointbar formation. 2. Solutions, so-called mitigation solutions, which do not deal with the direct causes themselves.

Solutions from the first type are related to the causes of pointbar formation, which are depicted in the following figure.

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Sideways flow abstraction in the upper part of the vertical

Discharge Flow width increase of adjustments the summer bed

Side channel Spiral motion Bend Cut-off Pointbar formation Curvature Groyne extension adjustments

Overshoot phenomenon Submerged Vanes

Figure 3-12: Possible solutions of the first type Two causes for pointbar formation are determined; change of the lateral slope due to the secondary flow and on top of that the overshoot phenomenon. According to the previous sections, the overshoot phenomenon does not play a dominant role in this project. Therefore, for this project no alternatives are generated which aim to influence the overshoot phenomenon. The spiral motion intensity depends on the discharge and the curvature of the flow. By changing these two aspects, both the spiral motion and the lateral sediment transport capacity will be affected, therefore, these two aspects form the basis of a number of alternatives below.

The alternative of the second type is more or less a mitigating solution. It does not take away the prime cause of pointbar formation, but it decreases the effect of pointbar existence itself. At the start of this thesis project, a possible solution of the pointbar influence was the application of a side channel. A more detailed description will be given below.

The following alternatives have been generated: The first six alternatives are of solution type 1 and the last one belongs to the second type of solution.

1. Sideways flow abstraction of water from the upper part of the vertical. This basic idea of this (theoretical) alternative is to diminish the secondary flow and lateral sediment transport; see Figure 3-13 and Figure 3-14.

Figure 3-13: Normal secondary flow in a river Figure 3-14: Adjusted secondary flow bend

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By lowering the summer dikes in the outer bend, a part of the winter bed will be flooded, during high runoffs, when the water level exceeds a particular level. Due to this width increase and corresponding decrease of flow velocity, the slope of the water level might be less steep, resulting into a smaller resultant of the hydraulic pressure, which might reduce the intensity of the secondary flow. As the secondary flow is reduced, the potential lateral sediment transport will be smaller as well as the amount of transported sediment from the outer bend, ultimately leading to a smaller bed level rise in the inner bend.

However, this alternative is only effective when the winter bed at the northern side of the Waal actually transports water. If the winter bed is not able to retract water from the main river, it will be a temporal storage facility and work like a ball bearing, which implies that the alternative fails. Water is only abstracted, when the slope of the parallel ‘channel’ is the same or steeper than the bottom slope of the main river. In Figure 3-15, a possible alignment of the side channel is shown. In this example, the side channel has a length of 5.5 km. This corresponds to a slope of 1.3*10 -4, which is steeper than the river slope. The side channel will therefore be able to retract water from the river. Besides the inlet of the parallel channel, there has to be an outlet as well. To create an outlet, and taking into account the equilibrium bed level slope, the channel must cross the polder near Gendt.

Figure 3-15: Alternative 1: Side channel alignment To create a parallel channel, the following adjustments to the surroundings should be executed: • The height of the local summer dike must be decreased over 1.8 km. • Present obstacles (camping, shipyard) in the winter bed, should be removed and/or relocated elsewhere. • Setback of the Waaldijk (2 km). • The polder near Gendt should be adjusted to be able to deal with flowing water instead to store water (channel excavation, removal of small dikes, change the alignment of several channels and ditches, etc). • Creation of an outlet between the side channel and the river Waal. • 6.5 km side channel excavation

The interventions above are not popular and will increase friction between the community and river authorities. Taking into account the present topography, the adjustments will lead to significant financial investments and will have undoubtedly consequences for the local economy, and the natural environment (both positive and negative). Previous research of

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Duel, During, Specken [1994] has shown that the application of a side channel has a positive effect on the biodiversity and will enhance the amount of species in the area. The quantification of this last aspect is not an element of interest in this thesis and will therefore not be taken into account by the selection of alternatives.

2. Dike setback. The basic idea behind this alternative is to increase the flow width in the bend, which creates a reduced water depth and a smaller propagation velocity of both the water and sediment movement towards the inner bend. However, the theory above is only valid when the winter bed does not significantly contribute to the water transport capacity of the summer bed. However, in reality the winter bed does transport water during the high water season and therefore the assumption is quite mediocre.

Due to the increase of flow width, both the theoretical 1-D and 2-D morphological timescales will decrease, which is noticeable from the sensitivity analysis of section 3.3.4, but the increase of bed level due to the overshoot phenomenon should not be forgotten during low water season.

To guarantee sufficient draught for inland navigation, especially during the low discharges, the present groynes should be extended in the floodplain. The expansion of the width cannot be implemented on the northern side of the river Waal; first, because it will lead to a sharper flow curvature of the bend and therefore to an increase of pointbar height. Secondly, the space needed for the dike setback is present on the southern side of the river Waal (Millingerwaard). A rough sketch of the alignment of dike set back and principles of this alternative are depicted in Figure 3-16 and Figure 3-17.

Figure 3-16: Overview dike set back and groyne extension Figure 3-17: Principle of dike setback and groyne extension Due to the presence of houses on the dike near river mark 869.00 km, it is not possible to create an extended dike setback. When a larger dike setback is required to decelerate the flow, a relocation of these houses, is suggested.

3. Creation of extra flow capacity in the winter bed. In contrary to the previous one, which tries to decrease the flow curvature and velocity, this alternative aims to decrease the discharge through the bend or summer bed itself and increases the flow through the winter bed. Nowadays the winter bed mainly has a storage function during high water season. According to Sieben [1999], a lowering of the summer dikes is an adequate way to change this storage function into a flow function.

One of the options is to create a parallel channel or so-called side channel in the winter bed. However, application of a side channel is only effective when the channel actually has sufficient water abstraction ability. To accomplish this, a so-called bend cut-off might be an

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option. A bend cut-off is characterized by a reduced length in which the water flows from point A to point B. In theory, this smaller length leads to a steeper slope and therefore the side channel is able to retract water from the main river. A reduced discharge through the main river might lead to less morphological activity and therefore the pointbar formation might be positively affected.

The morphological changes are hard to determine, because the inlet at the river forms a bifurcation. In the last years, the experience and predictability of bifurcations has increased, but there is still a lot of uncertainty in its complex behaviour. Another complicating factor is the location of the bifurcation itself, according to the figures below, the inlet is situated close to the main bifurcation (Pannerdensche Kop) of the river Rhine. It is not excluded, that a possible inlet in the Millingerwaard will have a significant influence on the discharge and sediment distribution between the rivers Waal and Rhine.

Figure 3-18: Alternative 3a; side channel layout Figure 3-19: Alternative 3b; side channel layout

In figures above, just two options for the alignment of the side channels are shown. In Figure 3-18 the alignment of the side channel follows the old riverbed of the Waal in the 18 th century. Excavations are only needed in the upstream part of the channel. On the contrary, Alternative 3b, (depicted in Figure 3-19), the side channel should be excavated entirely.

Rivers do not only transport water, but sediment as well. Generally, when only water is abstracted from the river overall sedimentation the main channel occurs downstream of a bifurcation in (1-D effect). The ratio between transport capacity and the actual amount of sediment is disturbed and sedimentation is occurs. In order to reduce the sedimentation effect in the river, a number of options will be presented. Abstraction over the full height of water column from the outer part of the previous bend, which contains relatively more sediment than water in the inner bend, will establish that both water and sediment is abstracted from the river. Depending on the distribution of water and sediment over the branches, and the ratio between the actual transport capacity and amount of sediment in the individual branches, sedimentation or erosion will occur. Abstraction of only water in the upper part of the water column, (which contains less suspended sediment than in the lower part of the column) will always cause bed level increase in the main river. If the side channel retracts both water and sediment, a sand trap in the entrance of the channel saves the side channel for being silted up, but the side channel needs to be maintained anyway.

4. Bend cut-off This fourth alternative is one of the most radical ones, because the layout of riverbed has totally changed into one without a relative sharp bend, see Figure 3-20 and Figure 3-21. It is actually a river diversion.

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Figure 3-20: Alternative 4; Bend cut-off

Figure 3-21: Alternative 4b: Radical Bend cut-off

In Figure 3-20 only the bend at Hulhuizen is cut off and in Figure 3-21 even a more radical cut-off is depicted. In this figure, the sharp bend downstream of Gendt is cut-off as well. Morphologically, this layout is more favourable with respect to a guaranteed navigational width. Without the sharp bend, the spiral motion is nearly absent and the net lateral sediment transport, which causes the bed level rise to the inner bend, as well. Pointbar formation is therefore very unlikely to occur. However, the shifted riverbed will just like the side channel in the previous alternative, influence the water and sediment distribution of the bifurcation at the Pannerdensche Kop. The new riverbed has a smaller length and therefore a steeper slope, which retracts not only more water from the river Rhine, but sediment as well. Due to the new situation; the river bed upstream of the bend cut-off will erode and disturbs the present water and sediment distribution over the river Waal and the Pannerdensche Kanaal and it enhances the undesirable decrease of bed level in the area. To guarantee, the present distribution of water and sediment, an adjusted river management (weir) programme might be formulated, or a radical change of the geometry of the bifurcation itself might even be necessary. Although the bifurcation behaviour of the Pannerdensche Kop has been modified the last years, to establish a proper water and sediment distribution over the two branches, it will be a complex, but interesting challenge for river engineers to adapt the geometry of the bifurcation again to the new situation.

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It is not easy to create an alignment without a bend, when a bend is already present. Below, a small summary is made, of the activities, which should be executed and the problems, which may arise when the alignment of the bend of Hulhuizen is changed into one without a bend. In this summary, it is assumed that the bend near Gendt (in the Gendtsewaard) is also cut-off, because it is of no use to cut off a bend and reconnected to a sharp bend downstream. It is preferable to cut off the bend near Gendt as well.

• Total river excavation of 6.5 km (about 10 million m 3 of excavating material) • With a unit cost of € 2.50 per m 3 of excavated material, the total costs are around € 25 million but the sales of excavated material may have a compensative effect on the dredging costs. • What to do with it when the excavated material turns out to be polluted? • The old riverbed might be used as extra flowing capacity during high runoffs. • The polders (both the Millingerwaard and the Gendtsewaard) themselves should be adjusted. Take into account channels, ditches, actually, the total water management program should be adjusted. • It is hard to determine the consequences for the total natural environment. Nowadays, the natural function is one of the most important functions of this area and will be heavily violated when this alternative is being executed. The polders form the special habitat for different kinds of species and it is hard to relocate these habitats. • Initially, the bend cut-off will increase the slope and therefore erosion is likely to occur upstream of the bend cut-of and sedimentation downstream. • For t → ∞, the upstream bed level will be lowered over a distance of ∆L* i nitial . In which ∆L is the reduced length of the river due to the bend cut-off. • The bend cut-off will disturb the water and sediment distribution at the upstream bifurcation. Measures should be taken to counteract these perturbations. • The previous investment to create a fixed layer in the bend near Gendt seems to be waste money when this bend is cut-off as well. • A storage facility has to be removed from the Kekerdomsewaard and a stone factory from the Gendtsewaard.

5. Groyne extension downstream of the bifurcation in the inner side of the first bend. This fifth theoretical alternative is, just like the previous alternative, based on the adjustment of the water flow. However, in this alternative, the adjustment takes place just before the entrance of the second bend after the Pannerdensche Kop.

Figure 3-22: Alternative 5: Groyne extension downstream of Pannerdensche Kop

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By extending the length of the groynes on the northern side of the first bend, see Figure 3-22. the main flow might remain attached to the southern side of the river Waal and therefore “crosses” the river further downstream. This might imply, the spiralling motion in the bend will start further downstream and will be concentrated over a smaller length. Ultimately resulting into a sharper curvature of the flow, but over a smaller length in which sediment is transported to the inner bend. This principle might reduce the pointbar in length and height in the upstream part of the bend, but increase pointbar formation in the downstream part of the bend.

Other effects of this alternative are: • Due to the groyne extension, the roughness increases, which has a negative effect on the water level upstream. This effect is in strong disagreement with the present policy of the river authorities, in which no water rising activities are allowed. On the contrary, the present policy aims to decrease the water level as much as possible in order to increase the safety against flooding. • The extension of the groynes directly limits the navigational width, which forms a contradiction to the objective of the river authorities.

6. Application of submerged vanes in the river axis. This sixth alternative is based on intervention of transverse bottom sediment transport in the river bend, see Figure 3-23. The submerged vanes are placed along the river axis, and penetrate into the lowest part of the water column.

Figure 3-23: Alternative 6: Submerged vanes parallel along river axis This alternative is not supposed to block the secondary flow, but only the (bottom) sediment transport. Normally, sediment is transported (in the lowest part of the vertical) from the outer bend to the inner part, resulting into a lateral cross-slope of the bottom. When this transport is (partly) blocked, not all the sediment will reach the inner part of the bend and therefore the bed level will not rise as much as it usually does.

With this alternative actually two different channels are created, both are influenced by the spiral motion. In the channels themselves lateral sediment transport will occur and therefore, a saw tooth bottom profile will probably be established. When here is no sediment exchange between the channels, the height of the pointbar in the inner bend will be smaller than in the reference case.

In former studies, for example Wiersma [1997] and Jörissen [2004], submerged vanes were placed under an angle with the flow direction at a height of 0.2 or 0.4 times the water depth. This to create a counter spiral motion, which would reduce the spiral motion, caused by the river geometry. Unfortunately, this counter spiral effect has not been proved to be a sufficient

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pointbar-reducing alternative. A great disadvantage of this option was also the great risk for collisions with inland navigation vessels, due to the position of the vanes.

The presence of the vanes will not only cause a morphological reaction of the bed, but there are a number of consequences, which are listed below: • The execution or positioning of the vanes will form an obstacle to navigation. • Due to the constricted width of the (two) fairways, a ban for overtaking manoeuvres will be needed to minimize the risk of collisions with the vanes. • Directly beside the vanes a scour hole will appear. To guarantee the stability of the vanes, they should be long enough to be anchored deep into the bottom. Together with the material costs and the positioning of the vanes, this makes the alternative a costly one. • Other uncertainties are the maintenance dredging cost. The height of the vanes should be determined in such a way that the sediment motion is blocked. The moment when the vanes don not block this motion anymore, makes them ineffective and the pointbar will grow anyhow. At that moment, maintenance dredging is required. The dredging costs are not only a function of the amount of excavated material, it is also a function of the complexity. It is not hard to imagine that it is more complex to dredge near an underwater construction than to dredge in an area with no obstacles. • A consequence of this alternative might be that the ferry-service between the Millingerwaard and Hulhuizen might be relocated elsewhere, due to the depth requirements of the ferry.

7. Side channel to blow away the pointbar This final alternative is a solution of type 2, a mitigating one. Sideways, concentrated water flow to blow away the pointbar in the inner bend, see Figure 3-24.

Figure 3-24: Alternative 7; Side channel to blow away pointbar

By using artificial jets or a side channel, a specific discharge can be sideways added to the main river. From mechanical engineering point of view, the jet option is very interesting, but from civil engineering and environmental point of view, preference goes to the application of a side channel. The jet option will therefore not be taken not account. When a side channel is used, an inlet is needed to retract water. Just like the previous alternatives, which included a side or parallel channel the following aspects are important: • The influence on the present bifurcation Pannerdensche Kop.

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• The water and sediment ratio between the main river and the side channel and in the branches themselves. These aspects are important for the morphological change (sedimentation and erosion) near the bifurcation. • The pointbar appears during high water conditions, this implies, the side channel should be active mainly during this period. It is therefore important to know, when the assistance of the side channel is required. From environmental point of view, preference goes to a side channel, which transport water throughout the whole year. • The demand for water at the outlet forms the boundary condition of the geometry of the side channel. Take into account the length ratio between the main river and the side channel, the off take angles at the inlet and the orientation angle at the outlet, the choice when and how long the side channel should be active determines for example the geometry of the inlet. Will it be a hydraulic structure, like an artificial weir, or will it be just a lowered dike, which will be exceeded at a specific discharge.

3.7. Selection of alternatives In the previous section, multiple theoretical alternatives to limit the pointbar formation were generated. Every alternative has a different way of approach to influence the pointbar formation, for example: • Decrease the amount of discharge per metre width in the summer bed. • Increase of discharge capacity of the winter bed in different ways. • Artificially change the flow curvature.

To know how well the alternatives fulfil their goal to limit pointbar formation, they should be tested in a computational model or a scale model. Due to a lack of time, it is impossible to make a full (Delft3D) model with all the alternatives. Therefore, a selection has to be made for the most promising alternatives.

In order to make a founded decision of which alternative might be the most favourable one, all alternatives will be compared in a Multi Criteria Analysis. (MCA). First, the criteria and variables are determined, see Table 3-7. Before the MCA is executed, it should be stated that this qualitative MCA is only a way to visualize the characteristics of the individual alternatives and to compare them.. Therefore, the MCA has only a comparative function.

Table 3-7: Criteria and variables used in the MCA Criterion Variable

Functionality 1: Reducing pointbar formation 2: Nuisance during implementation Cost 3: Investment costs 4: Maintenance costs Environment 5: Impact 6: Physical fit

Before the MCA is executed, the variables are described first.

1. Reducing pointbar formation It is not known how all the alternatives will actually affect pointbar formation , therefore, the appraisal of the alternatives on the first variable is based on available literature.

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2. Nuisance during implementation The second variable indicates how much nuisance the alternative will cause for the surroundings, navigation, inhabitants, etc.

3. Investment costs Usually the costs are expressed in the unit of money, but here the alternatives are compared to each other and in the appraisal, the following aspects are taken into account: amount of excavated material, length of the channels, material costs, etc.

4. Maintenance costs This fourth variable ass the alternatives on the following aspects: dredging operations, material costs due to maintenance.

5. Impact The impact on the environment of the alternatives is based on the way the alternatives affect the present natural environment.

6. Physical fit The alternatives are assed on the way the alternatives fit into the present situation.

This MCA is meant to compare the alternatives in qualitative way. Therefore, the characteristics of the alternative will be judged by means of the variables and the score ranges from ++ to -- (positive to negative, respectively).

Table 3-8: Qualitative Multi Criteria Analysis

mation r sts osts t ce c ct a l fi Alternative p ca san si tment Im y pointbar fo s g Nui Ph inve Maintenance co

Reducin

1: Sideways abstraction - - - - ± - - - 2: Extra flow capacity in floodplain + + - ± + + 3: Dike set back - - + - + + 4: Bend Cut off + + - - - - + - - - - 5: Groyne extension - - - + + + + + + 6: Submerged vanes ± - - - - - + + 7: Side channel to blow away pointbar + - - ± + +

From the table above, the fourth alternative (bend cut off) turns out to be less favourable in comparison with the other alternatives. In addition, the sideways abstraction in the outer bed (alternative 1) and the application of submerged vanes (alternative 6) are not as positive as one might expect.

Besides the scores of the alternatives in Table 3-8, some remarks should be made about the individual alternatives.

For all alternatives, which are meant to increase the wet cross-section, in order to decrease the secondary motion and to reduce the bed level in the inner bed (2-D effect), it should be stated

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that an one-dimensional sediment motion should be expected. The actual bed level is a function of a combination of both mechanisms. It is still questionable which effect is dominant in a river bend.

Alternative 1: Sideways abstraction of water from the upper part of the vertical It is very unlikely that this alternative will be implemented in reality, because there is a lack of sufficient space to fit in this alternative. Furthermore, the abstraction does not only affect the hydraulics and morphology locally, but has a global effect as well. The effects on the upstream area are very important concerning the situation at Hulhuizen, due to the presence of the bifurcation. This first alternative is meant to decrease the intensity of the secondary motion, by interference of the 3-D water movement. There are still some question marks left about the interference of the secondary motion, see Sieben (1999).

Alternative 2: Dike setback This second alternative is based on the assumption that the winter bed does not contribute to the discharge of water, which is not realistic, considering the reduced dike height of the Millingerdijk.

During low water season, the groynes will guarantee a sufficient water depth, but between two consecutive groynes, the flow width locally increases, which will induce local sedimentation. Furthermore, the presence of groynes will intervene in the local situation. Due to the curved flow directions around the tip of the groynes, local erosion is expected and downstream of this scour hole where the flow directions diverges again, sedimentation will occur.

It is this complex interaction between the secondary flow (discharge), presence of groynes and the local flow direction, which determines whether this alternative succeeds in reducing the pointbar height or not. Therefore, it is recommendable to test this alternative in a (2-D) model.

Alternative 3: Creation of extra flow capacity in the winter bed This way of interference intense to reduce the bed level in the inner bed (2-D effect), but it also carries the one-dimensional effect; overall bed level rise downstream of the offtake. It is still questionable which effect is dominant in a river bend.

Furthermore, side channel appliance tends to attracts discharge from other branches. This implies when a side channel is applied, the amount of discharge through the river Waal will increase which is unfavourable for the discharge through the Pannerdensche Kanaal, Nederrijn and river IJssel. However, not only the discharge distribution over the river changes, but the sediment distribution as well, ultimately causing sedimentation in one branch and erosion in the other one.

It is hard to predict which phenomena dominate the local morphology in advance. Therefore, to get an idea of the influence of the several morphological phenomena, which belong to the application of a side channel, model computations are indispensable.

To deal with this problem, it is reasonable to make clear how the application of a side channel affects the pointbar formation first (due to a 2-D model). Secondly, to see how this interference affects the sediment and discharge distribution over the river Waal and Pannerdensche Kanaal, an one-dimensional model might be consulted.

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In advance, this alternative might looks interesting, but the exact results are still questionable. It is therefore recommendable to make the results visible by using (multiple) computational models (both 1-D and 2-D).

Alternative 4: Bend cut-off The pointbar exists only due to the presents of a bend. When there is no bend, there is mainly longitudinal flow and therefore the lateral sediment transport is marginal. Morphologically speaking to solve the matter of pointbar formation, a river alignment without a bends is preferable above a meandering river. Actually, it is the ultimate solution to get rid of pointbar formation. Generally, at lower discharge through a straight channel, alternate bars might be expected. But in the river Waal these bars are very unlikely to occur, due to the relative long morphological time scale. Taking the summation of this alternative in the previous section into account, the conclusion must be that this alternative is actually a quit radical one, not only when the costs are considered, but also the impact on the environment as well. This makes the alternative reprehensible.

Alternative 5: Groyne extension downstream of the bifurcation in the inner bend This alternative is a pure theoretical one and is a contradiction to the present river policy. In The Netherlands, water level rising activities are not aloud. Furthermore, this alternative indirectly opposes to the objective of this thesis, to increase the navigational width.

It is already mentioned above; this alternative is a pure theoretical and not a realistic one. Furthermore, the actual effect of the alternative is quit questionable, because it unlikely that the stream will attach longer to the southern bank of the bend due to the extended groynes. Therefore, this alternative will not be used in the next phase of his thesis.

Alternative 6: Application of submerged vanes in the river axis A number of disadvantages and consequences are listed in the previous section, but one of the most important one is that the alternative becomes ineffective, when sediment is able to pas the vanes. It is hard to determine in advance when this situation might occurs, but when it occurs maintenance dredging is still required. Application of this alternative does not imply that dredging activities are redundant.

An important disadvantage remains the chance of collisions, although it is reduced by placing them along with the river axis, compared to the project of Wiersma [1997]. This is actually only the true when the ships are able the pass the bend in their own channel, without drifting. This forms actually a significant question mark, because, the bend is relative sharp and the vessels on the river Waal are the largest inland navigation vessels of the Netherlands.

Together with the uncertainties about the costs of this alternative (both execution and maintenance costs) and the fact that it is (not yet) possible to model this alternative in Delft3D, this alternative will not be worked out in this project.

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Alternative 7: Side channel application to blow away the pointbar This last alternative interferes actually twofold into pointbar formation. 1. Due to the upstream water abstraction, the velocities in the bend will decrease, which causes a decrease of the spiral motion and therefore the lateral sediment transport capacity becomes smaller. 2. The outlet position might be able to limit the pointbar formation, by “blowing away” the sediment.

The combination of both interferences makes this alternative interesting. Therefore, this alternative will be used in the following computational modelling phase.

Conclusion: Concluded from the Multi Criteria Analysis, and the remarks in this section, the application of a side channel looks promising on first hand. Reducing the bed level in the inner bend by decreasing the amount of discharge through the summer bed sounds attractive, but the abstraction of water (and sediment) will initiate bed perturbations, which should be taken into account as well. Thereby, the Ministry of Transport, Public works and Water Management has shown particular interest in the application of side channels in order to reduce pointbar formation. Therefore, to determine the influence of side channel application will be next target of this thesis.

58 WL | Delft Hydraulics, RIZA, ON, TU Delft Side channels to improve navigability on the river Waal November 2005

4. Numerical modelling The numerical model Delft3D-sediment online is used for the morphological computations. WL | Delft Hydraulics has developed a unique, fully integrated computer software suite for a multi-disciplinary approach and 3D computations for coastal, river and estuarine areas. It can carry out simulations of flows, sediment transports, waves, water quality, morphological developments and ecology. It has been designed for experts and non-experts alike. The Delft3D suite is composed of several modules, grouped around a mutual interface, while being capable to interact with one another. Delft3D-FLOW, is one of these modules. Delft3D-FLOW is a multi-dimensional (2D or 3D) hydrodynamic (and transport) simulation program which calculates non-steady flow and transport phenomena that result from tidal and meteorological forcing on a rectilinear or a curvilinear, boundary fitted grid. In 3D simulations, the vertical grid is defined following the sigma co-ordinate approach. The flow module of this system, viz. Delft3D-FLOW, provides the hydrodynamic basis for other modules such as water quality, ecology, waves and morphology. The flow field generated by the Delft3D-FLOW module may be used as input for the morphological module Delft3D-MOR or the sediment transport module Delft3D-SED. Delft 3D is one of the most sophisticated numerical programs for depth averaged computations model schematisation

The area of interest of this project is the bed level of the river Waal at Hulhuizen.

There are a number of important assumptions and starting-points, which are relevant for the model used:

• The river model is about 15 km long, starts at Waal river mark 867.220 km and ends at 873.000 km. • The model simulates both the hydraulic and sediment motion in the summer bed on a curvilinear computational grid. The summer bed and therefore the computational grid is confined through a line over the tips of the groynes on both sides of the river Waal. • The model should simulate the bed level change in the summer bed in the first relative sharp bend downstream of the bifurcation Pannerdensche Kop. The computational grid should have a sufficient small grid size to simulate the bed level change accurately. Dunes and ripples are of no interest in this project, because these phenomena occur both on much smaller time and on length scales. • The model schematisation is based on a computational grid, which is available from a previous project of WL | delft Hydraulics, (Klaassen and Sloff [2000]). To adapt the computational grid, the land boundaries are used, which were on their turn based on Baseline schematisations (from WL | Delft Hydraulics). These land boundaries show both the summer bed and flood plain confinements. • For this thesis, a depth averaged 2-D computational model is used. The choice whether a 1-D or multi-dimensional model should be used depends on the type of problem (the degree of detail required), as well as on the amount of data that is available to calibrate and validate the model. It is imaginable that for a strategic planning of an entire river basin, a less detailed type of model might be used than for the study of scour around bridge piers, for example. Increased detail, both in terms of resolution and in terms of physical processes taken into account, requires more computational effort and a larger amount data. Based on the problem definition, decisions have to be made about the number of dimensions in the model. In principle, river morphology concerns a 3-D problem. However, fully 3-D models are hardly available for river morphology and most problems do not need to be tackled by means of a ‘complete’ 3-D description.

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A 1-D approach is possible if the width-averaged values of the dependent variables give sufficient information for the problem to be solved. A 1-D model can be used, for instance, to estimate the continuation of the large-scale tilting of the river Waal that was observed in the last century. One -dimensional models are being used in assessing large- scale processes in large reaches of a river. Since the problem of this thesis is related to cross-sectional profile evolution (transverse bed slopes and “overshoot” pointbar formation in river bends), which develops at a larger scale than scour around bridge piers, this the degree of detail requires a 2-D model with a parameterisation for secondary flow or a 3-D model. Regions of rapidly varying flow conditions in combination with a complex morphodynamic situation, for instance the local scour development in time around groyne fields, revetments and bridge piers, require a 3-D model approach. The choice of using either a 1-D or a multi-dimensional approach is often a matter of computer capacity, budget and time available. • The computations are based on a uniform roughness value, because it is not (yet) possible use a spatial varying roughness coefficient. • For the morphological computation, the quasi-stationary approximation is assumed applicable. In the quasi-stationary approach to the morphological modelling, the model swaps between the hydraulic and morphological motion. This means that the bed is held fixed while computing the water motion and vice versa.

4.1. River geometry It is important for the two-dimensional morphological computations with Delft3D that the grid lines of the computational grid follow the summer bed. By following the summer bed, the computational grid does not have staircase confinements, which saves the computation from small oscillations of the bed level, which might harm it. The computational grid exists of 301 grid lines in longitudinal direction and 15 lines in transverse direction, coming down on grid cells, which vary from 42 to 60 m in longitudinal direction and 13 to 27 m in transverse direction. The bend at Hulhuizen has an averaged width of 260 m (15 grid cells), see Figure 4-1.

Figure 4-1: Initial computational grid Hulhuizen

60 WL | Delft Hydraulics, RIZA, ON, TU Delft Side channels to improve navigability on the river Waal November 2005

The spatial geometry or bathymetry of the river is determined by the allotment of a value for the bed level in every grid point.

4.2. Model input The model input for a Delft3D depth averaged computation consist of: Model parameters, initial conditions and boundary conditions

4.2.1. Model parameters Parameters, which do not vary during a computation, are model parameters. Important parameters (and their values) in a Delft3D depth averaged computation are depicted in Table 4-1.

Table 4-1: Model parameters for Delft 3D

Model Parameter value Unit

Gravitational Acceleration 9.81 m/s 2 Roughness 45 m1/2 /s Viscosity 2 m2/s Water density 1000 kg/m 3 Mean grain size 2 mm Dry bed density 1650 kg/m 3 Time step 30 s Morphological Factor differs per computation [-]

Previous projects, concerning the river Waal, has shown that the process in the river are quite good predictable when the above subset of values is used. These are determined by WL | Delft Hydraulics and RIZA. A time step of 30 seconds is needed to create numerical stability (concerning the courant number).

4.2.2. Initial conditions The first initial condition, which should be prescribed, is the bed level. Samples of a representative summer bed level are provided by RIZA, which are the results of multibeam measurements. By interpolation of the depth samples, a value for the bed level is allocated to the grid points. To get an impression of the density of the depth samples, see Figure 10-1 in Appendix 10. The resultant initial bed level is depicted in Figure 10-2 of Appendix 10.

The second parameter, which should be prescribed, is the water level. Delft 3D uses actually a staggered computational grid. In the gridpoints, the discharge is computed and between two gridpoints the water level.

It is even possible to save the local depth average velocities and use them as an initial condition in a next computation.

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4.2.3. Boundary conditions To start the computation, an upstream boundary as well as a downstream boundary is needed. In this thesis, two types of downstream boundaries are used: 1. Water level boundary (as a function of time) 2. Water level discharge relation (Q-h relation)

Depending on whether the computation was made with a constant discharge (upstream boundary) or a varying one, the downstream boundary is determined. When a constant discharge is prescribed, a downstream boundary of the first type was used. The downstream water level is calculated by adding the equilibrium water depth to downstream bed level. To save the computation for internal waves, when prescribing a varying discharge at the upstream boundary, a Q-h relation was determined for the downstream boundary.

The upstream boundary consists of fourteen small discharge boundaries. Due to the fact that the upstream boundary is located at the bifurcation point (Pannerdensche Kop), which is located in a bend, the discharge is not uniform distributed over the total river width. An adapted discharge boundary is therefore more corresponding to reality. Furthermore, when a uniform discharge boundary was applied, the morphological activity in the area of interest (bend at Hulhuizen) was not reproducible. Therefore, a skewed discrete discharge distribution of 10% was used, which means that on the northern bank, 10% extra discharge is prescribed and the most southern boundary ads 10% less discharge compared to the uniform discharge. An example for a fictitious discharge of 2800 m 3/s is depicted in Figure 4-2.

225 220 215 210 205 Q Discrete 200 Q 195 Q Uniform 190

Discharge (m^3/s) Discharge 185 180 175 0 20 40 60 80 100 120 140 160 180 200 220 240 260 Position along the river width (m)

Figure 4-2: Example Discrete upstream boundary condition

In order to determine the upstream boundary, the daily average discharges of the last twenty years are taken into account. The discharge of the river Waal is not constant throughout the whole year, so to simulate the river morphology correctly, a varying discharge should be used. The discharge during flood period is significantly different compared to the low water period. 3 When the discharge exceeds the bank full discharge (Q Lobith = 4000 m /s or Q Waal = 2700 m3/s), the discharge is characterized as a flood. The schematisation of the discharge is depicted in Appendix 10. It is very time consuming to use the actual discharge measurements as input variable, therefore a representative discharge discretisation determined.

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During the model runs, it turned out that the newest version of Delft3D SED is not able to deal with abrupt varying discharges and the model became instable. In order to deal with this problem, the difference between two consecutive steps should be smaller and the morphological factor should be reduced to one, which increases the computation time enormously Therefore, the model runs are executed with constant discharges. A constant discharge of 3500 m 3/s is a representative discharge for the flood period, because the amount of transported sediment is the same as in the schematised discharge and the 1D bed celerity turns out to be 1 km/yr, which is a general accepted bed celerity.

Rijkswaterstaat’s Oost Nederland has determined that the pointbar grows mainly during the flood period. Therefore, adaptations to the discharge are mainly focussed during the high water period. To determine the influence of the lateral abstractions of only water and secondly of both water and sediment, first a reference situation is created in which no water is abstracted. This contains a model run is executed with a discharge of 3500 m 3/s for a period, which corresponds to the flood period of 42 days. The averaged flood period of the last twenty years is about 39 days, but the last trend shows that the average flood becomes longer.

In the model runs, there is a lateral discharge abstraction simulated of both 250 m 3/s and 500 m3/s. To indicate the influence of the abstraction the bed level should be compared with the bed levels from the reference computation. This is done for the water and sediment abstraction as well.

A number of runs were a executed with a discharge of 4500 m 3/s, which is representative for a significant large flood peak.

4.3. Calibration The model was calibrated by using a constant discharge of 1600 m 3/s. At this discharge, the averaged amount of sediment through the river Waal of 300.000 m 3/yr is reproduced. This amount of sediment is deduced from the previous project of Klaassen and Sloff [2000]. Besides, this number is verified with the averaged daily discharge from the last 15 years. It turns out that the averaged amount of sediment transport coincides with a morphological bed wave of one kilometre per year, which is generally accepted as the characteristic 1-D bed celerity. When the resultant bed level does not differ very much from the initial situation after a sufficient computational time, the conclusion should be that the morphological processes in the model are stable and well reproduced.

During the calibration phase, the following adaptations were applied: • The skewness of 10% in the upstream discharge boundary was determined • The overall sediment transport coefficient was set to 0.40. • The coefficients for the influence of the bed slope were set to Ashld = 0.7 and Bshld= 0.5. • The coefficient of the secondary flow intensity was set to Espir = 1.0.

One of the most important modifications was applied at the computational grid in the inner bend of the river, to approach the initial bed level at the end of the computation. It turned out that the used land boundary(on which the grid was based) was out dated. A more up-to-date land boundary resulted in an expansion of the local flow width at the river marks (km and km). The flow with enlargements are caused by the local present groynes, which are too low and too short, this confirmed in Sieben and Huntelaar [2000]. This document describes the presence of a training wall in front of the Colenbrandersbos and downstream of this rigid

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structure point, the flow lines diverges. (The Colenbrandersbos is located just upstream of the most first flow with enlargement from the Pannerdensche Kop. The adapted computational grid is depicted in the following figures:

Figure 4-3: Final overall computational grid

Figure 4-4: Computational grid, bend Hulhuizen

The calibration made clear that the bend at Erlecom was not schematised properly. In reality, the morphological activity is limited due to the application of bendway weirs. With the installation of bendway Weirs, the secondary currents are redirected. Sediment is deposited between the bendway Weirs beneath the passing tows rather than building up as a point bar on the inside of the bend, which is favourable to the navigatiability. The model the influence of these weirs, morphological activity is limited artificially by reducing the thickness of the active sand layer. This model trick is applied in the outer part of the bend at Hulhuizen as well, to simulate the interaction with the surroundings. If this trick was not applied, any value for the bed level in the outer part of the bend is theoretically possible and ignoring the influence of groyne tips, which a fixed “bed” level for example.

64 WL | Delft Hydraulics, RIZA, ON, TU Delft Side channels to improve navigability on the river Waal November 2005

4.4. Sensitivity analysis

4.4.1. Introduction In reality, the input parameters do not have a constant value. In order to know how the results of the computational model depend to various values of the input parameters a sensitivity analysis has been executed. A number of parameters are adjusted during the analysis, but in the Appendix 10 only a small selection has been depicted. The following parameters are will be discussed: • Mean grain size diameter • Coefficient for the bed slopes (Ashld, Bshld) • Coefficient for the secondary flow intensity • Skewness of the discharge distribution at the upstream boundary.

The limited morphological activity was in the end phase of the sensitivity analysis; therefore, most of the runs did not contain this feature. Due to a lack of time, it was not possible to repeat all the runs.

To interpret the figures in Appendix 10 the following should be realised: The figures show the bed level of the two outer grid lines in longitudinal direction (n =2 and n=15) and colour of the lines represent the following:

The blue and red lines belong to the most northern grid line (n=2) and represent the bed level of the initial situation (T=0s) and final situation (T=750 days), respectively.

The green and orange lines belong to the most southern grid line (n=15) and represent the bed level of the initial situation (T=0s) and final situation (T=750 days), respectively.

4.4.2. Conclusion In this section, the most important conclusions are deduced from the figures of the sensitivity analysis, which are depicted in Appendix 10. The sensitivity analysis is executed with constant discharges. In the calibration phase, the morphological time factor was varied from one to one hundred. There was no significant difference noticeable. Therefore, the computations in the sensitivity analysis were executed for 7.5 days with a morphological factor of 100, simulating 750 days.

The parameters, which influence the results the most are: • The discharge distribution of the upstream boundary • The downstream boundary condition • The mean grain size diameter • The coefficient for the secondary flow intensity • The roughness coefficient

In the sensitivity analysis, the downstream boundary condition has been changed, but the results are not depicted in Appendix 10. The length of the computational model is about 15 km and the relaxation length of the river Waal is a multiple of it. It would have been too trivial to take the figures into account. The length about which the depth samples were provided was insufficient to cover the whole computational grid. Therefore, the bed level was interpolated over the whole grid. To determine the downstream water level, the equilibrium water depth is added to the downstream bed level. The resulting water (boundary) levels were equal to the water levels, resulting from the Sobek Rijntakken Model. This indicates that the bed level interpolation was correctly applied and the error in the downstream boundary condition is minimal. If there was an error in the downstream boundary, an option would have

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been to extend the computational grid. This would have increased the computational time tremendously.

As stated before the river Waal does have some characteristics, which have proven to be useful in previous project and are still applicable in numerical project like this.

Eventually the model was run with all the adaptations to the grid and active sand layer etc, which results into the following Figure:

Figure 4-5: Bed level N=2,15 T 750 days Engelund-Hansen, Q = 1600 m 3/s.

4.5. Side channel modelling There are a number of options to model a side channel in Delft3D. 1. Extend the numerical model and take the winter bed into account 2. Simulate a lateral abstraction of only water 3. Simulate a lateral abstraction of both water and sediment.

The first option is the most does have the most similarity with reality. By the extension of the model, the numerical grid should also take into account the winter bed. Due to this extension, the bed level of the flood plain is needed as well. By enlarging the model, the measure of uncertainty increases. Furthermore, the computational time increases tremendously. The realisation of a model like this is very labour intensive. Due to a lack of time, it was not possible to create a model like this.

In this project both the second and third option are used. The lateral abstraction is model by prescribing a sideways discharge withdrawal (as a function of time). For the second option the same model was used, which is prescribed in previous sections.

When the third option is used, Delft3D does not only withdraw water but also the equilibrium amount of discharge for this withdrawn amount of discharge. For these calculations, an

66 WL | Delft Hydraulics, RIZA, ON, TU Delft Side channels to improve navigability on the river Waal November 2005

adapted computational grid was used, because both the discharge as sediment are perpendicular abstracted. In reality, the abstraction is more smoothly than perpendicular. To model this, the both the inlet as outlet are moved into the floodplain, see Figure 4-6:

Figure 4-6: Adapted morphological grid Side channel

4.6. Side channel alignment There are a number of side channel simulated, which are depicted in the following figures. An important parameter for the abstraction ability is the ration between the length of the side channel and the abstraction length (river length in the river axis from inlet to outlet)

Side channel 1 The inlet of this side channel is situated 600 m downstream of the upstream boundary and is modelled as two point abstractions. The distance between them is about 50 m. The outlet is schematised as two outlet points as well. The mutual distance is comparable with the inlet.

Figure 4-7: Side channel 1 The length characteristics are: • The length of the side channel is about 2.6 km. • The abstraction length is 3.31 km. • The ratio between them is: 0.79

Side channel 2 The idea behind this option is to blow away the point bar, by situating the outlet in the inner bend.

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Figure 4-8: Side channel 2 The length characteristics are: • The length of the side channel is about 2.1 km. • The abstraction length is 2.21 km. • The ratio between them is: 0.95

Side channel 3 To see what happens when the abstraction length is increased, this third side channel is created. Both lengths are increased, but the ratio between them is smaller, which indicates a positive abstraction characteristic of the side channel.

Figure 4-9: Side channel 3 The length characteristics are: • The length of the side channel is about 4.4 km. • The abstraction length is 5.8 km. • The ratio between them is therefore: 0.76

68 WL | Delft Hydraulics, RIZA, ON, TU Delft Side channels to improve navigability on the river Waal November 2005

Side channel 4 This last option is actually a fictitious option, because in reality a side channel alignment like this one is not applicable in the present infrastructure. Therefore it is actually a principle alternative.

Figure 4-10: Side channel 4

The length characteristics are: • The length of the side channel is about 2.8 km. • The abstraction length is 2 km. • The ratio between them is therefore: 1.4

The ratio indicates that the water abstraction ability is less positive compared with the other side channels.

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5. Results

5.1. Introduction In this chapter, the results of the numerical Delft3D model are presented and discussed. First, the reference situations are determined. In the third and fourth section the results of the discharge withdrawal are shown. The computations have been executed with two different amounts of discharge (250 and 500 m 3/s). Furthermore, the results of the lateral abstraction of both water and sediment are shown as well. Due to a lack of time, these computations have only been executed for a discharge of 500 m 3/s.

A number of computations was repeated with a constant discharge of 4500 m 3/s. The results of these computations are presented in the sixth section.

The seventh section describes the morphological analysis, which is based on the results of the previous sections and the expected one-dimensional morphological reaction.

The chapter ends with a discussion about the navigable width and gives a rough indication of the dimensions of the simulated side channel, respectively.

The tables in this chapter show the maximum pointbar heights.

5.2. Reference situation The reference situations have been determined with discharges of 3500 m 3/s and 4500 m 3/s, for a period of 42 days. The results for the bed level, the cumulative change of bed level and the depth-averaged velocity at this date are depicted in Appendix 11.

The following observations are derived for both discharges: • Both computations show an increase of bed level at the flow width enlargements. The bed level changes the most at a discharge of 4500 m 3/s. The pointbar heights of both locations are depicted in Figure 11-1 and Figure 11-4 in Appendix 11 • There are two points of particular interest, the two extreme pointbar heights in the inner bend. • Both computations show an increase of bed level directly downstream of the upstream boundary, which was expected, due to the small curvature. • The cross-sectional depth-averaged maximum velocities are crossing the river as they are supposed to do, which indicates that the model simulate a net momentum transfer to the outer bend.

Table 5-1: Reference pointbar heights for Q = 3500 m 3/s and Q= 4500 m 3/s

Pointbar height Q = 3500 m3/s Q = 4500 m3/s Unit

Location 1 7.75 8.40 m + NAP Location 2 7.95 8.40 m + NAP

In order to make the influence of the lateral discharge (and sediment) withdrawal explicit, the reference bed levels will be subtracted from the resulting bed levels.

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5.3. Discharge withdrawal at a constant discharge of 3500 m 3/s

5.3.1. Results for discharge withdrawal of 500 m 3/s This section shows the results of the lateral withdrawal of 250 and 500 m3/s. First, the bed level differences for the four side channel alignments, with a withdrawn discharge of 500 m 3/s, are depicted. To compare the results of the different side channel alignments accurately the scale limits are kept constant in this main document. The figures with the adapted scales are shown in Appendix 12.

Discharge withdrawal of 500 m 3/s. • The red areas indicate bed levels that are higher than in the reference situation (sedimentation spots). • The blue areas indicate erosion spots. • The white areas indicate no significant bed level change.

(bed level Channel1) − (bed level ref.) (m) 3 5 x 10 12−Apr−2003 00:00:00 4.33 2.6

2.2 4.325 1.8

1.4 4.32 1 → 4.315 0.6 0.2

4.31 −0.2

y coordinate (m) −0.6 4.305 −1

−1.4 4.3 −1.8

4.295 −2.2 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.6 −3 Figure 5-1: Bed level difference between Channel 1 and Reference situation [m]

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(bed level Channel 2) − (bed level ref.) (m) 3 5 x 10 12−Apr−2003 00:00:00 4.33 2.6

2.2 4.325 1.8

1.4 4.32 1 → 4.315 0.6 0.2

4.31 −0.2

y coordinate (m) −0.6 4.305 −1

−1.4 4.3 −1.8

4.295 −2.2 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.6 −3 Figure 5-2: Bed level difference between Channel 2 and Reference situation [m]

(bed level Channel3) − (bed level ref.) (m) 3 5 x 10 12−Apr−2003 00:00:00 4.33 2.6

2.2 4.325 1.8

1.4 4.32 1 → 4.315 0.6 0.2

4.31 −0.2

y coordinate (m) −0.6 4.305 −1

−1.4 4.3 −1.8

4.295 −2.2 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.6 −3 Figure 5-3: Bed level difference between Channel 3 and Reference situation [m]

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(bed level Channel 4) − (bed level ref.) (m) 3 5 x 10 12−Apr−2003 00:00:00 4.33 2.6

2.2 4.325 1.8

1.4 4.32 1 → 4.315 0.6 0.2

4.31 −0.2

y coordinate (m) −0.6 4.305 −1

−1.4 4.3 −1.8

4.295 −2.2 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.6 −3 Figure 5-4: Bed level difference between Channel 4 and Reference situation [m]

The maximum pointbar heights are compared in Table 5-2: Table 5-2: Pointbar height comparison

Pointbar height Reference Channel 1 Channel 2 Channel 3 Channel 4 Unit

Location 1 7.75 7.24 7.20 7.24 7.20 m + NAP Location 2 7.95 7.68 7.60 7.65 7.60 m + NAP

The following observations are derived from the figures and table above: • Sedimentation occurs downstream of the withdrawal location. • Erosion occurs downstream of the confluence of the side channel and the main river. • The lateral withdrawal of 500 m 3/s causes a decrease of pointbar height, of about 50 cm for the first location and about 20 – 30 cm for the second location. • Between the offtake and confluence, no significant morphological activity is noticeable, except for the pointbar locations. • The results of channel 1 and channel 3 are very much alike. Despite the difference in side channel length, no significant bed level difference is noticeable. This indicates that the abstraction length is small compared to the length of backwater curve (h/3*i) of the river, which is more than 25 km. The abstraction length varies from 2 – 6 km. This means, the water level between the confluence and offtake does not differ very much from the reference situation. This is confirmed by Figure 5-5, only at the confluence and offtake the water level differs, but this forced by the withdrawal and confluence themselves.

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(water depth Channel 3) − (water depth ref.) (m) 3 5 x 10 12−Apr−2003 00:00:00 4.33 2.6

2.2 4.325 1.8

1.4 4.32 1 → 4.315 0.6 0.2

4.31 −0.2

y coordinate (m) −0.6 4.305 −1

−1.4 4.3 −1.8

4.295 −2.2 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.6 −3 Figure 5-5: Water level difference between Channel 3 and reference situation

5.3.2. Results for discharge withdrawal of 250 m 3/s At a constant discharge of 3500 m 3/s, 250 m 3/s of water is abstracted from the main river. This abstraction is simulated for the first three channels. The fourth channel was actually a fictitious channel, which cannot be implemented, due to a lack of space in the outer bend. Despite the absence of the computation, an estimation is made for the pointbar heights of channel 4 by interpolating the heights between the reference situation and the withdrawal of 500 m 3/s. The figures, which show the results of this computation, are compared with the reference situation and depicted in appendix 11. The pointbar heights are summarized in Table 5-3.

Table 5-3: Pointbar height at a withdrawal of 250 m3/s

Pointbar height Reference Channel 1 Channel 2 Channel 3 Channel 4 Unit

Location 1 7.75 7.50 7.50 7.45 7.50 m + NAP Location 2 7.95 7.80 8.10 7.80 7.70 m + NAP

Some remarks about the computations: The figures in Appendix 12 make clear that the bed level differences between the several side channel options are mainly concentrated at the offtake and confluence areas. Figure 5-6 zooms in at the bend and shows the cumulative bed level change in the bend itself at a small vertical scale. There are a number of spots in the outer bend where sedimentation is observed (red spots), while the erosion spots are concentrated on the pointbars and in the inner bend (blue spots).

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0.75

0.65

(bed level Channel 3) − (bed level ref.) (m) 0.55 5 x 10 10−Apr−2003 00:00:00 4.33 0.45

4.328 0.35 0.25

→ 4.326 0.15 4.324 0.05 4.322 −0.05

y coordinate (m) 4.32 −0.15

4.318 −0.25

4.316 −0.35 1.96 1.965 1.97 1.975 1.98 1.985 1.99 5 x coordinate (m) → x 10 −0.45 −0.55

−0.65 −0.75 Figure 5-6: Bed level change in the bend it self of side channel 3 (blown-up)

The results of the previous section and this one, indicate that a discharge withdrawal tends to reduce the pointbar heights, but introduces more morphological activity at the offtake and confluence areas. The morphological activity of the first and third channel is similar and differs only due to the moved offtake and confluence points.

Side channel two has a totally different morphological influence on the pointbar, due to the position of the confluence near the bars. This is shown in the Figures 12-7 and 12-8 of Appendix 12.

5.3.3. Results for discharge and sediment withdrawal of 500 m 3/s As stated in the previous chapter, a special morphological grid is needed to simulate the offtake and confluence more realistically. In order to reduce the number of adjustments to the grids, it is chosen to simulate only side channel one.

The cumulative erosion and sedimentation pattern of side channel one is depicted in Figure 5-7. In Appendix 12 (Figure 12-9), the same figure is shown with a reduced vertical scale.

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(bed level Channel 1) − (bed level ref.) (m) 5.028 5 x 10 12−Apr−2003 00:00:00 4.33 4.358

3.687 4.325 3.017

2.346 4.32 1.676 → 4.315 1.006 0.3352

4.31 −0.3352

y coordinate (m) −1.006 4.305 −1.676

−2.346 4.3 −3.017

4.295 −3.687 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −4.358 −5.028 Figure 5-7: Bed level difference due to the abstraction of water and sediment.

Table 5-4 shows the pointbar heights due to the abstraction of 500 m 3/s only and the abstraction of both water and sediment. This means that an equilibrium amount of sediment at a discharge of 500 m 3/s is withdrawn.

Table 5-4: Pointbar heights due to water and sediment abstraction at Q =3500 m 3/s

Pointbar height Reference Water Water+ sediment Unit

Location 1 7.95 7.24 7.12 m + NAP Location 2 7.95 7.68 7.70 m + NAP

This table shows that the withdrawing of sediment causes an extra reduction of the first pointbar height of about 10 cm. The effect on the second pointbar is hardly noticeable. Figure 5-8 shows the average bed level of a line, which is located about 200 m from the northern bank. This line forms more or less the borderline between the navigation channel and the pointbar. It shows the bed level change as a function of time. The three lines indicate the pointbar heights for the three different situations:

• Reference situation, constant discharge • Water (500 m 3/s) withdrawal • Water (500 m 3/s) and sediment withdrawal

The figure shows that the pointbar growth is reduced by the withdrawal of water and is even more reduced when both water and sediment are abstracted. Another interesting detail is the different equilibrium pointbar height. The reference line shows an equilibrium height at 6.80 m, whereas the other lines have their equilibrium at 6.34 m. This difference is ascribed to the decreased amount of discharge.

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Another interesting detail is the pointbar development after 300 days. The bed level increases due to the passing of the 1D bed level wave. In reality, the bed wave will not reach the pointbar locations within one year.

8,5 8,25 8 7,75 7,5 Reference 7,25 Water 7 Water&Sed 6,75 6,5

Bed level Bed [m] development 6,25 6 0 100 200 300 400 500 600 700 800 Time [days]

Figure 5-8: Bed development borderline as a function of time for Q = 3500 m 3/s

5.4. Discharge withdrawal at a constant discharge of Q = 4500 m 3/s

5.4.1. Results for discharge withdrawal of 250 m 3/s The computations were already made with a constant discharge of about 3500 m 3/s. This discharge is supposed to be comparable to a flood period of 42 days. A number of computations have been repeated with a discharge of 4500 m 3/s, to indicate how the bed level reacts to a strong forcing. Again, the pointbar heights are summarized in the following table. The bed levels are compared to the reference situation at T = 42 days. The bed level figures are depicted in Appendix 13.

Table 5-5: Maximum pointbar heights due to water (500 m 3/s) abstraction at after 42 days

Pointbar height Reference Channel 1 Channel 2 Channel 3 Unit

Location 1 8.40 8.40 8.40 8.40 m + NAP Location 2 8.40 8.6 9.10 8.60 m + NAP

The table above shows that a discharge withdrawal of 250 m 3/s is not sufficient to decrease the pointbar heights. This conclusion is supported by the figures of Appendix 13, which make clear that sedimentation is expected, instead of erosion due to the abstraction of 250 m 3/s. The sedimentation pattern is noticeable over a significant part of the bend.

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5.4.2. Results for discharge withdrawal of 500 m 3/s For a constant discharge of 4500 m 3/s and a discharge withdrawal 500 m 3/s the bed level differences have been determined for the channels one, three and four. Unfortunately, the computation of channel 2 crashed and could not be repeated.

Table 5-6: Maximum pointbar heights due to water (500 m 3/s) abstraction at after 42 days

Pointbar height Reference Channel 1 Channel 3 Channel 4 Unit

Location 1 8.40 7.90 7.95 7.20 m + NAP Location 2 8.40 8.20 8.20 7.60 m + NAP

This table shows again that the results of channel one and three are very much alike. Despite the absence of the results of channel two, the conclusion of this section should be that a discharge withdrawal of 500 m 3/s is needed to decrease the pointbar height with half a metre.

5.4.3. Results for discharge and sediment withdrawal of 500 m 3/s One computation have been made to indicate how the bed level is affected by withdrawing 500 m 3/s and the corresponding equilibrium amount of sediment.

(bed level side channel 1) − (bed level side 4500 ref.) (m) 4.5 5 x 10 12−Apr−2003 00:00:00 4.33 3.9

3.3 4.325 2.7

2.1 4.32 1.5 → 4.315 0.9 0.3

4.31 −0.3

y coordinate (m) −0.9 4.305 −1.5

−2.1 4.3 −2.7

4.295 −3.3 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −3.9 −4.5 Figure 5-9: Bed level change between channel 1 and reference situation at T= 42 days

The following table shows that the first pointbar is more sensitive for the abstraction than the second one. When not only water is abstracted, but sediment as well, the bed level of the first bar is reduced with ten centimetres extra.

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Table 5-7: Maximum pointbar heights due to water and sediment abstraction at Q =4500 m 3/s

Pointbar height Reference Water Water & sediment Unit

Location 1 8.40 7.90 7.80 m + NAP Location 2 8.40 8.20 8.30 m + NAP

Table 5-7 shows the maximum pointbar height, whereas the development of the borderline between the navigation channel and pointbar is depicted as a function of time in Figure 5-10. The lines of Figure 5-10 are comparable with the ones of Figure 5-8, but due to the higher discharge, the equilibrium eights are different and the lines are steeper, which indicates that the morphological response of the bed is faster. Again, the 1D bed level shock wave is observed here as well.

9 8,75 8,5 8,25 8 7,75 Reference 7,5 Water 7,25 Water&Sed 7 6,75 6,5 Bed levelBed development [m] 6,25 6 0 100 200 300 400 500 600 700 800 Time [days]

Figure 5-10: Bed development borderline as a function of time for Q = 4500 m 3/s

The conclusion of this section should be that during the first 200 days, the pointbar formation for the higher discharge (Q = 4500 m 3/s) is less affected by a side channel than for the lower discharge (Q = 3500 m 3/s). To affect the pointbar height significantly, more discharge should be withdrawn. Furthermore, the morphological time scale at Q = 4500 m 3/ is significantly smaller than at the Q = 3500 m 3/s. This is observed from Figure 5-10.

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5.5. Results for flood computations In the previous sections, the results were described for computations with constant discharges. In reality, the discharge varies continuously, therefore computations were made with a varying discharge as well. After the computations have been executed, a comparison was made between the results of the flood computation and the non-varying discharge of 3500 m3/s. First, the comparison is made between the reference situation (no abstraction at all) and the situation that both water and sediment are abstracted, see Figure 5-11.

(bed level HW Channel 1 − (bed level HW ref.) (m) 1.5 5 x 10 25−May−2003 12:00:00 4.33 1.3 1.1

4.325 0.9 0.7

4.32 0.5 → 0.3

4.315 0.1

−0.1

y coordinate (m) 4.31 −0.3

−0.5

4.305 −0.7

−0.9 4.3 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 −1.1 x coordinate (m) → 5 x 10 −1.3 −1.5 Figure 5-11: Bed level difference at the end of flood period

In the bend itself, the bed levels do not differ very much, but the figure shows that only the pointbar at the first location is reduced with 20 cm, see also Appendix 14, Figure 14-2.

In Appendix 14, Figure 14-3 shows the difference between the results of the flood computation and the non-varying discharge of 3500 m3/s. indicates that the difference between the computations with the varying and non-varying discharge is quite significant. The two pointbars are 60 cm and 75 cm higher in case of the varying discharge, respectively. In order to make the pointbar formation explicit, Figure 5-12 and Figure 5-13 show how the borderline changes and the bed level of pointbar location 1, during flood period. Figure 5-12 shows that the borderline does not change very much, due to the averaging process along the grid line, but locally, the bed level changes significantly. The figure might give the wrong impression of the morphological activity during flood periods. First, the lines in Figure 5-12 go down (Q = 1170 m 3/s) and eventually, when the discharge increases, the average borderline level increases. Be aware of the relatively fine vertical scale!

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6,25

6,2

6,15 Reference Water&sed 6,1

6,05 Bed level Bed development [m]

6 0 20 40 60 80 100 Time [days]

Figure 5-12: Bed development borderline as a function of time for flood period

7,5

7,25

7

6,75 Reference 6,5 Water&Sed

6,25

Pointbar location 1 [m] 6

5,75 0 20 40 60 80 100 Time [days]

Figure 5-13: Pointbar height as a function of time [m]

Figure 5-13 shows the averaged bed level change of the first pointbar location. It indicates that the pointbar grows mainly during the highest discharges (as observed from the depth measurements from the Ministry of Public Works and Water Management). The horizontal parts in the figure correspond to the low-water period (Q = 1170 m 3/s).

When 500 m 3/s of water and the averaged amount of sediment transport are withdrawn, the pointbar will grow more slowly and at the end of the flood period, its height will be smaller as well. Furthermore, the pointbar height increases more during rising water than it reduces during falling water. This is indicated by the steepness difference between the rising period and falling period.

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5.6. Morphological analysis In the previous section, the question arose whether the bed level in the inner part of the bend would decrease, despite the expected one-dimensional sedimentation pattern. Actually, the question was, which morphological effect is dominant in the bend of Hulhuizen?

The figures and tables in the previous section of this chapter and the accompanying figures in the Appendices show the results of both 1-D and 2-D morphological reactions together. Now the results are known it is interesting, whether the 1-D and 2-D morphological effects can be derived from them.

5.6.1. 1-D morphological phenomena Reference is made to section 2.3.4, which describes the expected 1-D morphological effects. Due to the lateral discharge withdrawal the following 1-D phenomena should be noticed: 1. Initial erosion growing upstream from the offtake 2. Initial sedimentation growing upstream from the confluence 3. Sedimentation shock wave propagating downstream from the offtake 4. Erosion expansion wave propagating downstream from the confluence

Due to a lack of time, it is not possible to identify all the phenomena in all the computations. Therefore, the choice is made to identify them for the computation with a constant discharge of 3500 m 3/s and a discharge withdrawal of 500 m 3/s according to the alignment of the first side channel. The results of the computation are depicted in Figure 5-14. It should be stated that the scale limits are adapted to identify the morphological phenomena easier.

It is hard to see the initial erosion wave propagation upstream from the offtake. It looks like there is some sedimentation propagation towards the upstream, but it is hard to tell whether this is caused by the application of the side channel or the local position in the inner part of the first bend. It is reasonable to ascribe the absence of the initial erosion wave due to the small distance to the upstream boundary. In Figure 15-1 of Appendix 15, the offtake location is blown-up, to provided a better look at this location. The initial sedimentation wave, which should propagate upstream from the confluence, is difficult to identify as well. It should be taken into account that the confluence is directly downstream of the second flow width enlargement. When the flow has passed the widening, it accelerates due to the local flow constriction, therefore it is difficult to ascribe the local erosion to the application of the side channel or this constriction. The sedimentation shock wave from the offtake propagating downstream is clearly visible in Figure 5-14, just like the expansion erosion wave downstream of the confluence. These phenomena can totally be ascribed to the application of the side channel. Figure 15-2 of Appendix 15 shows the sedimentation spot directly downstream of the confluence, which is caused by the separated flow. Reference is made to section 2.3.2 and Figure 2-7, where the phenomena are explained.

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0.75

0.65 (bed level Channel 1) − (bed level ref) (m) 5 0.55 x 10 12−Apr−2003 00:00:00 4.33 0.45

0.35

4.325 0.25 → 0.15

4.32 0.05

−0.05 y coordinate (m) 4.315 −0.15 −0.25

−0.35 4.31 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 −0.45 5 x coordinate (m) → x 10 −0.55

−0.65 −0.75 Figure 5-14: Bed level difference between reference situation and side channel 1.

5.6.2. 2-D morphological phenomenon The two-dimensional morphological effect is the tilting of the transverse bed slope. Considering Figure 5-14, it is concluded that the inner part of the bend does not change very much, but the outer bed tends to be filled up. This indicates that the bed level difference between inner and outer bed decreases, which means the cross-slope decreases. This phenomenon is observed halfway through the bend at river mark 869.5 km. At the two flow width enlargements, almost the same phenomenon is observed. Due to the abstraction, the depth averaged velocity is reduced, which causes a decrease of secondary flow and lateral sediment transport. Appendix 15 shows the depth averaged flow velocities for both the reference situation and the side channel application at T = 42 days.

5.7. Navigable width This project tries to indicate how the pointbar formation in the inner bend affects the navigable width. An economic and navigation optimization study by Rijkswaterstaat [1993] resulted in the future norm for a minimum navigable width for the river Waal of 170 m at a level of OLR - 2.80 m. The OLR is a prescribed water level, which is based on a discharge of 818 m 3/s through the river Waal. By comparing the bed levels of the Delft3D computations with the bed level of the OLR norm, it is shown whether the bend of Hulhuizen matches this norm. The OLR norm is gathered by subtracting 2.80 metres from the prescribed (OLR) water level.

The first subsection describes the situation after a flood period and the second subsection describes the situation after the consecutive low water period.

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5.7.1. Navigable width after flood

The following two figures indicate where the bend of Hulhuizen exceeds the OLR bed level. The red colour indicates where the norm is exceeded. The black line indicates the river axis.

6 5.333 4.667 4 morphologic grid 5 x 10 3.333 4.33 2.667 2 → 4.325 1.333 0.6667 0 4.32 −0.6667 y coordinate (m) −1.333 −2 4.315 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 −2.667 5 x coordinate (m) → x 10 −3.333 −4 −4.667 −5.333 −6 Figure 5-15: Initial situation

5

4.375

3.75

morphologic grid 3.125 5 x 10 4.33 2.5 1.875

→ 1.25 4.325 0.625

0 4.32 −0.625 y coordinate (m) −1.25

4.315 −1.875 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.5 −3.125

−3.75

−4.375 −5 Figure 5-16: Result after flood period

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The average bend width is about 260 m. Figure 5-15 shows that the initial condition exceeds the norm already (navigable width 140 m). However, the situation gets worse during a flood period, the computations show that the navigable width reduces to 115 m. The computation with a varying discharge reduces the navigable width the most. The navigable widths in the other computations vary between 115 and 130 m. This is shown in the figures below, where the most critical cross-sections of the computations: Q = 3500 m 3/s, Q = 4500 m 3/s and the flood computation (varying discharge) are shown. In all the computations the critical cross-section (least navigable width) occurred at the same location in the first flow width enlargement, see Figure 5-17

4.241

3.711

morphologic grid 3.181 5 x 10 4.33 2.651 2.121 4.328 1.59

→ 4.326 1.06

4.324 0.5302

4.322 0 −0.5302

y coordinate (m) 4.32 −1.06 4.318 −1.59 4.316 1.96 1.965 1.97 1.975 1.98 1.985 1.99 −2.121 5 x coordinate (m) → x 10 −2.651

−3.181

−3.711 −4.241 Figure 5-17: Location critical cross-section

The colours in the three figures below represent the various computations.

Green : Initial bed level (T = 0 days) Black: Reference bed level (T = 42 days) Red: Bed level due to water (500 m 3/s) abstraction only (T = 42 days) Blue : Bed level due to water (500 m 3/s) and sediment abstraction (T = 42 days)

A positive elevation means that the norm is exceeded (inner bend) and a negative elevation indicates that the resultant bed level does not conflict with the norm (outer bend).

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12−Apr−2003 00:00:00 4

3

2

1 →

0 elevation (m) −1

−2

−3

−4 0 50 100 150 200 250 300 distance along cross−section m=57 (m) → Figure 5-18: Critical cross-section Q = 3500 m 3/s

12−Apr−2003 00:00:00 5

4

3

2

1 →

0

elevation (m) −1

−2

−3

−4

−5 0 50 100 150 200 250 300 distance along cross−section m=57 (m) → Figure 5-19: Critical cross-section Q = 4500 m 3/s

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24−May−2003 00:00:00 4

3

2

1 → 0

−1 elevation (m)

−2

−3

−4

−5 0 50 100 150 200 250 300 distance along cross−section m=58 (m) → Figure 5-20: Cross-section HW computation

The distance of a horizontal line at an elevation of zero metre, to the crossing with the coloured lines, indicates the navigable width.

The navigable width increase with seven metres (from 130 m to 137 m) at a river discharge of 3500 m 3/s due to the application of a side channel. The other computations do not show a significant increase of navigable width, when a side channel is applied.

Figure 5-19 and Figure 5-20 make clear that it is worthwhile to apply a side channel to decrease the pointbar height and therefore to decrease the amount of dredging material. However, a discharge withdrawal of 500 m 3/s on a total river discharge of 3500 m 3/s and 4500 m3/s is not very effective to increase the navigable width.

5.7.2. Navigable width after low water period A number of computations have been made to indicate the change of navigable width during a low-water period. The bed level resulting from the flood period was used in a following computation. This computation was executed with a constant discharge of 1170 m 3/s for eight months (averaged low water discharge from the last 20 years), assuming no dredging activities have been executed, so all the sediment remains in the system.

The 1-D bed shock wave (from the flood period) propagates further downstream during the low-water season, but it will not reach the initial critical cross-section. At the end of the low- water season, the computations show that the bed level decreases over almost the entire critical cross-section, which causes an increase of the navigable width of 23 metre, see Figure 5-21 (The same colours are used as in the previous section).

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04−Nov−2003 00:00:00 4

3

2

1 →

0 elevation (m) −1

−2

−3

−4 0 50 100 150 200 250 300 distance along cross−section m=57 (m) → Figure 5-21: (Bed level - OLR) development in critical cross-section after low water season.

Furthermore, Figure 5-22 shows that the critical cross-section has moved to the spot, which the 1-D bed shock wave was able to reach. The bed level change due to the passing shock wave is depicted in Figure 5-23. The navigable width decreases here from 148 m to 108 m.

For completeness, Appendix 16 shows the actual bed level in the river Waal at the end of the flood period and at the end of the low water period.

The results of this section are derived from the flood period computation with a constant discharge of Q = 4500 m3/s. The bed level of this computation was used as the initial bed level for the low water computation. Results from the other low water computations show a similar morphological behaviour; • Downstream propagation of the 1-D bed shock wave • Erosion at the critical cross-section (from flood period) • New critical cross-section in the upstream part of the bend, caused by the 1-D bed shock wave.

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morphologic grid 4.6 5 x 10 4.025 4.33 3.45

2.875 4.325 2.3

1.725 4.32 → 1.15

0.575 4.315 0

−0.575 y coordinate (m) 4.31 −1.15

−1.725 4.305 −2.3

−2.875 4.3 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 −3.45 x coordinate (m) → 5 x 10 −4.025 −4.6 Figure 5-22: Overview navigable width after low water period

04−Nov−2003 00:00:00 3

2

1

0 →

−1 elevation (m) −2

−3

−4

−5 0 50 100 150 200 250 distance along cross−section m=40 (m) → Figure 5-23: (Bed level - OLR) in new critical cross-section development after low water season.

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5.8. Side channel dimensions In order to get an impression of the dimensions of a side channel, which retracts 500 m 3/s from the river Waal, a rough estimation for the dimensions is made for side channel 1.

Figure 5-24: Side channel 1 alignment The length characteristics are: • The length of the side channel is about 2.6 km. • The abstraction length is 3.31 km. • The ratio between them is: 0.79

Due to the length ratio of 0.79, the side channel slope (I) is about 1.39*10 -4.

The side channel width (B) is assumed to be 100 m (this is a plausible dimension, considering the discharge).

WL | Delft Hydraulic uses a WAQUA model, in which a space varying hydraulic roughness is used for the Millingerwaard. By interpolation of the roughness from this model, a Chézy value of 40 m 1/2 /s was derived.

By application of the empirical relations of section 2.3.4 for the hydraulic computation, the water depth becomes:

2 3 2   Q  3 500  h 4.83 =1  =1  = m 5.30 BC* I 2  100*40* (1.39*10−4 ) 2  ( ) 

The Millingerwaard does not have a smoothed surface. It varies between 11.2 and 12.5 m above NAP reference level. At a river discharge of 5000 m 3/s, the water level is about 14 m above NAP reference level. This indicates that some excavation work is needed.

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6. Conclusions This report describes the morphological processes in river bends. Of particular interest is the pointbar formation the inner part of the bend in the river Waal near Hulhuizen, The Netherlands.

Every year, during flood period, the bed level in the inner bend increases rapidly and causes width restrictions to navigation in the subsequent low water period. Several studies have been executed to reduce this pointbar formation. Side channels are applied nowadays to increase the river’s flood conveyance capacity and the biodiversity in the floodplains, but never with the intention to reduce the pointbar formation. This thesis is focussed, on floodplain interventions, especially side channels, meant to reduce the effect of pointbar formation on the navigable width.

This study shows that floodplain interventions and in this case side channel application is indeed an effective way to reduce the pointbar height. Nevertheless, the results of the side channel computations did not show a significant positive effect on the navigable width for a simulation period of one year. In order to increase the navigable width significantly a much larger discharge should be withdrawn from the river.

The numerical computations, showed that the critical cross-section (position in the bend where the navigable width standard is violated the most) is located at the first main channel enlargement. It is reasonable to attribute the navigable width reduction to this enlargement, which might be reduced by adjusting the dimensions or alignment of the local summer levee, in order to prevent the flow to diverge. Furthermore, the dimensions of the local groynes should be adapted to guarantee a navigable water depth during low water season.

In order to simulate the local morphology, the following three morphological phenomena were taken into account:

1. tilting of the transverse bed slope (axi-symmetrical solution) 2. overshoot phenomenon 3. 1-D bed wave

It turns out, that the tilting of the transverse bed slope causes the restriction to the navigable width, because the analytical model showed:

• The overshoot phenomenon is only likely to occur at relatively small discharges (sufficiently high B/h ratio). However, the corresponding morphological time scale is too long to ensure significant bed level increase. Therefore, the navigable width problem cannot be attributed to this phenomenon.

• At higher discharges, the damping length becomes positive, which implies a rapidly decaying amplitude of the overshoot. The bed level in the inner bend tends to grow faster, towards the axi-symmetric solution, without overshooting it. The morphological time scale belonging to this phenomenon is relatively small compared to the one for the overshoot phenomenon at low-water. Therefore, the tilting of the transverse bed slope at the higher discharges is dominating the morphological activity in the river bend and the axi-symmetric solution (height and time scale) is highly sensitive for the discharge through the main channel.

The conclusions above correspond well to the observations of the Ministry of Transport, Public Works and Water Management, which show an increase of the pointbar height mainly during rising water.

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A Delft3D model (2D depth-averaged computations) was used to determine the influence of a lateral extraction of water and sediment, (simulation a side channel). The withdrawn water and sediment were led back into the river further downstream. Important was the ratio between the expected one-dimensional sedimentation and the two-dimensional rotation of the transverse bed slope. The computations were made for different side channel alignments. The following conclusions are derived from the computations of one side channel in particular:

• The model showed indeed that a one-dimensional bed wave propagates downstream from the offtake and travelled a distance of 850 to 900 metre per year. Therefore, the offtake location should be chosen such that the one-dimensional bed level wave cannot reach the critical cross-section, because when the bed wave does reach the bend, the navigable width decreases enormously.

• The bed level in the inner bend increases less fast when water is abstracted.

• Lateral withdrawal of water only has not only a positive effect on the pointbar formation (speed), but it is also able to reduce its height. In order to reduce the pointbar height at higher discharges, however, relatively more water should be withdrawn than at smaller.

• Lateral withdrawal of both water and sediment decreases the pointbar height and formation (speed) even more than when only water is withdrawn.

Table 6-1: Pointbar height difference (m) due to extraction of 500 m 3/s

Pointbar height difference Q =3500 m 3/s Q =4500 m 3/s Varying discharge Unit

Location 1 0.5 0.6 0.2 m Location 2 0.2 0.1 0.1 m

• Computations for the low water season showed: o Downstream propagation of the 1-D bed wave o Erosion at the critical cross-section (from flood period) o New critical cross-section in the upstream part of the bend, caused by the 1-D bed wave.

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7. Recommendations Practical recommendations: • It is observed from the computations and depth measurements by the Ministry of Transport, Public Works and Water Management, that the largest morphological activity and critical navigable width occur near the flow enlargements. It is recommendable to adjust the summer levee alignment, so as to prevent the flow to diverge. Furthermore, the dimensions of the local groynes should be adapted to guarantee a sufficient navigable depth during low water season.

Model recommendations: • In reality, the river Rhine receives less sediment due to the appearance of river dams and mining in Germany, which enhances the subsidence process. It might be interesting to include this subsidence process in the present type of study, although the time scales differ substantially.

• The numerical computations in this study were made with a uniform grain size. It might be interesting to make the computations with a non-uniform grain size. It is recommended to use a varying discharge, because at a constant discharge, only a limited amount of fractions will participate in the morphological processes.

• Most of the numerical computations with Delft3D are executed with constant discharges. It does provide some insight into the concept of side channel application. Yet, a varying discharge will cause a more active riverbed, because every change of discharge initiates new perturbations in the system. This corresponds more to reality than a constant discharge. If sufficient computer time is available, it worthwhile to extend the computation over a longer period, in order to include the bed level inheritance from the previous flood periods.

• In order to model the influence of the side channel and the exchange of water and sediment in a better way, it is recommended to extend the model by implementing the floodplain. Furthermore, Delft3D SED-online should be adjusted to simulate spilling process over the summer levees, which makes the exchange of flows between floodplain and main channel possible.

• The application of a side channel in the river Waal will attract water (and sediment) from the Pannerdensch Kanaal. In order to simulate this phenomenon accurately, the present model should be extended upstream and the Pannerdensch Kanaal should be included as well. Alternatively, one might consider computing the desired amount of water and sediment through the river Waal and its side channel, first, followed by a 1-D computation, for the larger system, to indicate the water and sediment distribution between the two branches.

• Side channel application was introduced as an alternative for maintenance dredging, as a means to maintain the desired navigable width. This study shows that side channel application does not increase the navigable width, but it reduces the pointbar height. It might be interesting to start an economic analysis whether it is feasible to use a side channel to reduce the dredging costs, based on the reduced pointbar height.

WL | Delft Hydraulics, RIZA, ON, TU Delft 93 Side channels to improve navigability on the river Waal November 2005

References Ashmore, P.E. (1982), Laboratory modelling of gravel braided stream morphology. Earth Surface Processes 7, 201-25. Bendegom, L. (1947), Some considerations on river morphology and river improvement. De Ingenieur, Vol. 59, No. 5, Best, J.L. (1986), The morphology of river channel confluences. Progress in Physical Geography, Vol. 10, No. 2, pp.157-174 Best, J.L. and Reid, I. (1984), Separation zone at open channel junctions, Proceedings of American Society of Civeil Engineers, J. of Hydr. 110, pp. 1588-94 Bradbrook, K.F. Biron, P.M. Lane, S.N. Richards, K.S. Roy, A.G. (1998), Investigation of controls on secondary circulation in a simple confluence geometry using a three- dimensional numerical model, Hydrological Processes, Hydrol. Process. Vol. 12 pp. 1371-1396. Breen, L. van, (2002), Morphological response to large-scale floodplain lowering along the river Waal; a stochastic approach. Technische Univeristeit Delft, Delft. Bulle, H, (1926), Untersuchungen über die Geschiebeableitung bei der Spaltung von Wasserläufen. VDI-Verlag, Berlijn Duel, H. During, R. Specken, B. (1994): Nevengeulen, Verkenning naar de ecologische betekenis van inrichtingsvarianten, INRO-TNO P.93/ECO/02, RIZA, Lelystad. Engelund, F. and Hansen, E. (1967), A monograph on sediment transport in alluvial streams. Teknisk Forlag, Copenhagen. Jansen P.PH, et al (1979), Principles of river engineering. Pitman, London Jörissen, J.G.L., Vriend, H.J. de, Bokhout, F.M. (2004), Toets Bodemschermen Hulhuizen, Bouwdienst Rijkswaterstaat, Utrecht. Kjerfve, B. Shao, C.C. and Stapor, F.W. (1979), Formation of deep scour holes at the junction of tidal creeks: an hypothesis, Marine Geology 33, M9-M14. Klaassen, G.J. Sloff, C.J. (2000), Voorspelling bodemligging en herstel operaties voor baggeren op de Waal, WL |Delft Hydraulics, Delft Koch, F.G. and Flokstra, C. (1980), Bed level computations for curved alluvial channels, In Proc. XIX-th Congress IAHR, New Delhi, Vol 2 Subject A(d). Meerendonk, E. van, and N. Struiksma (1996), Waalbochten Hulhuizen, verbetering bevaarbaarheid door middel van schermen., WL |Delft Hydraulics, rapport Q2214, Delft. Middelkoop, H. (1998), Twee rivieren. Rijn en Maas in Nederland, Rijkswaterstaat, RIZA, Arnhem. Mosselman, E. (2001), Morphological development of side channels, CFR project report 9, IRMA-SPONGE and Delftcluster, WL | Delft Hydraulics, Delft. Mosley, M.P. (1976), An experimental study of channel confluence, J. of Geology , 535-62. Lambeek, J.J.P. and Mosselman, E. (1998), Huidige en historische rivierkundige parameters van de Nederlandse Rijntakken, WL | Delft Hydraulics, Delft. Rijkswaterstaat (1992), Onderzoek verbetering Waalbochten, Fase 1, Rijkswaterstaat directie Gelderland. Rijkswaterstaat (1993), Toekomstvisie Waal Hoofdtransportas, Eindrapportage, Fase 1, Rijkswaterstaat Gelderland. Rijkswaterstaat, Adviesdienst Verkeer en Vervoer (2004), Kerncijfer goederen vervoer. Rijkswaterstaat, Adviesdienst Verkeer en Vervoer (2004), Vervoersprognose 2003-2009 Schoor, M.M. and A.M. Sorber (1998), Morfologie natuurlijk. Brochure, RWS, RIZA Schoor, M.M., H.P. Wolfert, G.J. Maas, H. Middelkoop & J.J.P. Lambeek (1999), Potential for floodplain rehabilitation based on historical maps and present-day processes along the River Rhine, The Netherlands. In: Floodplains: Interdisciplinary approaches. Eds. S.B. Marriott & J. Alexander, Geological Society, London. Schropp, M.H.I. (1991), Morfologische aspecten bij het ontwerpen van nevengeulen, Rijkswaterstaat, RIZA.

94 WL | Delft Hydraulics, RIZA, ON, TU Delft Side channels to improve navigability on the river Waal November 2005

Sieben, J, (1999), Lokale morfologische effecten door verlaging van zomerkaden, RWS, RIZA Arnhem. Werkdocument 99.152 X. Sieben, J and Huntelaar, N.H. (2000), Oever belijning bij het Colenbrandersbos, Rivierkundige vergelijking van alternatieven, Werkdocument 2000.164.X Sieben, J, (2005) Presentation at the 8 th International Conference on Fluvial Sedimentology. Sloff, C.J. (2004), Tweedimensionale bodemveranderingen in de vaarweg van de Waal. WL |Delft Hydraulics, rapport Q3811, Delft. Sloff, C.J. and N. Struiksma (1997), Detailontwerp bodemschermen Hulhuizen., WL | Delft Hydraulics, rapport Q2303, Delft. Struiksma, N. (1983), Pointbar initiation in bends of alluvial rivers with dominant bed load transport. R 657-XVII, W 308 part III. Struiksma, N. (1985), Prediction of 2-D bed topography in rivers. J. of Hydr. (ASCE), Vol. 111, No. 8 Struiksma, N. Olesen, K.W. Flokstra, F. Vriend, H.J. de, (1985), Bed deformation in curved alluvial channels. J. of Hydr. Res., Vol 23, No. 1 Odgaard, A. J. (1981), Transverse bedslope in alluvial channels bends. J. of the Hydr. Div., ASCE, Vol. 107, No. 12. Taal, M. (1994), Evaluatie Baggerproef Hulhuizen, RIZA, Rijkswaterstaat, Lelystad, WL | Delft Hydraulics, Rapport Q1699, Taal, M. (1994), Evaluatie Baggerproef Hulhuizen. Bijlage E, RIZA, Rijkswaterstaat, Lelystad Vriend, H.J. de, and Struiksma, N. (1983), Flow and bed deformation in river bends. In. River Meandering, Proc. Conf. Rivers 1983, New Orleans, Ed. C.M. Elliot, ASCE, 1984. Vriend, H.J. de (1981), Steady flow in shallow channel bends, Delft Univ. of Technol., Depth. Of Civil Engrg., Communications on Hydraulics Vuren, S. van. Breen, L. van: (2003) Morphological impact of floodplain lowering along a low-land river: a probabilistic approach. Proceeding XXX IAHR Congress Water engineers and research in learning society: Modern Developments and Traditional Concepts, Thessaloniki, Greece, August 2003 Wiersma, F.E. (1997), The modelling of submerged vanes, A means of fairway improvement in river bends. WL | Delft Hydraulics (1990), Geulen in uiterwaarden, Fase 1 literatuuronderzoek, Q1163, Delft

WL | Delft Hydraulics, RIZA, ON, TU Delft 95

Appendix

Side channels to improve navigability on the river Waal

November 2005

Author: Corstiaan van Dam

Appendix November 2005

Contents APPENDIX 1: BASIC THEORY ON WATER MOVEMENT ON RIVERS...... 1

APPENDIX 2: FLOW THEORY IN RIVER BENDS...... 3

VERTICAL DISTRIBUTION OF TRANSVERSE VELOCITIES ...... 5

APPENDIX 3: LINEAR ANALYSIS OF RIVER MORPHOLOGY...... 7

APPENDIX 4: DISCHARGE AS A FUNCTION OF TIME ...... 13

APPENDIX 5: SEDIMENT TRANSPORT FORMULAS...... 14

APPENDIX 6: RESULTS ANALYTICAL MODEL...... 16

APPENDIX 7: RESULTS SENSITIVITY ANALYSIS...... 18

APPENDIX 8: SENSITIVITY ANALYSIS OF ENGELUND-HANSEN...... 30

APPENDIX 9: SENSITIVITY ANALYSIS OF MEYER-PETER-MÜLLER ...... 32

APPENDIX 10: NUMERICAL MODELLING...... 37

MODEL INPUT ...... 38 SENSITIVITY ANALYSIS : E NGELUND -HANSEN ...... 38

APPENDIX 11: RESULTS REFERENCE SITUATION...... 44

3 REFERENCE SITUATION Q = 3500 M /S...... 44 3 REFERENCE SITUATION Q = 4500 M /S...... 46

APPENDIX 12: RESULTS FOR DISCHARGE WITHDRAWAL FOR Q=3500 M 3/S .48

3 DISCHARGE WITHDRAWAL OF 500 M /S...... 48 3 DISCHARGE WITHDRAWAL OF 250 M /S ...... 50

APPENDIX 13: RESULTS FOR DISCHARGE WITHDRAWAL FOR Q=4500 M 3/S .53

3 DISCHARGE WITHDRAWAL OF 250 M /S...... 53 3 DISCHARGE WITHDRAWAL OF 500 M /S...... 54

APPENDIX 14: RESULTS OF THE DISCHARGE VARYING COMPUTATIONS ....56

APPENDIX 15: MORPHOLOGICAL ACTIVITY...... 58

APPENDIX 16: NAVIGABLE WIDTH...... 60

WL | Delft Hydraulics, RIZA, ON, TU Delft i

Appendix November 2005

ii WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 1 November 2005

Appendix 1: Basic theory on water movement on rivers

The three-dimensional equations of motion describe the conservation of mass and the conservation of momentum as expressed by Newton’s second law.

Conservation of mass:

∂U ∂ V ∂ W + + = 0 A1.1 ∂x ∂ y ∂ z

Conservation of momentum:

2 ∂U ∂ (U ) ∂()UV ∂ () UW ∂z + + + +=g w 0 A1.2 ∂∂tx ∂ y ∂ z ∂ x 2 ∂V ∂()UV∂ (V ) ∂ () VW ∂z + + + +=g w 0 A1.3 ∂∂tx ∂ y ∂ z ∂ y

A right-handed coordinate system is used, the components of velocity in the x, y and z directions are denoted by U, V and W respectively; g is the acceleration due to gravity and Z w is the water level above a horizontal reference level. In the equations, the fluid density ( ρ) is assumed constant, the geostrophic acceleration due to earth rotation has been neglected as well as the viscosity terms. The third momentum equation for the vertical direction has been omitted by the assumption that vertical accelerations in the fluid are neglectable compared to gravity. As a consequence, the acceleration due to gravity is balanced only by the vertical gradient of pressure P.

∂P = − ρg A1.4 ∂z which can be integrated directly to:

P=ρ gz( w − z ) A1.5

Generally, river flow is turbulent, which means that the velocity components and pressure fluctuate about their mean values: u , v , w and p

U= u + u ' A1.6

In the next phases of this project, the actual velocity will be equalled to the mean velocity, omitting herby the turbulent components, which are of minor importance on the length and time scale of a river system.

No system of differential equations is complete without boundary conditions. At the riverbed, the normal component of velocity must vanish:

∂z ∂ z ub+ v b − w = 0 A1.7 ∂x ∂ y

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Appendix November 2005

In addition, the tangential velocity component must vanish (no-slip condition). No water can cross the water surface, so:

∂z ∂ z ∂ z w+u w + v w −= w 0 A1.8 ∂t ∂ x ∂ y

The condition of constant pressure at the surface has already been applied Eq. (05). In addition, the stresses vanish at the surface, assuming wind influence to be absent:

τxz= τ yz = 0 A1.9

For most applications, knowledge of the full three-dimensional flow structure is not required. It is sufficient to use depth or cross-sectional mean values. These can be obtained by a second averaging procedure, namely integration over the water depth (and afterwards over the cross- section). For the equitation of continuity this gives:

zw ∂u ∂ v ∂ w  + +  dz = 0 A1.10 ∫ ∂x ∂ y ∂ z zb  

Interchanging the order of integration and differentiation, taking into account the variations with x (and t) of the bed level and applying the boundary conditions of the Eq. (07), (08), resulting in:

∂z ∂ ∂ w +hu + v hv = 0 A1.11 ∂t ∂ x() ∂ y ()

Where u and v are now the depth mean velocities (not time-mean values, used previously):

1 zw 1 zw u = udz v = vdz h ∫ h ∫ zb zb

Where h= z w - z b A similar operation can be applied to the momentum equations, with the result:

∂ ∂2 ∂ ∂z 1 hu+α hu + v α huv ++= gh w τ 0 A1.12 ∂∂tx() ( 1) ∂ y() 2 ∂ x ρ xb

∂ ∂ ∂ 2 ∂z 1 hv+α huv + v α hv ++= gh w τ 0 A1.13 ∂∂tx() ()2 ∂ y( 3 ) ∂ y ρ yb

Where τ xb and τ yb are components of the bottom stress and the α-coefficients represents corrections for the fact that the mean of a product of two variables is not equal to the product of the means of these variables. They depend on the velocity profiles and generally lie between 1 and 1.1. Usually they are disregarded.

2 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 2 November 2005

Appendix 2: Flow theory in river bends

Generally, in river sections with an irregular shape the flow structure will be complicated by lateral inhomogeneity. An analysis can be made by applying the vertically averaged equations, (see Eqs. A2.14 and A2.15), which still include lateral variations. These are also applicable to overland flow in flood plains. Generally, the full equations have to be used. To solve these equations numerical methods are needed. To obtain an insight into the subject, simplifications can be introduces by assuming the water depth to be constant and the α- coefficients are neglected. The following theory is a short summary, derived from Jansen [1979]. For the steady flow, the equations are as follows:

∂u ∂ v + = 0 A2.14 ∂x ∂ y ∂u ∂ u ∂z τ u+ v + g w += xb 0 A2.15 ∂x ∂ y ∂ zρ h ∂v ∂ v ∂z τ u+ v + g w +=yb 0 A2.16 ∂x ∂ y ∂ yρ h

If the bottom friction is neglected and the flow assumed to be irrotational, the velocity components can be derived from a potential function.

∂φ ∂φ u= v= ∂x ∂y

From the equation of continuity, it can be shown that the potential satisfies the Laplace’s equation, which describes the potential flow:

∂2φ ∂ 2 φ + = 0 A2.17 ∂x2 ∂ y 2

This shows that the lateral velocity variations are governed by elliptic equations and that, in simple cases, the potential flow is applicable. In case of a circular bend and the flow is uniform along the bend the equation can be rewritten to:

∂2φ1 ∂ φ + = 0 A2.18 ∂r2 r ∂ x where r is the radial coordinate. By integration, it is found that: ∂φ r= const A2.19 ∂x The constant must be zero as the radial velocity component ∂φ ∂ r vanishes at the banks. It follows that the phi is a function of the angular position θ only. Due to the assumed uniformity, this must be a linear function:

φ=c θ + d A2.20

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Appendix 2 November 2005

(c and d are constants) then the tangential velocity component u is:

1 ∂φ c u = = A2.21 r∂θ r

This equation shows that the velocity is inversely proportional to the radius of curvature of the streamline. This is only valid in the entrance of a bend. Downstream in the bend the velocity maximum shifts outwards from the inner bend and consequently the flow is not uniform

In the river bends the flow structure is actually three-dimensional, due to the centripetal acceleration. All water particles in a vertical experience the same lateral (radial) pressure gradient. The centripetal acceleration required to keep the particles in a circular path is larger near the surface than near the bottom, due to bed friction the horizontal velocity distribution is not uniform in the vertical in a bend. Therefore, near the surface the particles tend to move outward and near the bottom they tend to move inward, a so-called helical flow takes place. The mathematical explanation is described below.

Concentrating on a steady flow, all derivatives in time are zero and assuming hydrostatic pressure distribution Eq. (05). The momentum equation in transverse direction of the bend with constant z-level reads:

u2 ∂ ∂ h =−ρghz() −=− g A2.22 r∂ y ∂ y

Furthermore, Bernouilli’s law can be applied with one constant γ over the entire flow field.

u2 +h = γ A2.23 r

Differentiating this equation in radial direction results in:

u∂ u u 2 + = 0 A2.24 g∂ r r

∂ ∂ Realizing that = − , the equations (22) and (24) together read: ∂r ∂ y

∂u u 2 ∂u u u + = 0 or = − A2.25 ∂r r ∂r r

The solution for this differential equation describes the lateral distribution of the longitudinal velocity in a river bend:

c u = − A2.26 r

Because of bed friction the velocity at the water surface is greater than the vertically averaged velocity, while near the bed it is smaller. Therefore:

4 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 2 November 2005

u2 ∂ h > − g near to the surface A2.27 r∂ y u2 ∂ h < − g near to the bed A2.28 r∂ y

The result of this is, that water near to the surface is heading slightly towards the outer bend, while water flowing near to the riverbed id diverted slightly towards the inner bend.

Vertical distribution of transverse velocities When using again a right-handed coordinate system, the components of velocity in the s, r and z directions are denoted by u, v and w respectively. The equations of motion for horizontal steady flow without the convective inertia terms read:

∂z 1 ∂ τ gw− sz = 0 A2.29 ∂sρ ∂ z u2 ∂z 1 ∂τ −+g w −rz = 0 A2.30 r∂ rρ ∂ z

By integrating Eq. (29) vertically, the tangential stress component τsz will vary linearly from surface to bottom:

z∂z  z τ= τ1 −=− ρ gh w  1 − A2.31 sz b h∂ s  h

According to the mixing length theory, this shear stress can be related to gradients in the longitudinal velocity;

2 2  1 2 2 ∂u ∂ u   ∂ v  τsz = ρ l   +    A2.32 ∂z ∂ z   ∂   as the radial and vertical components v and w will be small relative to u, the relation becomes approximately:

∂u ∂ u τ= ρ l 2 A2.33 sz ∂z ∂ z m+1 z  1 m Adopting the power-law profile u=   u for the vertical distribution of the m h  longitudinal velocity leads to the following expression for the mixing length:

z  1− 1 m z l= kh   1 − A2.34 h  h

Assuming heterogeneity this mixing length is used to relate the vertical gradients in the transverse velocity to the shear stress:

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Appendix 2 November 2005

∂∂vv z2− 2 m  zvv  ∂∂ τ= ρl2 = κρ h  1 −  A2.35 rz ∂∂zz h  hzz  ∂∂

Entering the power-law profile and Eq. (35) in Eq. (28) and leads to an expression for the ∂z transverse velocity v, with the lateral water surface slope w as an unknown value. ∂r However, if the resulting equation is combined with the condition that there can be no net h flow qn =∫ udz = 0 the following expression results: 0 3 ∂z ()m +1 u2 w = A2.36 ∂r mm2 () + 3 gr

This extra equation leads to a description of the vertical distribution of the transverse velocity:  z  1 m  2   r v1 mm()+1 z  1 m mm2 () + 1 h  1 −ξ m+2  A2.37 =2  −  + ∫ m dξ  huκ  m+3 h  m + 20 1 − ξ    This theoretical profile corresponds well with measured profiles and is depicted in Figure 6 of Paragraph 2.1. The transverse component of the bottom shear stress results from combining Eq. (A2.35) and (A2.37):

2 u2 2m + 1  ()  τbr = − ρ h 2 A2.38 rmm()()+2 m + 3 

Whereas the tangential component for the bottom stress is:

u2 τ= − ρ g A2.39 sb C 2

The angles δ between the resultant bottom stresses and the river axis are given by: 2 h m 2 tan δ = − A2.40 κ 2 r()() m+2 m + 3

6 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 3 November 2005

Appendix 3: Linear analysis of river morphology

The set of equations, using the Cartesian coordinate system depicted in Fig. 1 is:

∂hu ∂ hv + = 0 A3.41 ∂x ∂ y ∂u ∂ u ∂ τ u+ v + g() hz ++=bx 0 A3.42 ∂xyz ∂ ∂ b ρ h ∂v ∂ v ∂ τ u+ v + g() hz ++=by 0 A3.43 ∂xyy ∂ ∂ b ρ h

Figure 3-1: Coordinate system for depth-averaged flow

The above set of equations contains a number of assumptions: • the pressure distribution is hydrostatic • the velocity distribution adapts immediately to the bed topography, expressed by neglecting the time derivatives. The assumption is based on the argument that the adaptation time of the flow is small with respect to the time scale at which the bed level changes occur Jansen… (et al.)[1979] • the so-called effective stresses describing the horizontal exchange of momentum, by the turbulent shear stresses, and the spiral motion, are negligible. This assumption is questionable because the effect of the spiral motion in bends can give rise to a significant shift of the main flow streamlines to the outer bank De Vriend [1981]. • a low Froude number is assumed, which allows for a rigid lid approximation of the free surface.

In the momentum equations, the water surface slope can be interpreted as a gradient of the piezometric head. The components of the bed shear stress in the momentum equation are related to the depth-averaged velocity using Chézy’s relation:

(ρgu u2+ v 2 ) τ = A3.44 bx C 2 (ρgv u2+ v 2 ) τ = A3.45 by C 2

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Appendix 3 November 2005

According to Eqs. (44) and (45), the direction of the bed shear stress coincides with the direction of the depth-averaged velocity, which is only true for non-curved flow. Here, it is assumed that, for curved flow, the influence of this deviation on the main flow is negligible.

In the sediment motion model only bed load transport is considered and it is assumed that grain sorting effects are negligible. The development of the bed level z b can be described by the continuity equation for the sediment:

∂z ∂ s ∂s b+ x +y = 0 A3.46 ∂t ∂ x ∂ y where s x, and s y are the components of the volumetric sediment transport, including pores, per unit length in the x and y direction, respectively. These components can be expressed per unit of the total volumetric sediment transport s t.

sx= s t cos α A3.47

sy= s t sin α A3.48

The direction α of the sediment transport will not coincide with the direction δ of the bed shear stress, when the bed slopes are non-zero, as a consequence of the downslope gravity force acting on the grains moving along a sloping bed (both lateral as longitudinal). This effect is taken into account in the formula of ( Van Bendegom [1947] and Koch and Flokstra [1980]):

1 ∂z sin δ − b fθ ∂ y tan α = s A3.49 1 ∂z cos δ − b fsθ ∂ x

u2+ v 2 in which the shields parameter is defined as θ = 2 , and a shape factor f s (value C∆ D 50 between 1 and 2) for the grains. For a review on the f s(θ), reference is made to Odgaard [1981]. In the present model, the following expression is adopted:

0.3 D  fs ()θ= 9  θ 0 A3.50 h0 

The lateral near bed velocities induced by the spiral flow is taken into account in the formulation of the bed shear stress vector via

v   ah  δ =arctan  − arctan A  A3.51 u   R * 

2 in which A=1 − gκ c , when the velocity profile is logarithmic ( Jansen et al κ 2 ( ) [1979]), and k is the Von Karman constant. The expression has been derived for locally fully developed spiral flow with R* defining the local radius of curvature of the streamline.

8 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 3 November 2005

h u2+ v 2 R = A3.52 * I

A measure of the spiral flow intensity is described by I, which leads via:

ChI∂ h β +I = u2 + v 2 A3.53 g ∂s R

Ch to the damping length λ= β . As this concerns the transverse bed shear stress a ss g coefficient β is 0.6 is adopted, according to De Vriend [1981].

The zero-order solution of the simplified mathematical model, for a straight channel, is obtained from Chézy’s law, the continuity condition and a sediment transport model. If the x- axis coincides with the river axis, the solution reads:

2 Q  3 h0 =   A3.54 BC i s  Q u0 = A3.55 Bh 0

sx = f( u 0 ) A3.56

The first order solution is obtained by superimposing a small perturbation onto the zero-order solution, e.g. h = h 0 + h’, u = u 0 + u’ and v = v 0, in which the perturbations must comply with h′
h 0 etc. Finally, substituting the perturbed variables into the steady mathematical model and neglecting second and higher order terms leads to a linearized model.

    ∂∂uguh' '' ∂∂ vg ' u0 u0 +2 2 +−    u0 +2 v '  = 0 A3.57 ∂∂y xCuh0 0   ∂∂ x xCh 0  ∂u' ∂ h ' ∂ v ' h+ u + h = 0 A3.58 0∂x 0 ∂ x 0 ∂ y ∂s' ∂ tan α x +s = 0 A3.59 ∂x0 ∂ y

' bu ' sx = s 0 A3.60 u0 v'h ∂ v '1' ∂ h tan α = +A 0 + A3.61 u0 uxf 0 ∂(θ ) ∂ y

The system of equations above is linearized and a double harmonic perturbation is introduced:

ˆ h′ = hexp ikx( + kyw ) A3.62

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Appendix 3 November 2005

where ĥ is a complex number in which the absolute value gives the amplitude/ modulus the phase of the perturbation, i = − 1 , k w is the wave number in lateral direction and k is a complex wave number in longitudinal direction. The imaginary part of k describes the development of the amplitude of the perturbation in the flow direction. The solution of the remaining variables is in a similar form. Impermeable side walls put constraints onto the transverse wave number, namely:

π k= m A3.63 w B in which m = 1,2,3,… for the present purpose m = 1 does apply. Eq (61) written in the following way, shows the adaptation length of damping (L D) and the wavelength of the system (L P):

x   2π h′ = hˆ exp −   sin () x + φ A3.64 LD   L P in which : λ 1b − 3  w =IP −1 −  A3.65 LD 2 2  λ 1b − 3  2 2π w =()b + 1 IP−1 −− IP − 2   A3.66 LP 2 2 

Substituting the general solution into the linearized mathematical model, yields the following polynomial from which the wave number k can be obtained:

  42 3 2 λw b ()()()kλγw bk+ λγ w iAf s θ −−+1  λs 2  A3.67   2 12 λw b b − 3 λw λ w ()kλγθw131+() Af s −−+ () ki λ w −−= 0 2λs 2  2 λs λ s

This polynomial always has two purely imaginary roots of different sign. The part of the solution, which corresponds to the negative imaginary root, i.e., an exponentially growing perturbation, vanishes due to a condition imposed at the downstream boundary. The magnitude of the positive imaginary root is generally relatively large, which implies that this part of the solution damps out rapidly, and therefore it will only be noticeable close to the inflow boundary. Consequently, the form of the solution will generally be dominated, to a large extent, by the two remaining roots, which mostly have the form:

k= ± kr + ik i A3.68

These roots characterize two identical growing/damping harmonic perturbations. In some cases, all roots are purely imaginary, which implies that the harmonic character of the solution vanishes. The complex roots mainly depend on the ratio of the adaptation length of the bed topography and the adaptation length of the main flow (λs / λw), see Struiksma [1983].

The used model leads to a couple of important parameters. In the first place, a adaptation length scale for the bed perturbations (sediment motion):

10 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 3 November 2005

2  2 0.3 h0B h 0 B D λs=2f s () θ = 9 2  θ A3.69 πh0 π  h 0 h 0

This length scale is proportional to the water depth and the square of the width/depth-ratio. Secondly, an adaptation length of the main flow:

C2 h λ = A3.70 w 2g

The relaxation length scale of the main flow is proportional to the water depth and inversely proportional to the friction factor (the value of C increases as friction decreases). This means that the adjustment process proceeds faster if the bed resistance increases. These length scales indicates how fast (in space) the sediment motion and water motion adapts to a perturbation.

The previous derivation is based on the stationary approach (equilibrium situation), all time depended terms are ignored. If the time depended terms are were taken into account and the derivation is redone, the general solution of the derivation would be:

ˆ hxt'( ,) = hce + h exp ikx( + ω t ) A3.71

In which k is the wave number and real. The frequency ω, however, is unknown and can be complex (meaning that the waves grow or decay exponentially) and a function of the non- dimensional wave number k λw and the interaction parameter. Continuing the derivation, leads to a time scale (2D) for the movement of a large riverbed perturbation, which reads:

2  −1 b −1 2 π  λ   2 w L   p  λs Ts= T o  −1 + 2  A3.72 2π  λw  1+ λw   Lp  

hλ in which, T = s (1D time scale) 0 s Before the comparison is made between the results of the model and the dredging test, the applicability of the model is described. According to Struiksma et al… [1985], the first order analysis provides a description of the upstream and downstream influence of a local bed and/or flow disturbance. A value larger than about 0.25 for the ratio λs/λw (interaction parameter), corresponds with value for most natural rivers. Furthermore, the strong downstream influence of the entrance of the bend, i.e. the small relative damping k i/k r implies that, generally, it is not possible to predict the bed level accurately in natural river bends from local values of depth, flow velocity and a local radius of curvature as has been attempted by several scientists (see the review given by Odgaard [1981]).

The magnitude of the bed and flow disturbance at the entrance to a circular bend can be estimated by the difference between the zero-order in the straight reach and in the bend. The zero-order solution in the bend, in his turn, can be obtained partly from Chézy’s law, in which

WL | Delft Hydraulics, RIZA, ON, TU Delft 11

Appendix 3 November 2005

the lateral variation of the longitudinal water surface slope, i.e. Ri s = Rci sc has to be taken into account, and partly from the axi-symmetrical lateral bed slope equation for fully developed circular bend flow. This equation originates from the Equations (49) and (50) (of Appendix 3) with the main flow and sediment transport parallel to the river-axis (v/u = 0 and tan α = 0); it reads:

∂z h b = − Af θ A3.73 ∂ys R

So, the principal conclusion from the foregoing and the test of Struiksma et al… [1985] is that the point bar (and therefore also pool) formation in river bends cannot be described on the basis of local conditions only, i.e. the lateral balance between the upslope force induced by the spiral flow and the downslope gravitational force both acting on the grains moving along the bed. The lateral bed slope in a bend is also influenced by transitional effects due to a difference between the conditions upstream and those in the bend. These transitional effects will cause a pattern, which should be added to the solution of the axi-symmetrical solution. In the context of this report, these extra bars will be known by overshoot bars. Mathematically, the theoretical bed level due to both phenomena is:

x   2π  H=−− H0 1 exp   cos () x + φ  A3.74 LD   L P 

The waveform of the longitudinal bed profiles in “long” circular bends is explained with the linear analysis of the water and sediment motion for the steady state. The main result of this analysis is that it leads to estimates of the wave length and bed oscillation damping rates. At the present, however, good agreement with measured data can only be obtained by using a calibration factor in the sediment transport direction equation. This indicates that more research is needed to establish a quantitatively predictive model. The result of the linear analysis can be used to reduce the number of runs with non-linear models and hence the computational expenses. A much more simplified linear analysis, in which the influence of streamline curvature is totally neglected, clearly indicates which effects are the most important for the bed deformation in alluvial rivers. The wave length and damping are shown to depend mainly on the ratio between the adaptation lengths of the bed topography λs and the main flow λw. This conclusion has been corroborated by extensive linear analysis. In physical terms, it implies that the wave length and damping is primarily determined by a dynamic response of the bed to the changing distribution of the water and sediment motion at the bend entrances (exits).

12 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 4 November 2005

Appendix 4: Discharge as a function of time

4000

3500

3000

2500

2000 Discharge (m3/s) Discharge 1500

1000 1992-10-23 1992-12-12 1993-01-31 1993-03-22 Date

Figure 4-1: Discharge on the river Waal (Nov '92 - March '93)

WL | Delft Hydraulics, RIZA, ON, TU Delft 13

Appendix 5 November 2005

Appendix 5: Sediment transport formulas

A power law formula is used, which approaches the transport formula of Engelund-Hansen. This power law equation looks like:

s= m ⋅ u b A5.75

0.05 in which: m = and b = 5. 3 2 g⋅ C ⋅ D 50 ⋅∆ As stated above, the power law formula approaches the actual sediment transport formula, A5.75:

 3  2 2 u* u s=0.05 g ∆ D    A5.76 gD∆  gD ∆ 

This formula is semi-empirical and the applicable range of it is determined by Engelund- Hansen by 0.07 < θ > 6 and a grain size between 0.19 and 0.93 mm. In this project, the Shields parameter remains between these limits see Figure 5-1, and with a D50 of 2 mm, the grain size as well.

0,50

0,45

0,40

0,35

0,30

0,25

0,20 Shiels [-] parameter

0,15

0,10 0 1000 2000 3000 4000 5000 6000 7000 Discharge (m^3/s)

Figure 5-1: Shields parameter [-]

The Engelund-Hansen method has proven to describe the sediment transport of the river Waal correctly in several previous projects. Nevertheless, in the sensitivity analysis, the Meyer-Peter-Müller formula will be used as well. In contrary to this last method, the Engelund-Hansen formula is a total transport formula, in which both the transport of bed material and suspension is taken into account. The formula of Meyer-Peter-Müller describes only the transport of bed material, which is calculated in the following way:

1 2 2 3 Sb =8 D50() ∆ gD 50 ()µθ − 0.047 A5.77 in which µ is a ripple factor, θ the Shields parameter 0.047 the critical Shields value.

14 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 5 Novemberber 2005

The ripple factor is a measure for the bed form and is calculated as a function of the roughness:

3 C  2 µ =   A5.78 C90  in which the C 90 is related to the D 90 as follows:

12 h  C90 = 18log   A5.79 D90 

In previous projects, the calculations with a ripple factor of 0.7 has proven to give sufficient accurate results. Just like the transport formula of Engelund-Hansen, the Meyer-Peter-Müller method is also simplified by a power law approach in which the exponent is substituted by:

3 b = A5.80 0.047 1− µθ

The ratio of the fall velocity and the shear flow velocity gives an indication of which transport formula should be used. W When s >1, the Meyer-Peter-Müller method has proven to give accurate results. u*

For D 50 = 2 mm, the fall velocity is calculated by:

Ws ≈1.1 ∆ gD 50 A5.81 and the shear flow velocity by:

g u= u A5.82 * C e

In which the u e is the equilibrium flow velocity. W In this thesis, s >1 over the full range of 1000 < Q > 6000 m 3/s. u* Although this ratio is larger than one, the first calculations were made with the power law formula, belonging to the Engelund-Hansen approach, because in the projects of Taal [1992] and Wiersma [1997], which took place at the bend of Hulhuizen, the same formula was used.

WL | Delft Hydraulics, RIZA, ON, TU Delft 15

Appendix 6 November 2005

Appendix 6: Results analytical model

700 300000

600 250000

500 200000

400 150000

300 100000

200 50000

1D Time1D (days) scale 0 100 Time2D (days) scale 0 1000 2000 3000 4000 5000 6000 0 -50000 0 1000 2000 3000 4000 5000 6000 -100000 Discharge (m^3/s) Discharge (m^3/s)

Figure 6-1: 1D Morphological time scale Figure 6-2: 2D Morphological time scale

1400 1,60

1200 1,40 1,20 1000 1,00 800 λw 0,80 600 λs 0,60 400 0,40

Adaptation Lengths (m) Lengths Adaptation 200 0,20 Interaction parameter IpInteraction parameter [-] 0 0,00 500 1500 2500 3500 4500 5500 6500 500 1500 2500 3500 4500 5500 6500 Discharge (m^3/s) Discharge (m^3/s)

Figure 6-3: Adaptation length scales Figure 6-4: Interaction parameter IP

350000 10000 300000 9000 250000 8000 200000 150000 7000

100000 6000 50000 5000 0 4000 Damping length Ld (m) Ld length Damping 500 1500 2500 3500 4500 5500 6500

-50000 (m) Lp pointbar Wavelength -100000 3000 -150000 500 1500 2500 3500 4500 5500 6500 Discharge (m^3/s) Discharge (m^3/s)

Figure 6-5: Damping length, Ld Figure 6-6: Wave length, Lp

16 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 6 November 2005

3,00E+01 2,50E-05

2,50E+01 1,50E-05 5,00E-06 2,00E+01 -5,00E-06 500 1500 2500 3500 4500 5500 6500 1,50E+01 -1,50E-05

1,00E+01 -2,50E-05

1D Bed celerity (m/s) celerity Bed 1D 5,00E+00 -3,50E-05 2D Bed Celerity (m/s) Celerity Bed 2D -4,50E-05 0,00E+00 500 1500 2500 3500 4500 5500 6500 -5,50E-05 Discharge (m^3/s) Discharge (m^3/s)

Figure 6-7: Bed celerity (1D) Figure 6-8: Bed celerity (2D)

8,00E-04 7,00E-04 6,00E-04 5,00E-04 4,00E-04 3,00E-04 2,00E-04 1,00E-04 Sediment transport Sediment(m2/s) transport 0,00E+00 500 1500 2500 3500 4500 5500 6500 Discharge (m^3/s)

Figure 6-9: Sediment transport So (m 2/s)

6,00 Q = 1000 Q = 1250 Q = 1500 4,00 Q = 1750 Q = 2000 Q = 2250 2,00 Q = 2500 Q = 2750 Q = 3000 0,00 Q = 3250 0 1000 2000 3000 4000 5000 6000 Q = 3500 Bed levelBed (m) -2,00 Q = 3750 Q = 4000 Q = 4250 -4,00 Q = 4500 Q = 4750 Q = 5000 -6,00 Q = 5250 Discharge (m^3/s) Q = 5500

Figure 6-10: Bed level, axial Symmetrical solution and overshoot phenomenon

WL | Delft Hydraulics, RIZA, ON, TU Delft 17

Appendix 7 November 2005

Appendix 7: Results sensitivity analysis

The reference values of T 0, T 2D, H 0 and L D, L P and IP are shown as a function of the discharge in the first column at the right side of the tables, respectively.

Table 7-1: Sensitivity analysis T 0 (days)

Q (m 3/s) To (days) C (m 1/2 /s) B (m) r (m) Iw (-) reference 43 47 225 300 11001200 1,0 E-4 1,2 E-4

1000 644 658 631 387 1.068 644 644 725 579 1500 346 354 339 208 574 346 346 389 311 2000 223 227 218 134 369 223 223 250 200 2500 158 162 155 95 262 158 158 178 142 3000 120 122 117 72 198 120 120 134 107 3500 94 96 92 57 157 94 94 106 85 4000 77 79 75 46 128 77 77 87 69 4500 64 66 63 39 106 64 64 72 58 5000 55 56 54 33 91 55 55 61 49

Table 7-2: Sensitivity analysis T 2D (days)

Q (m 3/s) T 2D (days) C (m 1/2 /s) B (m) r (m) Iw (-) reference 43 47 225 300 11001200 1,0 E-4 1,2 E-4

1000 -4.689 -4.377 -5.081 4.910 -4.988 -4.689 -4.689 -7.573 -3.415 1500 3.787 4.897 3.087 617 -4.530 3.787 3.787 2.642 7.540 2000 808 888 743 265 11.370 808 808 759 890 2500 384 410 362 152 1.505 384 384 385 390 3000 232 245 221 99 683 232 232 239 228 3500 158 166 151 68 407 158 158 165 153 4000 115 121 110 - 276 115 115 121 110 4500 88 92 84 - 202 88 88 91 84 5000 68 71 64 - 155 68 68 67 65

18 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 7 November 2005

Table 7-3: Sensitivity analysis H 0 (m)

3 1/2 Q (m /s) Ho (m) C (m /s) B (m) r (m) Iw (-) reference 43 47 225 300 11001200 1,0 E-4 1,2 E-4

1000 0.98 1.02 0.95 0.95 1.01 1.03 0.94 0.97 0.99 1500 1.36 1.41 1.31 1.32 1.40 1.42 1.30 1.35 1.37 2000 1.71 1.77 1.65 1.66 1.76 1.79 1.64 1.69 1.72 2500 2.04 2.12 1.97 1.99 2.10 2.14 1.96 2.02 2.06 3000 2.36 2.45 2.28 2.30 2.43 2.47 2.27 2.30 2.38 3500 2.67 2.77 2.58 2.60 2.75 2.80 2.56 2.65 2.70 4000 2.98 3.09 2.87 2.89 3.06 3.11 2.85 2.95 3.00 4500 3.27 3.39 3.16 3.18 3.37 3.42 3.13 3.24 3.30 5000 3.56 3.69 3.44 3.46 3.66 3.72 3.41 3.52 3.59

Table 7-4: Sensitivity analysis L D (m)

3 1/2 Q (m /s) Ld (m) C (m /s) B (m) r (m) Iw (-) reference 43 47 225 300 1100 1200 1,0 E-41,2 E-4

1000 1.069 -2.688 -3.684 5.576 -1.418 1.069 1.069 -4.655 -2.436 1500 737 6.843 4.929 1.347 -4.062 737 737 3.477 12.614 2000 503 1.998 1.888 871 18.252 503 503 1.572 2.426 2500 361 1.289 1.274 679 3.558 361 361 1.099 1.493 3000 272 996 1.002 571 2.153 272 272 878 1.133 3500 213 832 845 501 1.612 213 213 747 937 4000 172 725 742 450 1.321 172 172 659 813 4500 125 650 667 412 1.137 142 142 595 725 5000 106 593 611 382 1.009 120 120 546 660

Table 7-5: Sensitivity analysis L P (m)

3 1/2 Q (m /s) Lp (m) C (m /s) B (m) r (m) Iw (-) reference 43 47 225 300 11001200 1,0 E-4 1,2 E-4

1000 3.374 3.249 3.499 2.872 4.252 3.374 3.374 3.268 3.484 1500 3.377 3.236 3.519 3.049 3.948 3.377 3.377 3.316 3.442 2000 3.508 3.350 3.666 3.341 3.936 3.508 3.508 3.479 3.544 2500 3.702 3.524 3.883 3.767 4.011 3.702 3.702 3.711 3.710 3000 3.957 3.752 4.167 4.430 4.131 3.957 3.957 4.018 3.926 3500 4.285 4.042 4.536 5.652 4.284 4.285 4.285 4.429 4.199 4000 4.720 4.421 5.035 9.289 4.469 4.720 4.720 5.006 4.547 4500 5.909 5.364 6.538 - 4.610 5.909 5.909 7.221 5.297 5000 7.926 6.839 9.421 - 4.948 7.926 7.926 14.872 6.394

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Appendix 7 November 2005

Table 7-6: Sensitivity analysis IP (-)

3 1/2 Q (m /s) IP (-) C (m /s) B (m) r (m) Iw (-) reference 43 47 225 300 11001200 1,0 E-4 1,2 E-4

1000 1.36 1.41 1.32 0.86 2.15 1.36 1.36 1.23 1.50 1500 0.84 0.87 0.81 0.53 1.32 0.84 0.84 0.75 0.92 2000 0.59 0.62 0.57 0.37 0.94 0.59 0.59 0.53 0.65 2500 0.45 0.47 0.44 0.29 0.72 0.45 0.45 0.41 0.50 3000 0.36 0.38 0.35 0.23 0.58 0.36 0.36 0.33 0.40 3500 0.30 0.31 0.29 0.19 0.48 0.30 0.30 0.27 0.33 4000 0.26 0.27 0.25 0.16 0.41 0.26 0.26 0.23 0.28 4500 0.22 0.23 0.22 0.14 0.35 0.22 0.22 0.20 0.25 5000 0.20 0.20 0.19 0.12 0.31 0.20 0.20 0.18 0.22

6,00

4,00 Q = 1000 Q = 1250 2,00 Q = 1500 Q = 2000 0,00 Q = 3000 0 1000 2000 3000 4000 5000 6000 Q = 4000 Bed level Bed [m] -2,00 Q = 5000 Q = 5500 -4,00

-6,00 Longitudinal position [m]

Figure 7-1: Reference case

20 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 7 November 2005

4,00

3,50

3,00

2,50 Hmax [m] Hmax/H0 [-] 2,00 H0 [m]

1,50

1,00

0,50 500 1500 2500 3500 4500 5500 6500 Discharge (m^3/s)

Figure 7-2: Reference case (m)

8,00

6,00 Q = 1000 4,00 Q = 1250 2,00 Q = 1500 0,00 Q = 2000 0 1000 2000 3000 4000 5000 6000 -2,00 Q = 3000 Q = 4000 Bed level Bed [m] -4,00 Q = 5000 -6,00 Q = 5500 -8,00

-10,00 Longitudinal position [m]

Figure 7-3: Hydraulic roughness = 43 m 1/2 /s

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Appendix 7 November 2005

4,50

4,00

3,50

3,00 Hmax [m] 2,50 Hmax/H0 [-]

2,00 H0 [m]

1,50

1,00

0,50 500 1500 2500 3500 4500 5500 6500 Discharge (m^3/s)

Figure 7-4: Hydraulic roughness = 43 m 1/2 /s

5,00

4,00 Q = 1000 3,00 Q = 1250 2,00 Q = 1500 Q = 2000 1,00 Q = 3000 0,00 Q = 4000 Bed level Bed (m) 0 1000 2000 3000 4000 5000 6000 Q = 5000 -1,00 Q = 5500 -2,00

-3,00 Longitudinal position (m)

Figure 7-5: Hydraulic roughness = 47 m 1/2 /s

The line of Q = 5500 m 3/s is missing in the figure above, because the interaction parameter drops below the 0.25 and the linear theory is limited applicable. Therefore, this line is not shown.

22 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 7 November 2005

4,00

3,50

3,00

2,50 Hmax [m] Hmax/H0 [-] 2,00 H0 [m] 1,50

1,00

0,50 500 1500 2500 3500 4500 5500 6500 Discharge (m^3/s)

Figure 7-6: Hydraulic roughness = 47 m 1/2 /s

2,50

2,00 Q = 1000 1,50 Q = 1250 Q = 1500 1,00 Q = 2000

Bed levelBed [m] Q = 3000 0,50

0,00 0 1000 2000 3000 4000 5000 6000 7000 Longitudinal position [m]

Figure 7-7: B = 225 m

Just like Figure 7-5, the lines of the highest discharges are not shown, because of the limited applicability of the linear theory.

WL | Delft Hydraulics, RIZA, ON, TU Delft 23

Appendix 7 November 2005

4,00

3,50

3,00

2,50 Hmax [m] Hmax/H0 [-] 2,00 H0 [m] 1,50

1,00

0,50 500 1500 2500 3500 4500 5500 6500 Discharge (m^3/s)

Figure 7-8: B= 225 m

8.00 7.00 6.00 5.00 Q = 1500 4.00 Q = 2000 3.00 Q = 3000 2.00 Q = 4000 1.00 Q = 5000 Bed levelBed (m) 0.00 Q = 5500 -1.00 0 1000 2000 3000 4000 5000 6000 -2.00 -3.00 Longitudinal position (m)

Figure 7-9: B = 300 m

In Figure 7-9, the smallest discharges are removed from the figure, because the unstable situation makes the bed level grow enormously and ruin the figure.

24 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 7 November 2005

7,00

6,00

5,00 Hmax [m] 4,00 Hmax/H0 [-] H0 [m] 3,00

2,00

1,00 500 1500 2500 3500 4500 5500 6500 Discharge [m^3/s]

Figure 7-10: B = 300 m

8,00

6,00 Q = 1000 4,00 Q = 1250 Q = 1500 2,00 Q = 2000 Q = 3000 0,00 Q = 4000

Bed levelBed (m) 0 1000 2000 3000 4000 5000 6000 -2,00 Q = 5000 Q = 5500 -4,00

-6,00 Longitudinal position (m)

Figure 7-11: R = 1100 m

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Appendix 7 November 2005

4,50

4,00

3,50

3,00 Hmax [m] 2,50 Hmax/H0 [-]

2,00 H0 [m]

1,50

1,00

0,50 500 1500 2500 3500 4500 5500 6500 Discharge [m^3/s]

Figure 7-12: R = 1100 m

6,00

4,00 Q = 1000 Q = 1250 2,00 Q = 1500 Q = 2000 0,00 Q = 3000 0 1000 2000 3000 4000 5000 6000 Q = 4000 Bed level Bed (m) -2,00 Q = 5000 Q = 5500 -4,00

-6,00 Longitudinal position (m)

Figure 7-13: R = 1200 m

26 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 7 November 2005

4,00

3,50

3,00

2,50 Hmax [m] Hmax/H0 [-] 2,00 H0 [m] 1,50

1,00

0,50 500 1500 2500 3500 4500 5500 6500 Discharge [m^3/s]

Figure 7-14: R = 1200 m

4,00

3,00 Q = 1000 2,00 Q = 1250 Q = 1500 1,00 Q = 2000 Q = 3000 0,00 Q = 4000

Bed level Bed (m) 0 1000 2000 3000 4000 5000 6000 -1,00 Q = 5000 Q = 5500 -2,00

-3,00 Longitudinal position (m)

Figure 7-15: Iw = 1.0 E-4

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Appendix 7 November 2005

4,00

3,50

3,00

2,50 Hmax [m] Hmax/H0 [-] 2,00 H0 [m] 1,50

1,00

0,50 500 1500 2500 3500 4500 5500 6500 Discharge [m^3/s]

Figure 7-16: Iw = 1.0 E-4

10,00 8,00 6,00 Q = 1000 4,00 Q = 1250 Q = 1500 2,00 Q = 2000 0,00 Q = 3000 -2,00 0 1000 2000 3000 4000 5000 6000 Q = 4000 Bed level Bed (m) -4,00 Q = 5000 -6,00 Q = 5500 -8,00 -10,00 Longitudinal position (m)

Figure 7-17: Iw = 1.2 E-4

28 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 7 November 2005

4,00

3,50

3,00

2,50 Hmax [m] Hmax/H0 [-] 2,00 H0 [m] 1,50

1,00

0,50 500 1500 2500 3500 4500 5500 6500 Discharge [m^3/s]

Figure 7-18: Iw = 1.2 E-4

WL | Delft Hydraulics, RIZA, ON, TU Delft 29

Appendix 8 November 2005

Appendix 8: Sensitivity analysis of Engelund-Hansen

800 700

700 600 600 500 500 b = 3 400 400 b = 5 300 300 b = 7 T 1D T [days] 1D 200 200 2D Time2D [days] scale 100 100

0 0 0 1000 2000 3000 4000 5000 6000 7000 0 1000 2000 3000 4000 5000 Discharge [m^3/s] Discharge [m^3/s]

Figure 8-1: 1D time scale for b = 3, 5, 7 Figure 8-2: 2D time scale for b = 3

700 700

600 600

500 500

400 400

300 300

200 200 2D Time2D [days] scale 2D Time2D scale [days] 100 100

0 0 1000 2000 3000 4000 5000 6000 2500 3000 3500 4000 4500 5000 5500 6000 Discharge [m^3/s] Discharge [m^3/s]

Figure 8-3: 2D time scale for b = 5 Figure 8-4: 2D time scale for b = 7

3.50

3.00

2.50 Q = 1000 Q = 1250 2.00 Q = 1500

1.50 Q = 2000 Q = 3000 Bed level Bed [m] 1.00 Q = 4000

0.50

0.00 0 1000 2000 3000 4000 5000 6000 Longitudinal position [m]

Figure 8-5: Bed level [m] for b = 3

30 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 8 November 2005

3.00

2.50

2.00 Hmax [m] 1.50 Hmax/H0 [-] H0 [m] 1.00

0.50

0.00 500 1500 2500 3500 4500 Discharge [m^3/s]

Figure 8-6: Hmax, H0 and ratio Hmax/H0 for b = 3

8.00 7.00 6.00 5.00 4.00

3.00 Q = 2000 2.00 Q = 3000 1.00 Q = 4000 Bedlevel[m] 0.00 -1.00 0 1000 2000 3000 4000 5000 6000 -2.00 -3.00 -4.00 Logitudinal position [m]

Figure 8-7: Bed level, b = 7

8.00

7.00

6.00

5.00 Hmax [m] 4.00 Hmax/H0 [-]

3.00 H0 [m]

2.00

1.00

0.00 500 1500 2500 3500 4500 5500 6500 Discharge [m^3/s]

Figure 8-8: Hmax, H0 and ratio Hmax/H0 for b = 7

WL | Delft Hydraulics, RIZA, ON, TU Delft 31

Appendix 9 November 2005

Appendix 9: Sensitivity analysis of Meyer-Peter-Müller

9.00E-04 8.00E-04 7.00E-04 6.00E-04 5.00E-04 St. E-H 4.00E-04 Sb MPM 3.00E-04 2.00E-04 1.00E-04 Sediment transport [m^2/s] Sediment transport 0.00E+00 0 1000 2000 3000 4000 5000 6000 Discharge [m^3/s]

Figure 9-1: Sediment transport capacity by different formulas: Engelund-Hansen power law and Meyer- Peter-Müller original bed load transport formula

700

600

500

400 T 1D

300 T 2D

200 Time [days] scales

100

0 0 1000 2000 3000 4000 5000 6000 Discharge [m^3/s]

Figure 9-2: Time scales 1D and 2D by Meyer-Peter-Müller [days]

1.50 4000 3500 1.25 3000 1.00 2500 0.75 2000 1500 0.50 1000

0.25 (m) Ld length Damping 500 Interaction parameter Ip Interaction parameter [-] 0.00 0 500 1500 2500 3500 4500 5500 6500 1500 2500 3500 4500 5500 6500 Discharge [m^3/s] Discharge (m^3/s)

Figure 9-3: Interaction parameter M-P-M [-] Figure 9-4: Damping length [m]

32 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 9 November 2005

5.00

4.00

3.00 Q = 1000 2.00 Q = 1500 Q = 2000 1.00 Q = 3000

Bed levelBed [m] 0.00 Q = 4000 0 1000 2000 3000 4000 5000 6000 -1.00

-2.00 Discharge [m^3/s]

Figure 9-5: Bed level [m] (overshoot and axi-symmetric solution by Meyer-Peter-Müller original)

7.00

6.00

5.00

4.00 Hmax [m] Hmax/H0 [-] 3.00 H0 [m]

2.00

1.00

0.00 500 1500 2500 3500 4500 5500 6500 Discharge (m^3/s)

Figure 9-6: Hmax, H0 and Hmax/H0 for B = 260 m

At a discharge of 1350 m 3/s the calculation shows a asymptotic behaviour, just like in the Engelund-Hansen computation, therefore, at a discharge of 1250 m 3/s the damping length is negative and the solution is unstable. At discharges larger than 4000 m 3/s the interaction parameter drops below 0.25 and the linear theory is not applicable any more. This explains the absence of the higher discharges in Figure 9-5.

WL | Delft Hydraulics, RIZA, ON, TU Delft 33

Appendix 9 November 2005

35

30

25

20 E-H 1D 15 M-P-M 1D

10

1D bed celerity [m/s] bed celerity 1D 5

0 1000 2000 3000 4000 5000 6000 7000 Discharge [m^3/s]

Figure 9-7: 1D bed celerity for Engelund-Hansen and Meyer-Peter-Müller

1.5E-05

1.0E-05

5.0E-06 E-H 2D M-P-M 2D 0.0E+00 500 1000 1500 2000 2500 3000 3500 4000 4500

2D bed 2D celerity [m/s] -5.0E-06

-1.0E-05 Discharge [m^3/s]

Figure 9-8: 2D bed celerity for Engelund-Hansen and Meyer-Peter-Müller

Table 9-1: Comparison Hmax between E-H and M-P-M

Discharge [m^3/s] Hmax [m] E-H Hmax [m] M-P-M Difference [%]

1500 2.39 2.28 -4.73% 1750 2.41 2.19 -9.08% 2000 2.46 2.21 -10.16% 2250 2.53 2.27 -10.10% 2500 2.60 2.35 -9.58% 2750 2.68 2.45 -8.87% 3000 2.77 2.55 -8.09% 3250 2.86 2.65 -7.26% 3500 2.95 2.76 -6.42% 3750 3.05 2.88 -5.55% 4000 3.15 3.00 -4.62%

34 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 9 November 2005

700

600

500 T 1D (B=260m) 400 T 2D (B=260m) 300 T 1D (B=300m) T 2D (B=300m) 200

100 1D and 1D time 2D [s] scales 0 0 1000 2000 3000 4000 5000 6000 7000 Dicharge [m^3/s]

Figure 9-9: Time scales for B= 260 m and B = 300m

7.00 6.50 6.00 5.50 b (B=300m) 5.00 b (B=260m) 4.50

Values for b [-] 4.00 3.50 3.00 0 1000 2000 3000 4000 5000 6000 7000 Discharge (m^3/s)

Figure 9-10: Values for b=f(Q) [-], for B = 260m and B = 300 m

9.0E-04 8.0E-04 7.0E-04 6.0E-04 5.0E-04 Sb (B=300m) 4.0E-04 Sb (B=260m) 3.0E-04 2.0E-04 1.0E-04 Sediment transport Sediment(m^2/s] transport 0.0E+00 1000 2000 3000 4000 5000 6000 7000 Discharge [m^3/s]

Figure 9-11: Sediment transport capacity (bed load)

WL | Delft Hydraulics, RIZA, ON, TU Delft 35

Appendix 9 November 2005

10.00

8.00

6.00 Q = 1500 Q = 2000 4.00 Q = 3000 Q = 4000 2.00

Bed level (m) Bedlevel Q = 5000 Q = 5500 0.00 0 1000 2000 3000 4000 5000 6000 -2.00

-4.00 Discharge (m^3/s)

Figure 9-12: Bed level for B= 300 m

10.00 9.00 8.00 7.00 Hmax [m] 6.00 Hmax/H0 [-] 5.00 H0 [m] 4.00 3.00 2.00 1.00 500 1500 2500 3500 4500 5500 6500 Discharge (m^3/s)

Figure 9-13: Hmax, H0 and Hmax/H0

36 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 10 November 2005

Appendix 10: Numerical modelling

Figure 10-1: Initial computational grid and depth samples from 2003 Interpolation of the depth samples results in the following bed level in the bend.

Figure 10-2: Initial bed level

WL | Delft Hydraulics, RIZA, ON, TU Delft 37

Appendix 10 November 2005

Model input Discharge schematisation.

8000 7000 6000 5000 Q Measured 4000 Q Discrete 3000 2000 Discharge [m^3/s] Discharge 1000 0 0 50 100 150 200 250 300 350 400 Occurency per year

Figure 10-3: Discharge schematisation

Sensitivity analysis: Engelund-Hansen

16−Mar−2003 00:00:00 8

7

6

5

4 →

3

elevation (m) 2

1

0

−1

−2 0 2000 4000 6000 8000 10000 12000 14000 16000 distance along cross−section n=14 (m) →

Figure 10-4: Reference computation D 50 = 2.0 mm

38 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 10 November 2005

16−Mar−2003 00:00:00 10

8

6

→ 4

2 elevation (m)

0

−2

−4 0 2000 4000 6000 8000 10000 12000 14000 16000 distance along cross−section n=2 (m) →

Figure 10-5: D 50 = 1.0 mm

Figure 10-6: D 50 = 2.5 mm

When the mean grain size is decreased with 50% the amount of transported sediment increases, because the sand particles are easily picked up, therefore the morphological developments are more intense. This is confirmed by Figure 10-5. When the mean grain size is increased to 2.5 mm, the results do not vary significantly.

WL | Delft Hydraulics, RIZA, ON, TU Delft 39

Appendix 10 November 2005

01−Mar−2003 00:00:00 10

8

6

4 → 2

0 elevation (m)

−2

−4

−6

−8 0 2000 4000 6000 8000 10000 12000 14000 16000 distance along cross−section n=15 (m) → Figure 10-7: Ashld = 0.85

16−Mar−2003 00:00:00 10

8

6

4 → 2

0 elevation (m)

−2

−4

−6

−8 0 2000 4000 6000 8000 10000 12000 14000 16000 distance along cross−section n=14 (m) → Figure 10-8: Ashld= 1.2 When the coefficients of the bed slopes (Ashld and Bshld) are varied, the morphological activity do not change very much, this is depicted in the two figures above.

40 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 10 November 2005

01−Mar−2003 00:00:00 10

8

6

→ 4

2 elevation (m)

0

−2

−4 0 2000 4000 6000 8000 10000 12000 14000 16000 distance along cross−section n=14 (m) → Figure 10-9: Espir = 0.7

16−Mar−2003 00:00:00 10

8

6

4 → 2

0 elevation (m)

−2

−4

−6

−8 0 2000 4000 6000 8000 10000 12000 14000 16000 distance along cross−section n=14 (m) → Figure 10-10: Espir = 1.5

The Espir parameter is a coefficient which influences the secondary flow intensity. When this parameter is reduced, the influence of the spiral motion decreases, which ultimately reduces the transverse sediment transport capacity in bends, see Figure 10-9. The opposite reaction is noticeable in Figure 10-10.

WL | Delft Hydraulics, RIZA, ON, TU Delft 41

Appendix 10 November 2005

16−Mar−2003 00:00:00 10

5 → elevation (m)

0

−5 0 2000 4000 6000 8000 10000 12000 14000 16000 distance along cross−section n=2 (m) → Figure 10-11: Upstream boundary 15%

When the discharge distribution in the upstream boundary is changed, the flow in the bend is changed s well. In this case the distribution became skewer and therefore the morphological reaction was more intense, which means that more erosion is noticeable in the outer bend and the inner bend is more accreted.

08−Mar−2003 12:00:00 8

7

6

5 → 4

3 elevation (m)

2

1

0

−1 0 2000 4000 6000 8000 10000 12000 14000 16000 distance along cross−section n=15 (m) → Figure 10-12: Difference between Engelund- Hansen and Meyer-Peter-Müller

42 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 10 November 2005

Green line: Initial bed level at N = 15 (T=0) Dark blue line: Initial bed level at N = 2 (T =0) Orange line: Bed level MPM at N = 15 (T=3yrs) Light blue line: Bed level EH at N = 15 (T=3yrs) Dark red: Bed level MPM at N = e (T=3yrs) Brown line: Bed level EHat N = 15 (T=3yrs)

For completeness, a number of computations are repeated with the Meyer-Peter-Müller transport formula, which results are depicted in Figure 10-12. The differences between the results of both transport formulae are minimal.

WL | Delft Hydraulics, RIZA, ON, TU Delft 43

Appendix 11 November 2005

Appendix 11: Results reference situation

Reference situation Q = 3500 m3/s.

bed level in water level points (m) 5 7 x 10 12−Apr−2003 00:00:00

6 4.325

5 4.32 →

4

4.315

distance (m) 3

4.31 2

4.305 1 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 5 distance (m) → x 10 0

Figure 11-1: Reference bed level at t=42 days

44 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 11 November 2005

1.5 cum. erosion/sedimentation (m) 5 x 10 12−Apr−2003 00:00:00 1.3

1.1

4.325 0.9 0.7

4.32 0.5

→ 0.3

0.1 4.315 −0.1 distance (m) −0.3 4.31 −0.5

−0.7 4.305 −0.9

1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 −1.1 5 distance (m) → x 10 −1.3 −1.5 Figure 11-2: Cumulative erosion and sedimentation at t=42 days

depth averaged velocity, magnitude (m/s) 5 1.7 x 10 12−Apr−2003 00:00:00 4.33

1.6

4.325 1.5

4.32

→ 1.4

4.315 1.3 distance (m) 4.31 1.2

4.305 1.1

4.3 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 1 5 distance (m) → x 10 0.9 Figure 11-3: Depth averaged velocity at t=42 days

WL | Delft Hydraulics, RIZA, ON, TU Delft 45

Appendix 11 November 2005

Reference situation Q = 4500 m3/s.

8 bed level in water level points (m) 5 x 10 10−Apr−2003 00:00:00 4.33 7

4.325 6

4.32 5 →

4.315 4

distance (m) 3 4.31

2 4.305

1 4.3 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 distance (m) → x 10 0

Figure 11-4: Reference bed level at t = 42 days

cum. erosion/sedimentation (m) 3.5 5 x 10 08−Feb−2007 00:00:00 4.33 3.033 2.567

4.325 2.1 1.633

4.32 1.167

→ 0.7

4.315 0.2333

−0.2333 distance (m) 4.31 −0.7

−1.167

4.305 −1.633

−2.1 4.3 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 −2.567 distance (m) → 5 x 10 −3.033 −3.5 Figure 11-5: Cumulative erosion/sedimentation at t = 42 days

46 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 11 November 2005

depth averaged velocity, magnitude (m/s) 5 1.8 x 10 10−Apr−2003 00:00:00 4.33

1.7 4.325

1.6

4.32

→ 1.5

4.315 1.4 distance (m) 4.31 1.3

4.305 1.2

4.3 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 1.1 5 distance (m) → x 10 1 Figure 11-6: Depth averaged velocity at t=42 days

WL | Delft Hydraulics, RIZA, ON, TU Delft 47

Appendix 12 November 2005

Appendix 12: Results discharge withdrawal for Q=3500 m 3/s

Discharge withdrawal of 500 m3/s. In the following figures, the area of interest is the bend itself, therefore the scale limits are adapted, which means that the offtake and confluence bed level difference are off-scale.

(bed level Channel1) − (bed level ref.) (m) 0.75 5 x 10 12−Apr−2003 00:00:00 4.33 0.65

0.55 4.325 0.45

0.35 4.32 0.25 → 4.315 0.15 0.05

4.31 −0.05 distance (m) −0.15 4.305 −0.25

−0.35 4.3 −0.45

4.295 −0.55 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 distance (m) → x 10 −0.65 −0.75 Figure 12-1: Bed level difference Channel 1 and reference situation at t=42 days [m]

48 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 12 November 2005

(bed level Channel 2) − (bed level ref.) (m) 0.75 5 x 10 12−Apr−2003 00:00:00 4.33 0.65

0.55 4.325 0.45

0.35 4.32 0.25 → 4.315 0.15 0.05

4.31 −0.05 distance (m) −0.15 4.305 −0.25

−0.35 4.3 −0.45

4.295 −0.55 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 distance (m) → x 10 −0.65 −0.75 Figure 12-2: Bed level difference Channel 2 and reference situation at t=42 days [m]

(bed level Channel 3) − (bed level ref.) (m) 0.75 5 x 10 12−Apr−2003 00:00:00 4.33 0.65

0.55 4.325 0.45

0.35 4.32 0.25 → 4.315 0.15 0.05

4.31 −0.05 distance (m) −0.15 4.305 −0.25

−0.35 4.3 −0.45

4.295 −0.55 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 distance (m) → x 10 −0.65 −0.75 Figure 12-3: Bed level difference Channel 3 and reference situation at t=42 days [m]

WL | Delft Hydraulics, RIZA, ON, TU Delft 49

Appendix 12 November 2005

(bed level Channel 4) − (bed level ref.) (m) 0.75 5 x 10 12−Apr−2003 00:00:00 4.33 0.65

0.55 4.325 0.45

0.35 4.32 0.25 → 4.315 0.15 0.05

4.31 −0.05 distance (m) −0.15 4.305 −0.25

−0.35 4.3 −0.45

4.295 −0.55 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 distance (m) → x 10 −0.65 −0.75 Figure 12-4: Bed level difference Channel 4 and reference situation at t=42 days [m]

Discharge withdrawal of 250 m3/s Side channel 1

(bed level channel1) − (bed level ref.) (m) 2.5 5 x 10 12−Apr−2003 00:00:00 4.33 2.167

1.833 4.325 1.5

1.167 4.32 0.8333 → 4.315 0.5 0.1667

4.31 −0.1667

y coordinate (m) −0.5 4.305 −0.8333

−1.167 4.3 −1.5

4.295 −1.833 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.167 −2.5 Figure 12-5: Bed level difference Channel 1 and reference situation

50 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 12 November 2005

(bed level Channel 3) − (bed level ref.) (m) 2.5 5 x 10 10−Apr−2003 00:00:00 4.33 2.167

1.833 4.325 1.5

1.167 4.32 0.8333 → 4.315 0.5 0.1667

4.31 −0.1667

y coordinate (m) −0.5 4.305 −0.8333

−1.167 4.3 −1.5

4.295 −1.833 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.167 −2.5 Figure 12-6: Bed level difference Channel 3 and reference situation

(bed level Channel 2) − (bed level ref.) (m) 2.5 5 x 10 12−Apr−2003 00:00:00 4.33 2.167

1.833 4.325 1.5

1.167 4.32 0.8333 → 4.315 0.5 0.1667

4.31 −0.1667

y coordinate (m) −0.5 4.305 −0.8333

−1.167 4.3 −1.5

4.295 −1.833 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.167 −2.5 Figure 12-7: Bed level difference Channel 2 and reference situation

WL | Delft Hydraulics, RIZA, ON, TU Delft 51

Appendix 12 November 2005

0.75

0.65

(bed level Channel 2) − (bed level ref.) (m) 0.55 5 x 10 12−Apr−2003 00:00:00 4.33 0.45

4.328 0.35 0.25

→ 4.326 0.15 4.324 0.05 4.322 −0.05

y coordinate (m) 4.32 −0.15

4.318 −0.25

4.316 −0.35 1.96 1.965 1.97 1.975 1.98 1.985 1.99 5 x coordinate (m) → x 10 −0.45 −0.55

−0.65 −0.75 Figure 12-8: Bed level change in the bend it self of side channel 2 (blown-up)

morphologic grid 0.75 5 x 10 4.33 0.65

0.55 4.325 0.45

0.35 4.32 0.25 → 4.315 0.15 0.05

4.31 −0.05

y coordinate (m) −0.15 4.305 −0.25

−0.35 4.3 −0.45

4.295 −0.55 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −0.65 −0.75 Figure 12-9: Bed level difference due to the retraction of both water and sediment (blown up)

52 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 13 November 2005

Appendix 13: Results discharge withdrawal for Q=4500 m 3/s

Discharge withdrawal of 250 m3/s. A number of computations are repeated for a constant discharge of 4500 m3/s. The amount of retracted water in the following three figures is 250 m 3/s. The results of the computations Channel one and Channel three are equal, therefore only the figure of Channel three is shown.

(bed level Channel 2) − (bed level ref.) (m) 2.5 5 x 10 10−Apr−2003 00:00:00 4.33 2.167

1.833 4.325 1.5

1.167 4.32 0.8333 → 4.315 0.5 0.1667

4.31 −0.1667

y coordinate (m) −0.5 4.305 −0.8333

−1.167 4.3 −1.5

4.295 −1.833 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.167 −2.5 Figure 13-1: Bed level difference Channel 2 and reference situation

WL | Delft Hydraulics, RIZA, ON, TU Delft 53

Appendix 13 November 2005

(bed level Channel 3) − (bed level ref.) (m) 2.477 5 x 10 10−Apr−2003 00:00:00 4.33 2.147

1.817 4.325 1.486

1.156 4.32 0.8257 → 4.315 0.4954 0.1651

4.31 −0.1651

y coordinate (m) −0.4954 4.305 −0.8257

−1.156 4.3 −1.486

4.295 −1.817 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.147 −2.477 Figure 13-2: Bed level difference Channel 3 and reference situation

Discharge withdrawal of 500 m3/s. A number of computations are repeated for a constant discharge of 4500 m3/s. The amount of retracted water in the following three figures is 500 m 3/s.

(bed level Channel 1) − (bed level ref.) (m) 3 5 x 10 10−Apr−2003 00:00:00 4.33 2.6

2.2 4.325 1.8

1.4 4.32 1 → 4.315 0.6 0.2

4.31 −0.2

y coordinate (m) −0.6 4.305 −1

−1.4 4.3 −1.8

4.295 −2.2 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.6 −3 Figure 13-3: Bed level difference Channel 1 and reference situation

54 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 13 November 2005

(bed level Channel 3) − (bed level ref.) (m) 3 5 x 10 10−Apr−2003 00:00:00 4.33 2.6

2.2 4.325 1.8

1.4 4.32 1 → 4.315 0.6 0.2

4.31 −0.2

y coordinate (m) −0.6 4.305 −1

−1.4 4.3 −1.8

4.295 −2.2 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.6 −3 Figure 13-4: Bed level difference Channel 3 and reference situation

(bed level Channel 4) − (bed level ref.) (m) 3 5 x 10 10−Apr−2003 00:00:00 4.33 2.6

2.2 4.325 1.8

1.4 4.32 1 → 4.315 0.6 0.2

4.31 −0.2

y coordinate (m) −0.6 4.305 −1

−1.4 4.3 −1.8

4.295 −2.2 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 x coordinate (m) → x 10 −2.6 −3 Figure 13-5: Bed level difference Channel 4 and reference situation

WL | Delft Hydraulics, RIZA, ON, TU Delft 55

Appendix 14 November 2005

Appendix 14: Results of the discharge varying computations

The following figure shows the varying discharge, but the morphological factor is not processed, which means that horizontal (time scale) in the figure is not representative for the one used in the computation. Cross−section−1 5000

4500

4000 → /s) 3 3500

3000

2500 instantaneous discharge (m

2000

1500

15 Mar 29 Mar 12 Apr 26 Apr 10 May 24 May time → Figure 14-1: Varying discharge [m 3/s]

In the following figure, the bed level difference is shown between the reference situation and the situation where 500 m 3/s is withdrawn during at discharges larger than 3000 m 3/s. Not only water is withdrawn, but sediment as well.

56 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 14 November 2005

1.5

1.3

1.1 (bed level HW Channel 1 − (bed level HW ref.) (m) 5 0.9 x 10 25−May−2003 12:00:00 4.33 0.7

0.5 → 4.325 0.3

0.1

4.32 −0.1

y coordinate (m) −0.3

−0.5 4.315 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 −0.7 x coordinate (m) → x 10 −0.9

−1.1

−1.3 −1.5 Figure 14-2: Bed level difference between Channel 1 and reference situation

The next figure shows the difference of the bed level between the varying and non-varying discharge at the end of the flood period. The computational time is the same.

1.5

1.3

1.1 (bed level ref.) − (bed level constant discharge) (m) 5 0.9 x 10 16−Aug−2003 00:00:00 4.33 0.7

0.5 → 4.325 0.3

0.1

4.32 −0.1

y coordinate (m) −0.3

−0.5 4.315 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 5 −0.7 x coordinate (m) → x 10 −0.9

−1.1

−1.3 −1.5 Figure 14-3: Bed level difference between varying and non-varying discharge

WL | Delft Hydraulics, RIZA, ON, TU Delft 57

Appendix 15 November 2005

Appendix 15: Morphological activity

morphologic grid 5 x 10 4.328 0.75

0.65

0.55 4.326 0.45

0.35 4.324 0.25 → 0.15

4.322 0.05

−0.05

y coordinate (m) −0.15 4.32 −0.25

−0.35 4.318 −0.45

−0.55

4.316 −0.65 1.985 1.99 1.995 2 x coordinate (m) → 5 x 10 −0.75 Figure 15-1: Morphological activity at the offtake

morphologic grid 5 x 10 4.323 0.75

4.322 0.65 0.55 4.321 0.45

4.32 0.35 0.25 → 4.319 0.15

4.318 0.05

−0.05 4.317 y coordinate (m) −0.15

4.316 −0.25

−0.35 4.315 −0.45

4.314 −0.55

−0.65 4.313 1.96 1.962 1.964 1.966 1.968 1.97 1.972 5 −0.75 x coordinate (m) → x 10 Figure 15-2: Morphological activity at the confluence

58 WL | Delft Hydraulics, RIZA, ON, TU Delft Appendix 15 November 2005

depth averaged velocity, magnitude (m/s) 2 5 x 10 12−Apr−2003 00:00:00 4.33 1.9 1.8

4.325 1.7 1.6

4.32 1.5 → 1.4

4.315 1.3

1.2

y coordinate (m) 4.31 1.1

1

4.305 0.9

0.8 4.3 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 0.7 x coordinate (m) → 5 x 10 0.6 0.5 Figure 15-3: Depth averaged velocity, Reference situation

depth averaged velocity, magnitude (m/s) 2 5 x 10 12−Apr−2003 00:00:00 4.33 1.9 1.8

4.325 1.7 1.6

4.32 1.5 → 1.4

4.315 1.3

1.2

y coordinate (m) 4.31 1.1

1

4.305 0.9

0.8 4.3 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 0.7 x coordinate (m) → 5 x 10 0.6 0.5 Figure 15-4: Depth averaged velocity, Channel 3

WL | Delft Hydraulics, RIZA, ON, TU Delft 59

Appendix 15 November 2005

Appendix 16: Navigable width

8

7

bed level in water level points (m) 5 x 10 03−Mar−2003 00:00:00 6 4.33

5 → 4.325

4

4.32

y coordinate (m) 3

4.315 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 2 5 x coordinate (m) → x 10

1

0

Figure 16-1: bed level at the end of flood period

8

7

bed level in water level points (m) 5 x 10 04−Nov−2003 00:00:00 6 4.33

5 → 4.325

4

4.32

y coordinate (m) 3

4.315 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 2 2 5 x coordinate (m) → x 10

1

0

Figure 16-2: bed level at the end of low water period

60 WL | Delft Hydraulics, RIZA, ON, TU Delft