Wave-induced sediment transport at the small tidal inlet ‘Slufter’ of Texel, the Netherlands

Ralf Klein Breteler

MSc Thesis

Final version Utrecht, November 2009

Supervisors Prof. Dr. P. Hoekstra Dr. M. Van der Vegt

Department of Physical Geography Faculty of Geosciences Utrecht University

MSc Thesis

MSc Thesis

MSc Thesis

Wave-induced sediment transport at the small tidal inlet ‘Slufter’ at Texel, the Netherlands

Ralf Klein Breteler

MSc Thesis

Final version Utrecht, November 2009

Supervisors Prof. Dr. P. Hoekstra Dr. M. Van der Vegt

Department of Physical Geography Faculty of Geosciences Utrecht University

MSc Thesis

Preface

Preface

The 2008 research on the Slufter (Texel, the Netherlands) is part of a long term research program to develop a better understanding of the behaviour of small tidal inlets compared to more extensively studied larger inlet systems. The research has been carried out during 6 weeks in the period of September- October (storm season) and the central objective of the research is to gain insight the role of tidal- and wave-induced processes on the sediment transport patterns and morphologic development of Slufter systems.

The field campaign was carried out as part of the MSc-thesis Physical Geography – Coastal Systems. The research is related to general understanding of dynamics of small tidal inlets, a new line of research for dr. M. van der Vegt.

This research is subdivided into three interrelated subjects. This thesis presents the results of a process based field study on the effect of wave-driven processes on cross- and longshore sediment transport patterns in the breaker zone under calm conditions and on the spit-like platform (beach flat) when the Slufter system was completely inundated under storm conditions. Wiebe Kramer will focus on a more quantitative approach of the influence of tidal- and wave- driven processes on sediment import and export in the main channel of the Slufter system. Stijn van Puijvelde will discuss the influence of basin morphology on the behaviour of the system and vice versa

Thanks go to my fellow students for the great time and good atmosphere we had during the entire fieldwork. By their constructive discussions and perseverance the fieldwork was made a success. Additionally, I would like to express my gratitude to my two supervisors, prof. dr. P. Hoekstra and dr. Maarten Van der Vegt. I would also like to thank the technical staff Chris Roosendaal, Henk Markies and Marcel van Maarseveen. Without their help the fieldwork was not possible.

Finally acknowledgements go to Rijskwaterstaat for providing offshore data on waves and tides, Staatsbosbeheer and the Texel municipality for the necessary permits and the owners of Strand Paviljoen 29 for the provision of equipment storage facilities.

Preface

Contents

Contents

Preface ...... 5

Contents ...... 7

List of figures ...... 9

List of tables ...... 13

List of photographs ...... 15

Summary ...... 17

1 Introduction ...... 1 1.1 General problem ...... 1 1.2 Theory ...... 2 1.2.1 Slufter of Texel ...... 2 1.2.2 Stability of slufters ...... 3 1.2.3 Wave-induced hydrodynamics ...... 4 1.2.4 Wave-induced sediment transport ...... 6 1.3 Thesis objective and outline ...... 10

2 Field site and instrumentation ...... 12 2.1 Field work program and location ...... 12 2.2 Instruments ...... 14 2.2.1 Measuring Frames and sampling protocol ...... 14 2.2.2 Electromagnetic Flow Meter (EMF) ...... 15 2.2.3 Pressure Sensor ...... 15 2.2.4 Optical Backscatter Sensor (OBS) ...... 15 2.2.5 DGPS ...... 16 2.3 Data calibration ...... 16 2.4 Hydrodynamics calculations ...... 18 2.4.1 Wave heights ...... 18 2.4.2 Velocities ...... 19 2.5 Suspended sediment transport calculations ...... 21 2.5.1 Cross-shore sediment fluxes ...... 21 2.5.2 Longshore sediment fluxes ...... 23

Contents

3 General observations and conditions ...... 24 3.1 Offshore boundary conditions ...... 24 3.2 Geomorphologic change ...... 26

4 Hydrodynamics results ...... 30 4.1 Breaker zone ...... 30 4.1.1 Spatial and temporal differences in (relative) wave heights ...... 30 4.1.2 Mean currents ...... 32 4.1.3 Cross-shore mean currents ...... 33 4.1.4 Longshore mean currents ...... 37 4.1.5 Intra wave effects: wave skewness ...... 40 4.2 Beach flat (spit-like platform) ...... 42 4.2.1 Mean currents ...... 42 4.2.2 Intra wave effects: infragravity energy ...... 43

5 Sediment transport results ...... 45 5.1 Sediment transport in the breaker zone ...... 45 5.1.1 Concentrations and cross-shore velocity time series ...... 45

5.1.2 Cross-shore sediment fluxes (Hs,off < 1.0 m) ...... 46

5.1.3 Cross-shore sediment fluxes (Hs,off = 2-3 m) ...... 53 5.1.4 Depth-integrated longshore sediment fluxes...... 56

5.2 Sediment transport on the beach flat (Hs,off = 4-5 m) ...... 59 5.2.1 Concentrations and cross-shore velocity time series ...... 59 5.2.2 Cross-shore sediment fluxes ...... 60

6 Discussion ...... 67

6.1 Transport for moderate wave energy conditions (Hs,off < 3 m) ...... 67 6.1.1 Cross-shore sediment transport in the breaker zone ...... 67 6.1.2 Longshore sediment transport in the breaker zone ...... 68

6.2 Inundation beach flat (Hs,off > 4 m) ...... 69 6.3 Wave-driven influence on the Slufter system ...... 71 6.4 Future recommendations ...... 72

Conclusions ...... 73

References ...... 75

List of figures

List of figures

Figure 1.1 Satellite image of the Slufter system including scale. Image was taken some years ago (Google Earth image, 2008) Figure 1.2 The 10 year-period wind climate for Texel, obtained from the Texelhors meteorological station (KNMI, Verkaik, pers. comm. in Van der Molen, 2002). Wind directions are set from the North (0 degrees) and wind speed increases from the centre to the outside. The areas denote the number of hourly observations. Moderate SW storms dominate (>4000 observations) (Van der Molen, 2002). Figure 1.3 Progressively changing wave forms when approaching the shore (Grasmeijer, 2002) Figure 1.4 Change in form of path of water particles when approaching the shore (Grasmeijer, 2002) Figure 1.5 A wave signal for non-breaking waves. Infragravity energy is bound to gravity wave groups. Figure 1.6 The cross-shore distribution of the longshore current. Rr denotes the longshore force on the water column caused by excess flow momentum. A shear force T balances this force (Grasmeijer, 2002). Figure 2.1 Height contour map for the Slufter system based upon merged DGPS measurements and AHN data. Main- and miniframe locations are indicated on the map. Pre- and post-storm breaker zone sites are shown by respectively north- and southward located frame in the sea (Van Puijvelde, 2009). Figure 2.2 The calculation of Hs. Individual waves are isolated by the zero-down crossing method. Subsequently the top 1/3th of waves are averaged to obtain the significant wave height. Figure 2.3 Velocities in X and Y direction for 256 sec. Overall wave incidence angle is given by the alpha coefficient of the linear regression. Figure 3.1 Offshore boundary conditions during the fieldwork period. Offshore data from the Eierlandsche Gat wave buoy are taken from the 30-100 MHz spectrum and involve A) The significant wave height, B) The significant period, C) The wave angle relative to the North (The coastline is orientated at 303° N). D) The water levels determined from the frames in the breaker zone, E) The offshore tidal signal determined by T-tide F) the set-up or set-down. F) The day-averaged wind direction measured at the KNMI station at de Kooy, Texel, G) The day averaged wind speeds (dm/s). Figure 3.2 3D-map of the Slufter system based upon merged AHN and DGPS data (van Puijvelde, 2009). Figure 3.3 DGPS measurements of the lateral migration of the main channel and beach flat elevation for the period of 12/09 – 11/10. Figure 3.4 Coastal change in a cross-shore section close to (~ 50 m) the Slufter main channel inlet mouth. At 12/09 the cross-section of the Slufter was measured from the beach (right) over the beach flat and the channel (left). At 12/09 a ridge/runnel was visible near the Slufter inlet mouth which has completely disappeared during the first storm peak. Figure 3.5 Coastal change close to the location of the miniframes (second period). Frames were located close to the seaward end of the 07/10 profile and are referred to as 1 (landward) and 2 (seaward).

List of figures

Figure 4.1 The significant wave heights, Hs (m) for the fieldwork period; Offshore wave heights compared to locally measured wave heights in the breaker zone shortly updrift of the Slufter inlet.

Figure 4.2 The significant wave heights, Hs (m) for the last part of the fieldwork period. Figure 4.3 The relative significant wave height Hs/h, the residual water depth (h) and the significant wave height for the landward and seaward located frame. Inconsistencies occur at the start of the measuring series, so initial values of the measurement series are left out of analysis. Figure 4.4 Mean cross (U) and longshore (V) currents (m/s) in the breaker zone Figure 4.5 Spatial and temporal differences in mean cross-shore currents, water levels and (relative) significant wave heights. A,B) temporal differences for low and high wave conditions, A, C) Spatial differences for the land-and seaward frame. Figure 4.6 Relations between mean cross-shore currents and the relative significant wave heights. A,B) temporal differences for high and low wave conditions, A, C) Spatial differences for the land-and seaward frame. Figure 4.7 Mean longshore currents, wave incidence angle alpha in degrees to shore normal, Hs, Hs/h and h in the nearshore for the land and seaward frame. Longshore currents increase significantly when Hs> 0.2 and Hs/h > 0.3. Figure 4.8 The skewness of waves for the land and seaward frame in the same period for different relative significant wave heights. A trend line is plotted which indicates a positive relation between S and Hs-h. Figure 4.9 The skewness of waves for the seaward frame during two distinct wave height scenario’s for different relative significant wave heights. A trend line is plotted which indicates a positive relation between S and Hs-h. Figure 4.10 a) first period of the beach flat inundation; plotted are the water depth (h), the significant wave height and the wave-directed cross-shore velocity. First period is measured by the seaward frame and second period by the landward frame. Figure 4.11 Power spectral density of waves on the beach flat for a) initial flooding, b) peak flooding and c) water retreat based upon 256 sec. 8 halfway overlapping 512- points Fourier transforms. Figure 4.12 Dominance of free infragravity waves entering the basin, high-frequency oscillations exist as infragravity wave irregularities; all gravity waves have broken in the breaker zone in the nearshore. Infragravity waves are heavily skewed (onshore directed velocities are generally higher than offshore). Figure 5.1 The mean cross-shore current velocities (m/s), averaged concentrations (kg/m3) and sediment fluxes (kg/m2/s) for A,B) spatial differences in the cross shore and A,C) low-, and high-wave conditions Figure 5.2 Low wave conditions (seaward frame) - Measured 256 s averaged sediment fluxes a,b) high frequency, c,d) low-frequency, e,f) mean and g,h) net fluxes for the lowest (ca 5 cm) and highest (ca 20 cm) OBS sensor related to the relative significant wave height (Hs/h). Figure 5.3 Low wave conditions (seaward frame) – Oscillatory velocity- and concentration time series used for co-spectral analysis. a) High and low-frequency cross-shore velocity, b) suspended concentrations at the OBS at 5 cm, c) suspended concentrations at the OBS at 10 cm, d) suspended concentrations at the OBS at 20 cm. Figure 5.4 Low wave conditions (seaward frame) – Co-spectral analysis of cross-shore oscillatory velocities and sediment concentrations of frequency domain converted time-series: a) power spectral densities, b) co-spectra, c) coherence squared diagrams and d) phase diagrams.

List of figures

Figure 5.5 Low wave conditions (Landward frame) - Measured 256 s averaged sediment fluxes a,b) high frequency, c,d) low-frequency, e,f) mean and g,h) net fluxes for the lowest (ca 5 cm) and highest (ca 20 cm) OBS sensor related to the relative significant wave height (Hs/h). Figure 5.6 1) Low wave conditions (Seaward frame) - The relative contributions of 1 a,b) high- frequency, 1 c,d) low-frequency and 1 e,f) mean flows to net suspended sediment fluxes. 2) Low wave conditions (landward frame) - The relative contributions of 2 a,b) high-frequency, 2 c,d) low-frequency and 2 e,f) mean flows to net suspended sediment fluxes. Figure 5.7 High wave conditions (Landward frame) - Measured 256 s averaged sediment fluxes a,b) high frequency, c,d) low-frequency, e,f) mean and g,h) net fluxes for the lowest (ca 5 cm) and highest (ca 20 cm) OBS sensor related to the relative significant wave height (Hs/h). Figure 5.8 High wave conditions (landward frame) – Co-spectral analysis of cross-shore oscillatory velocities and sediment concentrations of frequency domain converted time-series: a) power spectral densities, b) co-spectra, c) coherence squared diagrams and d) phase diagrams. Figure 5.9 a) Concentration, b) velocity and c) suspended transport profile for a depth of z= 0.05 m – Hw and a mean longshore velocity of 0.15 m/s. Figure 5.10 a) Concentration, b) velocity and c) suspended transport profiles used for depth- integrated suspended longshore transport rates for low wave conditions. Figure 5.11 a) Concentration, b) velocity and c) suspended transport profiles used for depth- integrated suspended longshore transport rates for high wave conditions. Figure 5.12 The cross-shore distribution of depth-integrated suspended and time-averaged longshore transport rates constructed for part of the period used in cross-shore analysis, constructed by the product of depth-integrated transport profiles: a) landward frame and b) seaward frame Figure 5.13 Cross-shore mean velocities over the beach flat and measured concentrations to obtain the mean fluxes during the flooding events Figure 5.14 First beach flat largest inundation - Measured 5-min averaged sediment fluxes a,b) high frequency, c,d) low-frequency, e,f) mean and g,h) net fluxes for the lowest (ca 5 cm) and highest (ca 20 cm) OBS sensor related to the relative significant wave height (Hs/h). Figure 5.15 Beach flat largest inundation - The relative contributions of a,b) high-frequency, c,d) low-frequency and e,f) mean flows to gross suspended sediment fluxes. Figure 5.16 Second beach flat largest inundation - Measured 5-min averaged sediment fluxes a,b) high frequency, c,d) low-frequency, e,f) mean and g,h) net fluxes for the lowest (ca 5 cm) and highest (ca 20 cm) OBS sensor related to the relative significant wave height (Hs/h). Figure 5.17 First inundation - Peak flood condition (h = 0.8 and Hs/h = 0.3) - Velocity- and concentration time series used for co-spectral analysis. a) High and low-frequency fluxes of the cross-shore velocity, b) suspended concentrations at the OBS at 5 cm, c) suspended concentrations at the OBS at 10 cm, d) suspended concentrations at the OBS at 20 cm. Figure 5.18 Second inundation - Peak flood condition (h = 0.6 and Hs/h = 0.3) - Velocity- and concentration time series used for co-spectral analysis. a) High and low-frequency fluxes of the cross-shore velocity, b) suspended concentrations at the OBS at 5 cm, c) suspended concentrations at the OBS at 10 cm, d) suspended concentrations at the OBS at 20 cm. Figure 5.19 First inundation - Peak flood condition (h = 0.8 m , Hs/h = 0.3) – Co-spectral analysis of cross-shore oscillatory velocities and sediment concentrations of to frequency domain converted time-series: a) power spectral densities, b) co-spectra, c) coherence squared diagrams and d) phase diagrams.

List of figures

Figure 5.20 Second inundation - Peak flood condition (h = 0.8 m , Hs/h = 0.3) – Co-spectral analysis of cross-shore oscillatory velocities and sediment concentrations of to frequency domain converted time-series: a) power spectral densities, b) co-spectra, c) coherence squared diagrams and d) phase diagrams. Figure 5.21 First inundation - Initial flood (h = 0.5 m , Hs/h = 0.35) – Co-spectral analysis of cross-shore oscillatory velocities and sediment concentrations of to frequency domain converted time-series: a) power spectral densities, b) co-spectra, c) coherence squared diagrams and d) phase diagrams. Figure 5.22 First inundation – Falling tide and outflow (h = 0.55 m , Hs/h = 0.22) – Co-spectral analysis of cross-shore oscillatory velocities and sediment concentrations of to frequency domain converted time-series: a) power spectral densities, b) co-spectra.

List of tables

List of tables

Table 3.1 Storm conditions near the Slufter system Table 3.2 Sediment grain sizes at the slufter system as found by sieving in the FG lab. Grain sizes are averaged over 3 samples.

List of tables

List of photographs

List of photographs

Photo 2.1 The main frame and instruments: A) EMFs and OBS instruments B) Measurement construction assembled on main frame; The miniframe is not yet constructed on the main frame C) Main frame in live action Photo 2.2 Miniframes and instruments, configuration and live action. The datalogger can be seen on top of the miniframe. The single EMF is located left of the OBS triplet. Photo 2.3 DGPS base with the receiver on the right hand and the radio at the left hand. Photo 3.1 Merged photographs (ca 200°) of the completely inundated Slufter basin at 01/10. Photo 3.2 Initial pre-storm situation of the Slufter channel and mouth. Photo 3.3 The lateral migration of main channel. Photo 4.1 Infragravity waves entering the basin during a flooding event.

List of photographs

Summary

Summary

In September and October 2008 a field campaign was executed at the small tidal inlet ‘Slufter’ at Texel, the Netherlands. The aim is to improve our understanding of small tidal inlet systems. Measurements were done on hydrodynamics, sediment transport and (changes in) morphology.

This thesis focuses on the relative importance of wave-induced cross- and longshore sediment transport processes in the breaker zone under normal conditions and on the wave-induced cross-shore transport processes on the spit-like platform (beach flat) during inundation of the inland basin under storm and spring tide conditions (Hs,off = 4-5 m).

A storm occurred from 01/10 – 05/10 in which the basin of the inlet was completely inundated. During the inundation measurements were done on the spit like plat form (beach flat). The beach flat was subject to mean onshore velocities up to + 0.5 m/s. Highest waves entering the beach flat are in the far infragravity frequency band for the initial and peak flooding situations. Mean fluxes contribute to more than 75% of the net suspended sediment transport. Infragravity fluxes are dominant in the oscillatory velocity signal and are mainly onshore directed, contributing 15- 20% to the gross suspended transport.

During low-moderate wave energy conditions measurements were done in the breaker zone. In the breaker zone infragravity waves were important for net offshore transport during low wave conditions (Hs,off < 1 m). Mean fluxes, which are mainly offshore directed by wave– driven undertow and high-frequency fluxes, which are mainly positive due to wave skewness contributed stronger to the net transport than low-frequency fluxes, but frequently were of opposite sign. For high wave conditions (Hs,off = 2-3 m), net suspended transport was dominated by offshore directed mean fluxes, partly compensated by higher onshore high- frequency fluxes. Low-frequency fluxes were only a fraction larger than for low wave conditions.

Measured longshore currents show strong positive relation with the relative significant wave height. In the nearshore depth-integrated longshore fluxes are significantly higher than cross- shore fluxes.

Summary

Introduction

1 Introduction

1.1 General problem

In recent years natural development of coastal systems has become an important issue in the Netherlands. A particular example of natural development is limitation of human response in the case of local dune breaches. Small tidal inlets, in Dutch also known as ‘Slufters’ are created in this way.

Although extensive research is done on larger tidal inlet systems in the Wadden Sea, the Netherlands, the morphodynamic behaviour of slufters is still poorly understood. Present-day stability theory is not valid for small tidal inlets as it predicts that small inlets should close in a limited amount of time. It is however common that small tidal inlets can exist for decades and longer.

Opposed to large tidal inlet systems, Slufters are subject to larger differences in hydrodynamics and sediment transport patterns during storm/ calm weather conditions. During calm weather conditions tidal exchange is restricted to the main channel, whereas under storm and spring tide conditions the complete basin is inundated. It seems that overall flooding during storm conditions is important in small tidal inlet dynamics. It is however unclear which processes are important during such a flooding event.

Former research on small tidal inlets took place at the ‘Verdronken Zwarte Polder Slufter’ (25 ha) at Zeeuws-Vlaanderen (Zuijderwijk, 2006) and the Slufter (400 ha) at Texel (Reneerkens, 2003). In this research, extensive measurements are carried out at the Slufter system (Texel) which enable us to investigate the underlying processes important for the morphodynamic behaviour and stability of small tidal inlet systems.

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Introduction

1.2 Theory

1.2.1 Slufter of Texel

The Slufter, Texel (Figure 1.1) is located on the NW coast of the largest barrier island in front of the Dutch Wadden coast. Closest related to slufter systems are small wave-dominated tidal inlets, characterized by a small basin and frequent geomorphological reworking by wave activity.

Figure 1.1 Satellite image of the Slufter system including scale. Image was taken some years ago (Google Earth image, 2008)

The Slufter covers an area of about 400 ha (Durieux, 2005). The Slufter differs from most tidal inlet systems as for average tidal conditions, most parts of the Slufter are elevated above mean high water (MWL) (Reneerkens, 2003). Only tidal creeks are under direct influence of tides, whereas large parts of the basin are only inundated during spring tide and/or flooding events (Basisrapport Zandige Kust (1995) in Durieux, 2005). Mean tidal range is in the order of 1.4 m, and analysis of wave data from measuring station the Eierlandse Gat nearby show that mean significant wave height is 1.3 m from the west-southwest, with a mean period of 5 s (wind wave climate). Wind generated waves can reach heights of 6 m during storms, and surges of more than 2 m have been measured. Longshore currents can reach magnitudes of 2 m/s under combined influence of wind, waves and tides (Elias and Van der Spek, 2006). Wind direction is dominantly from the SW as can be seen in Figure 1.2 which shows wind data over a period of 10 years (1981-1991) from the meteorological station Texelhors. Moderate storms from the west dominate (Van der Molen, 2002) although it should be noted that severe storms commonly are from the NW.

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Introduction

Figure 1.2 The 10 year-period wind climate for Texel, obtained from the Texelhors meteorological station (KNMI, Verkaik, pers. comm. in Van der Molen, 2002). Wind directions are set from the North (0 degrees) and wind speed increases from the centre to the outside. The areas denote the number of hourly observations. Moderate SW storms dominate (>4000 observations) (Van der Molen, 2002).

In international literature, small tidal inlet systems often are situated in a swell-wave dominated environments. Often these systems have the tendency to close seasonally or permanently by longshore sediment transport. It should be stressed that the Slufter is situated under sea wave conditions where such processes are less likely to be observed and no river outflow occurs which could open the inlet.

1.2.2 Stability of slufters

One of the interesting aspects of the Texel Slufter is the relative stability of the Slufter system, while present-day stability theory predicts that small wave dominated systems should close in limited time. Large scale tidal inlet systems have extensively been studied and most stability theory is derived from these large systems. Two important stability relationships have been derived for these kinds of systems, i.e the dynamic equilibrium approach (Escoffier, 1940; O’Brien, 1969; Van de Kreeke, 1985) where tidal prism is related to cross-sectional area and the geomorphologic approach (Gao & Collins, 1993) where stability is related to tidal prism and longshore drift (see literature review Klein Breteler, 2008 and MSc thesis van Puijevelde, 2009 on Slufter 2008 Data DVD).

A simple indication often used for determining inlet stability is based upon the rate of change in geomorphologic characteristics (Gao & Collins, 1993). The empirical formula often used (Eq. 1.1) is

Ω = (1.1)

𝑟𝑟 𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡 3 where Ω is the tidal prism per spring tidal cycle (m ) and Mtot is the total amount of longshore drift (m3/year) (Gao and Collins, 1993; Castelle et al., 2007). Inlets can be classified from stable tidal dominated (r > 150) to unstable wave dominated systems (r < 20). According to this ratio the Slufter will be classified as unstable wave dominated system

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Introduction

Although classified as unstable by this ratio, the Slufter was created in 1858 during a heavy storm and still exists today. Therefore, doubt arises in the application of present-day stability theory to small tidal inlet systems. It must be noted that in recent years Slufter inlet stability has obtained an artificial character because the main channel is relocated each 4-5 years after it has migrated downdrift and started threatening the northern dune row.

1.2.3 Wave-induced hydrodynamics

Incident waves approaching the shore can be subdivided in sea and swell waves. Short waves are short waves locally formed, propagating in the area where they have been created. Short waves are characterized by high steepness, relative short periods (L/H = 20, T = 5-10 s) and more intensive breaking in the surfzone (Van Rijn, 1994). Flatter, longer period swell waves (L/H = 100, T = 10-30 s) are formed on the ocean and have traveled ahead of the wind field (Van Rijn, 1994). More breaking will occur in the nearshore zone under high energy short wave conditions.

When waves approach the shore they deform due to difference in propagation velocities between the crest and trough of the wave. Shoaling waves progressively change velocity and shape (Figure 1.3). Associated with the process of shoaling, waves become skewed: the onshore velocity under the wave crest increases as waves approach the shore (Yu et al., 2003; Grasmeijer, 2002) and becomes of shorter duration, whereas smaller offshore directed flows are of longer duration. Additionaly, nearly breaking waves have the tendency to become vertically asymmetric (toppled forward), which is usually referred to as asymmetry.

Figure 1.3 Progressively changing wave forms when approaching the shore (Grasmeijer, 2002)

The orbital motions (Figure 1.4) transform with decreasing water depths from a circular path to a elliptical path and eventually to a back and forth motion (Van Rijn, 1994).

Figure 1.4 Change in form of path of water particles when approaching the shore (Grasmeijer, 2002)

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Introduction

Above the trough level of waves, an onshore mass flux is present. The wave-induced mass flux is compensated by the undertow (Cayocca, 2001), an offshore directed mean current below the troughs of waves (Osborne and Greenwood, 1990). Near the beach wave energy is transferred to lower and higher frequencies. Higher frequencies ultimately produce turbulence whereas lower frequencies produce longer period infragravity waves which result in oscillations in current velocities (Russel, 1993).

Short waves approaching the shore typically show a grouped structure (Grasmeijer, 2002). For non- breaking short waves infragravity energy (T = 20-300 s) is still restricted to wave group trains as bound long waves. The bound long wave is forced by radiation stress variations due to the change in wave height. A higher radiation stress (Sxx ) under higher waves is balanced by lower water levels (Figure 1.5) and higher water levels under smaller waves (Longuet-Higgins and Stewart, 1964 in Grasmeijer, 2002). The bound long wave typically lags behind the wave groups when waves approach the shore (Elgar and Guza, 1985 in Grasmeijer, 2002). During short wave breaking, group bound long waves are gradually released as free waves (Baldock et al., 2003) until travelling with a propagation velocity of in the saturated breaking zone (Grasmeijer and Van Rijn, 1999 in Grasmeijer, 2002).

√𝑔𝑔ℎ

Figure 1.5 A wave signal for non-breaking waves. Infragravity energy is bound to gravity wave groups.

When oblique incident waves approach the shore they undergo refraction. This is caused by variations in water depth or the presence of a current such as near the mouth of a tidal inlet system. The relative significant wave height (Hs/h) is used in this report as conditional wave parameter. The most important advantage of the use of this parameter is its use as breaker criterion (Ruessink et al., 1998). Another advantage is its frequent use in international literature (Osborne and Greenwood, 1992; Ruessink et al., 1998). At Terschelling, onset of breaking occurred at Hs/h = 0.33 and all waves were broken at 0.59 (Van Enckevort and Reincke, 1996 in Ruessink et al., 1998).

Where waves break under an angle to the shore, a longshore current is generated in the surf zone due to excess flow momentum, resulting from a cross-shore gradient in the longshore directed radiation force (Sxy ) as formulated by Longuet-Higgins and Stewart (1964) in Van Rijn (1994). The momentum is spread in the cross-shore following the zone of wave breaking of an irregular wave field (Grasmeijer, 2002). Modeled wave-generated longshore currents are generated shortly before initial

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Introduction wave breaking, peak at maximal wave breaking and gradually decline in magnitude further shorewards (Figure 1.6).

Figure 1.6 The cross-shore distribution of the longshore current. Rr denotes the longshore force on the water column caused by excess flow momentum. A shear force T balances this force (Grasmeijer, 2002).

Additional driving forces of the longshore current comprise a longshore gradient in wave set-up and wave heights (Ranasinghe et al., 1999), wind and tides. The magnitude of the longshore current is determined by breaker height and the angle of wave incidence (θ max = 45°) (Van Rijn, 1994).

1.2.4 Wave-induced sediment transport

Waves are responsible for sediment transport in two ways; by stirring up sediment and by generating wave-driven cross- and longshore currents. Sand is suspended into the water column by wave orbital motions near the bed and/or breaking waves (Russel,1993).

Wave action increases bottom shear stress which increases the sediment concentration in the water column. Shear stress is generated as orbital motions of waves pass over the bottom. Part of the energy generated by shear stress is lost in bottom friction, yet another part is responsible for bedload- and suspended sediment transport (Gerritsen et al., 2003). Grains are picked up from bed level if the bottom shear stress is larger than a critical value (Eq 1.2);

b crit ; * 2 > *crit 2 (1.2)

τ > τ ρu ρu in which τb is the bottom shear stress, ρ is the density of water and u* is the friction velocity. If the bottom shear stress is smaller than the critical value, drag and lift forces on the particle are too small to overcome the gravity forces holding the grain connected to the bed (de Swart and Zimmerman, 2009).

Sediment transport includes bed load qb and suspended load transport qs. Both transport rates increase if the bottom shear stress τb is higher (de Swart and Zimmerman, 2009). Bedload transport occurs if

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Introduction

the friction velocity is larger than its critical value but smaller than the sediment settling velocity ws

(u*crit < u* < ws) whereas suspended load transport occurs if the friction velocity is higher than the settling velocity (u* > ws) (de Swart and Zimmerman, 2009).

For bedload transport, sediment is transported in a thin layer (some grain diameters thick) close to the bed. If grains enter the fluid region, they are transported as suspended load (de Swart and Zimmerman, 2009). Suspended transport is often computed by assuming a logarithmic velocity profile and a concentration profile derived from the balance between turbulent mixing and gravity forces acting on particles (Cayocca, 2001).

Cross-shore sediment transport

Cross-shore suspended sediment transport results from short waves, low frequency (infragravity) waves and mean currents (Osborne & Greenwood, 1992). Interaction of high and low frequency waves leads to different sediment transport directions under breaking and non breaking (shoaling) wave conditions (Van Rijn, 1993).

The net cross shore sediment transport net can be decomposed into the components of sediment transport induced by mean currents mean and oscillatory wave motion osc (which include gravity and infragravity bands) (Osborne & Greenwood, 1992; Russel , 1993; Ruessink et al., 1998) where c is the instantaneous suspended sediment concentration (kg m-3) and u is the instantaneous cross shore velocity (ms -1). Grouped shoaling waves generally induce onshore sediment transport rates at short-wave frequencies whereas at the same time produce offshore directed transport rates at low frequencies (Osborne and Greenwood, 1992b).

Skewness and asymmetry of propagating short waves generally induce onshore directed transport in the wave cycle. This depends however strongly on bed-form conditions and sediment characteristics. Field measurements indicate that asymmetric ripples can cause the sediment transport direction to shift to offshore directions with increasing wave asymmetry of a propagating wave (Osborne and Greenwood, 1992b). This effect is most pronounced at low heights above the bed. A shift in sediment transport direction occurs due to phase differences in concentration- and velocity fields. Reversal takes place if sediment elevated from the bed by the positive phase of wave motion is transported backwards by the offshore directed phase of wave motion while in concentration (Inman and Bowen (1962) in Osborne and Greenwood, 1992b). Phase differences between concentration and velocity fields are more pronounced under higher wave conditions, when increased oscillatory motion causes higher turbulence. Larger sediment quantities are carried into suspension and a longer time lag for particle settling will occur (Osborne and Greenwood, 1992b).

For short wave conditions suspended sediment concentrations increase dramatically, especially in the breaker zone, and sediment particles are mixed higher into the water column. Co-spectral analysis of cross-shore velocities by Osborne & Greenwood (1992a) show that sediment transport rates are also found to be larger for short wave frequencies than for swell frequencies, although sediment fluxes

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Introduction show considerable variability in on- and offshore direction and time-averaged sediment transport is quite balanced. Under short wave conditions the onshore directed oscillatory sediment transport is often balanced by a offshore directed transport caused by mean currents (Osborne and Greenwood, 1992a). Although sediment transport rates are larger for short waves, opposing transport processes often result in a mass balance in local sediment transport (Osborne & Greenwood, 1992a).

Generally, mean currents (undertow) and infragravity oscillatory motions cause offshore transport (Russel, 1993; Osborne & Greenwood, 1992). Dominance of on/ offshore transport is however strongly dependent on the type of low frequency waves. Group-bound long wave oscillations produce offshore directed sediment transport outside the surfzone. As described by Longuet-Higgins and Stewart (1962) in Osborne and Greenwood (1992b), this is caused by the offshore phase of low frequency modulation of the velocity field of group-bound long waves in combination with the sediment stirring effect of short waves in the wave group. During short wave breaking, group bound long waves can be released as free waves which can be trapped along the shore line as edge waves or reflect back as leaky waves (Baldock et al., 2003). Usually the shift to free long waves is associated with a onshore shift in net sediment transport shoreward of the region of wave breaking (Osborne and Greenwood, 1992a).

Longshore sediment transport

The longshore transport is the flow of sand along the shoreline under the influence of waves, tides and wind generated currents. Estimates of long shore transport rates have been collected over the world by sand accumulation at jetties, tracer methods (Vila-Concejo et al., 2004b; Balouin et al., 2005) and sediment trapping to obtain bed load transport rates. Longshore suspended sediment fluxes can either be calculated or obtained by concentration and velocity measurements (Miller, 1999). Calculation of longshore fluxes is commonly done by means of three methods: energetic methods, force balance methods and dimensional analysis (Van Wellen et al., 2000).

The longshore sediment flux can be computed (Eq. 1.3) from measured velocity and concentration profiles by time-averaging the products of the instantaneous concentration, ( , , ) and the ( , , ) instantaneous longshore velocity, 𝑐𝑐 𝑥𝑥 𝑧𝑧 𝑡𝑡𝑖𝑖 𝑣𝑣 𝑥𝑥 𝑧𝑧 𝑡𝑡𝑖𝑖 1 ( , ) = =1 ( , , ) ( , , ) (1.3) 𝑁𝑁 𝐹𝐹 𝑥𝑥 𝑧𝑧 𝑁𝑁 ∑𝑖𝑖 𝑐𝑐 𝑥𝑥 𝑧𝑧 𝑡𝑡𝑖𝑖 𝑣𝑣 𝑥𝑥 𝑧𝑧 𝑡𝑡𝑖𝑖 where ( , ) is the longshore sediment flux, expressed as the rate per unit area at position (x) in cross-shore direction and height (z) in the vertical. 𝐹𝐹 𝑥𝑥 𝑧𝑧

Under storm conditions, the wave-induced component of the longshore current becomes increasingly important. Yu et al (1993) and Miller (1999) found that in the wave breaking zone, maximum sediment concentrations are attained. In Miller (1999) the concentration term in Eq. 1.3 is often found

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Introduction to vary more strongly than the velocity term under low-moderate and storm conditions, although this depends strongly on local conditions.

The significance of waves on the longshore transport under storm conditions can be illustrated by the study of Kana & Ward (1980) in Miller (1999) who found that under storm conditions (H = 3.0 m) total suspension load can be about 10 times higher and longshore fluxes 60 times higher than in the calm period after the storm. Responsible factors include increased stirring by higher waves, stronger developed longshore currents and stronger progressive edge and shear waves. Because during storms transport rates are significantly higher, storm events can contribute significantly to the annual longshore sediment budget of an area.

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Introduction

1.3 Thesis objective and outline

The objective of this thesis is to improve our understanding of wave-induced hydrodynamics and sediment transport patterns at small tidal inlet systems a) in the nearshore zone and b) inside the system when inundated under storm conditions.

The dynamics of Slufters are different compared to larger inlet systems. Changes in water level are associated with strong differences in tidal exchange, which under normal conditions is restricted to the main channel but during storm and/or spring tide conditions is observed over the entire entrance over spit like platforms (here the platform is termed beach flat). The strong difference in dynamics is unique for Slufter systems. During normal conditions cross-and longshore currents occur in the nearshore. Especially longshore sediment transport is thought to be important for main channel migration and interaction with import/export patterns.

During inundation of spit-like platforms, cross-shore transport due to overwash also occurs inside Slufter systems. Up to now, no measurements have been done during inundation of spit-like platforms in such small systems, while it is expected that transport rates over such platforms are crucial for import/export of sediment because it occurs over such a large area.

We want to study and explain which wave-driven sediment transport patterns are important during normal and storm/spring-tide conditions and which hydrodynamic processes responsible for these patterns. Research questions are directed to a process-based approach of wave-driven influences.

Morphodynamics • What is the influence of wave-driven cross- and longshore transport processes on the morphodynamic behaviour of the Slufter system under storm- and low- moderate wave energy conditions?

Hydrodynamics • How does the magnitude and direction of wave skewness and mean cross-shore currents vary spatially and temporally in cross-shore direction in the breaking zone for high- and low wave conditions? • How does the magnitude and direction of the longshore current vary spatially and temporally across the breaker zone for varying wave incidence angles and wave heights? • How do wave characteristics and mean cross-shore currents vary spatially and temporally over the inundated beach flat during spring tide and/or storm surges?

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Introduction

Sediment transport • How does the magnitude and relative contribution of mean flows, infragravity and gravity oscillatory motions to the sediment transport fluxes vary spatially and temporally in cross- shore direction in the breaking zone for high- and low wave conditions? • How does the magnitude and relative contribution of mean flows, infragravity and gravity oscillatory motions to the sediment transport fluxes vary temporally over the inundated beach flat?

Thesis outline • Chapter 2 describes the fieldwork program and location including explanation of instruments and measurement equipment. Furthermore the chapter describes the methodology used for data analysis. Most formulas used for data calibration, hydrodynamics and sediment transport analysis are discussed. • Chapter 3 gives an overview of external boundary conditions present during the fieldwork, including tides, wind, waves and results on geomorphologic change of the Slufter area during the fieldwork. • Chapter 4 offers hydrodynamic results. Included are wave conditions during the fieldwork and the time-dependent character of the relative significant wave height. Wave asymmetry is

analyzed for high/low wave conditions using Hs/h as conditional parameter. Subsequently the chapter treats temporal and spatial variation in mean cross-shore currents. Also mean currents and waves propagating across the beach flat are described. Finally temporal and spatial

variations in longshore currents are analyzed for changing Hs/h and wave incidence angle. • Chapter 5 discusses the cross-shore sediment transport in the breaker zone and on the beach flat. In the breaker zone the contributions of mean and oscillatory fluxes are analyzed in cross-

shore direction for high and low wave conditions using Hs/h as conditional parameter. On the beach flat the temporal change in contribution and magnitude of sediment transport mechanisms will be analyzed by distinguishing an initial phase of submergence, a peak flooding phase with maximum water levels and a phase with falling tide. • Chapter 6 discusses and compares the importance of wave-driven cross-and longshore transport in the breaker zone and on the beach flat in relation to the morphodynamic behaviour behaviour of the system. Finally the chapter provides recommendations for future research. • Appendices contain additional information on beach flat data and a Slufter 2008 Data DVD.

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Field site and instrumentation

2 Field site and instrumentation

2.1 Field work program and location

The fieldwork program was executed in the period from 08/09/2008 to 17/10/2008 (For overview see Appendix, Table A1). Measurements were done at 4 different locations. Waves, water levels, velocities and suspended sediment concentrations were measured in the main channel, further upstream, in the breaker zone and on a beach flat adjacent to the main channel which was inundated under storm conditions (Figure 2.1).

Measurements in the main channel continued throughout the entire fieldwork period. Two mobile miniframes were used to measure sediment concentrations and velocities on different locations across the Slufter area. In the breaker zone and on the beach flat frames were located in a cross-shore array. In the breaker zone frames were oriented parallel to the coast whereas on the beach flat the frames were oriented in direction of main wave impact (at an angle of 19.3 and 17.8° SW to coastline orientation). Upstream frames were located at the largest meander bend and further upstream at the first channel bifurcation of the Slufter.

In the breaker zone measurements were carried out from 09/09 – 17/09 and 06/10 – 17/10. Only the second period provides reliable information on wave orbital motions (see: sampling protocol 2.2.1) Because of this only the second period is used for cross-shore hydrodynamics and sediment transport analysis. At the beach flat the frames measured during combined storm/spring tide conditions from 01/10 – 06/10. Only data from one frame was used during this period because the other frame gave unreliable results during this period.

Besides gathering data on velocities and sediment concentrations, geomorphologic change is mapped using DGPS and digital photo observations. Each day photo observations were made from the northern dune top. DGPS surveys were done multiple times along 13 channel transects and a north- south dune profile. Also coastal profiles were measured and a cross-basin transect. The inland basin was not mapped, because expected morphologic change was very small. For this area the AHN, a Digital Elevation Model (DEM) covered by laser altimetry measurements every 5 m across the Netherlands is used, based upon data from 2005 (So 3 years old at moment of measurements). Later on DGPS data and the AHN were merged into a DEM of the Slufter system as constructed by Van Puijvelde (2009).

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Field site and instrumentation

Figure 2.1 Height contour map for the Slufter system based upon merged DGPS measurements and AHN data. Main- and miniframe locations are indicated on the map. Pre- and post-storm breaker zone sites are shown by respectively north- and southward located frame in the sea (Van Puijvelde, 2009).

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Field site and instrumentation

2.2 Instruments

2.2.1 Measuring Frames and sampling protocol

The main frame (Photo 2.1) consisted of a ‘Truc Vert’ frame and mini frame. The Truc Vert frame measured continuously at 4Hz and was equipped with 2 pressure sensors, 8 OBS sensors and 3 EMFs. The data was saved at the Truc Vert datalogger and could be downloaded by fast Ethernet connection.

Photo 2.1 The main frame and instruments: A) EMFs and OBS instruments B) Measurement construction assembled on main frame; The miniframe is not yet constructed on the main frame C) Main frame in live action

Most data for mini frames (Photo 2.2) was collected at 4 Hz in bursts of 17 out of 30 minutes. It should be noted that the software program for the mini frames was replaced at 24/09 (table 1) because the original program measured continuously at 2Hz. This sampling frequency is insufficient to adequately measure wave orbital motions. The program was replaced by a 4 Hz protocol which measured in bursts of 17 out of 30 minutes. The mini frame was equipped with 1 pressure sensor, 1 EMF and 3 OBS sensors. The data was saved on a data logger and could be downloaded by a relatively slow COM-port connection.

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Field site and instrumentation

Photo 2.2 Miniframes and instruments, configuration and live action. The datalogger can be seen on top of the miniframe. The single EMF is located left of the OBS triplet.

2.2.2 Electromagnetic Flow Meter (EMF)

The EMF is used to measure instantaneous velocities in horizontal X and Y directions and produces an electric signal which corresponds to a certain velocity. On the main frame 3 EMFs were placed, whereas the mini frames were equipped with 1 EMF. At the main frame the EMFs were placed at heights of 15 cm, 25 cm and 65 cm above the bed, whereas the mini frame EMF is set at 15 cm above bed level, although slight variations in this height can occur due to bed level variations. The EMF is calibrated by means of laboratory-determined calibration curves and offsets. Accuracy amounts to 3%.

2.2.3 Pressure Sensor

The mini frames and mainframe were equipped with Keller pressure sensors at 10 cm above bed level. This sensor measures local pressure (water pressure and air pressure). Later local air pressure (measured at the base station) is subtracted from the total pressure signal to obtain the water pressure. The wave height and water level can then be determined assuming a constant sea water density.

2.2.4 Optical Backscatter Sensor (OBS)

The OBS is a sensor made for measuring suspended sediment concentrations in the water column. The OBS emits a beam of infrared light and detects sediment concentrations by measuring light scattered from suspended matter. The OBS needs to be calibrated by local sediment because the electric response depends heavily on size, form and composition of local material. OBS sensors function very well with either sand or mudlike fractions as suspended matter. Problems arise when sand is mixed with claylike fractions, because the OBS is more sensitive to mudlike fractions and then cannot be calibrated well. On the main frame 8 OBS sensors were constructed, whereas the mini frames were equipped with 3 OBS sensors at 5, 10 and 20 cm above bed level. Mini frames were, if possible frequently lifted up during the fieldwork to sustain the same OBS sensor heights, because the miniframes used to sink a couple of centimeters away in the sand due to scour. However, in the breaker zone and on the beach flat changes in sensor height relative to the bed level during severe

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Field site and instrumentation weather conditions could not be avoided. This is especially true for measurements at the beach flat, where two occurrences of disfunctioning pressure sensors were recorded. Most data however is reliable and can be used for processing.

2.2.5 DGPS

Differential Global Positioning System (DGPS) is used to measure X-, Y- and Z-coordinates of the Slufter area (Photo 2.3). Geomorphology and geomorphologic changes are mapped using DGPS. The DGPS system consist of a base and rover. The base is built up on a location with known X-, Y- and Z-coordinates, and corrects for the error with respect to the satellite signal. The correction is transmitted by a small radio tower to the mobile rover which measures the satellite signal. Accuracy of millimeters can be achieved for X- and Y-direction and centimeters for the Z-direction. Accuracy diminishes with increasing distance from the base receiver, although for the Slufter area decrease in accuracy remains within acceptable limits. Photo 2.3 DGPS base with the receiver on the right hand and the radio at the left hand.

2.3 Data calibration

Velocity, pressure and OBS signals are calibrated to obtain useful physical parameters. Velocity and pressure signals were calibrated before the fieldwork period, whereas OBS sensors had to be calibrated by using local beach sediments of Texel at the Physical Geography Laboratory in Utrecht.

For the velocities the following calibration formulas (2.1 and 2.2) were used to convert the electric signal (mV) into a the vectors Vx and Vy in m/s

= (2.1) 𝑬𝑬𝑬𝑬𝑬𝑬𝒙𝒙−𝑶𝑶𝑶𝑶𝑶𝑶𝒙𝒙 𝑽𝑽𝒙𝒙 𝜶𝜶𝒙𝒙𝑹𝑹𝑹𝑹𝑹𝑹𝒙𝒙

= (2.2) 𝑬𝑬𝑬𝑬𝑬𝑬𝒚𝒚−𝑶𝑶𝑶𝑶𝑶𝑶𝒚𝒚 𝑽𝑽𝒚𝒚 𝜶𝜶𝒚𝒚𝑹𝑹𝑹𝑹𝑹𝑹𝒚𝒚 Where Vx is the cross EMF velocity in m/s (positive velocity denotes onshore velocities) and Vy is the along EMF velocity in m/s (positive velocities denote northward flow). Later on, decomposition in factors is needed to correct offset in frame orientation to obtain U and V, cross- and longshore velocities respectively. and are the output signals of the EMF sensors (mV), and

𝐸𝐸𝐸𝐸𝐸𝐸𝑥𝑥 𝐸𝐸𝐸𝐸𝐸𝐸𝑦𝑦 𝑂𝑂𝑂𝑂𝑂𝑂𝑥𝑥

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Field site and instrumentation

are the offset values of the EMF, and are the amplification factors of the EMF and and denote the regression coefficients in X and Y direction respectively. 𝑂𝑂𝑂𝑂𝑂𝑂𝑦𝑦 𝛼𝛼𝑥𝑥 𝛼𝛼𝑦𝑦 𝑅𝑅𝑅𝑅𝑅𝑅𝑥𝑥

𝑅𝑅𝑅𝑅𝑅𝑅𝑦𝑦 The measured millivolt signal from the Keller pressure sensor is calibrated to a water pressure signal (mbar) by Eq. 2.3

= + (2.3) 𝑅𝑅𝑅𝑅𝑅𝑅𝑝𝑝𝑝𝑝 𝑝𝑝𝑤𝑤 𝛼𝛼𝑝𝑝𝑝𝑝 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐶𝐶𝑝𝑝𝑝𝑝 − 𝑝𝑝𝑎𝑎𝑎𝑎𝑎𝑎 Where is the pressure induced by sea water above the sensor, is the output signal of the Keller sensor in millivolts and is the local air pressure measured at base station. Furthermore 𝑝𝑝𝑤𝑤 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 denotes the regression coefficient of the pressure sensor, is the amplification factor and 𝑝𝑝𝑎𝑎𝑎𝑎𝑎𝑎 is the intercept. Subsequently the water pressure is transformed into local water level (and wave 𝑅𝑅𝑅𝑅𝑅𝑅𝑝𝑝𝑝𝑝 𝛼𝛼𝑝𝑝𝑝𝑝 𝐶𝐶𝑝𝑝𝑝𝑝 heights) by formula 2.4.

= + (2.4) 𝑝𝑝𝑤𝑤 ℎ𝑤𝑤 𝑔𝑔𝑔𝑔𝑤𝑤 ℎ𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 Where is the water depth, is the gravitational acceleration (9.81 m/s), is the density of sea water (1024 kg/m3) and is the height of the pressure sensor above bed level (0.1 m). Based on ℎ𝑤𝑤 𝑔𝑔 𝜌𝜌𝑤𝑤 the water depth, parameters such as tidal water levels, wind set-up and wave characteristics can be ℎ𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 determined.

OBS sensors were calibrated in the lab and a simple regression formula (2.5) is used to convert the millivolt signal to obtain sediment concentrations in g/L or kg/m3.

2 = + + (2.5) 𝐶𝐶 𝛼𝛼 𝛽𝛽 𝑂𝑂𝑂𝑂𝑂𝑂 𝛾𝛾 𝑂𝑂𝑂𝑂𝑂𝑂 where C is the concentration in kg/m3, OBS is the measured output signal in millivolts, is regression coefficient 1 and is regression coefficient 2 and is the intercept. The regression coefficients were 𝛽𝛽 based upon a concentration relation from 0- 35 kg/m3. Higher concentrations were omitted from 𝛾𝛾 𝛼𝛼 regression, because this improved range goes at expense of the accuracy of the relation. For relation 2.5, R2 values of 0.98 were attained.

Velocity and concentration data were despiked to improve data quality and decrease the amount of measurement errors. Concentration data are despiked by double derivative and absolute criteria. One smooth loop which has a weak derivative and small absolute criterion and one hard loop which consists of a strong derivative and high absolute criterion (see Slufter 2008 data DVD). This double method gave reasonable results. Values n are then replaced by the average of n-1, n-2, n+1 and n+2 when

1. ΔCn > 0.5Cn-1 if the absolute value of Cn > 0.05.

2. ΔCn > 0.01Cn-1 if the absolute value of Cn > 20.

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Field site and instrumentation

All velocity and concentration data are despiked. For the beach flat often stringent criteria had to be set, hereby accepting some data loss. Data which produced clearest signals in velocity and concentrations data is often used for analysis. For measurements on the breaker zone and beach flat no noise is found in OBS concentration data due to presence of claylike particles.

All data converting, calibration, hydrodynamic and sediment transport analysis were done in MATLAB-environment. All MATLAB scripts are written by Ralf Klein Breteler with the exception of the zero-down crossing script form Mori (2007) used in the wave script. All MATLAB scripts are found on the data DVD enclosed in the appendix.

2.4 Hydrodynamics calculations

2.4.1 Wave heights

To be able to distinguish wave heights, first the wave signal was filtered out of the water depth time series by subtracting the 5-min. average depth signal from the original signal. Wave heights and periods were isolated by means of the zero-down crossing method which is the most effective method when treating shallow water wave deformation (Grasmeijer, 2005). Statistical analysis was subsequently performed on the wave height data. The significant wave height Hs is calculated by averaging the highest 1/3th of the waves over a period of 5 minutes (Figure 2.2). Also Hrms, the root mean-square of wave heights is calculated and Hrms shows the same pattern as Hs.

Individual wave heights (H) and Hsignificant 1.4

1.2

1

0.8

0.6 H (m)H and Hs(m) 0.4

0.2

0 281.5 282 282.5 283 283.5 284 284.5 285 285.5 Julian day Figure 2.2 The calculation of Hs. Individual waves are isolated by the zero-down crossing method. Subsequently the top 1/3th of waves are averaged to obtain the significant wave height.

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Field site and instrumentation

Spectral analysis is applied to the oscillating term in the water level to obtain the frequency distribution of energy in waves. First, the time series-data are multiplied by a Hanning window to reduce the tails of peaks in the frequency spectrum. Then, to reduce noise in the data 8 50% overlapping 1024 points- Fast Fourier transforms are done to construct a power spectral density distribution which gives the squared values of the amplitudes of the cosine waves for different frequencies. Most important wave frequencies are determined which correspond to largest wave heights.

2.4.2 Velocities

To prepare velocity data for analysis, first velocities were decomposed into cross- and longshore velocities. On the beach flat the frames were orientated with an angle to the coastline. Based upon DGPS location, these angles are respectively 19.3° for the seaward frame and 17.8° for the landward 𝛼𝛼 frame (during the storm form 01/10-05/10). In this way the orientation of the frame corresponded to the dominant direction of wave propagation. To determine main water mass /sediment transport, velocity time series are decomposed into cross-shore (U) and alongshore (V) currents which are analogous to the coastline orientation according to formulas 2.6 and 2.7.

= ( ) + ( ) (2.6) = ( ) ( ) (2.7) 𝑉𝑉 𝑉𝑉𝑦𝑦 𝑐𝑐𝑐𝑐𝑐𝑐 𝛼𝛼 𝑉𝑉𝑥𝑥 𝑠𝑠𝑠𝑠𝑠𝑠 𝛼𝛼

𝑈𝑈 𝑉𝑉𝑥𝑥 𝑐𝑐𝑐𝑐𝑐𝑐 𝛼𝛼 − 𝑉𝑉𝑦𝑦 𝑠𝑠𝑠𝑠𝑠𝑠 𝛼𝛼 Based on cross- and longshore mean current and wave incidence angle analysis it turned out that frames in the breaker zone had approximately a 20° deflection to the shore line (after the storm under low-moderated wave energy conditions). The velocities and wave incidence angle α are corrected for this deflection. Furthermore the velocity time-series are decomposed into 5-min. averaged mean currents and oscillatory components. The oscillatory signals are further analyzed to determine the wave skewness/asymmetry and the wave incidence angle.

Shallow water wave deformation involves a change in orbital wave velocities. This change is analyzed by the skewness ratio of shoaling wave velocities. The shoreward velocity under wave crests grows progressively stronger than the offshore velocity of longer duration under wave troughs (Grasmeijer, 2002). The wave skewness (S) is defined as

= (2.8) + 𝑈𝑈𝑜𝑜𝑜𝑜 𝑆𝑆 𝑈𝑈𝑜𝑜𝑜𝑜 𝑈𝑈𝑜𝑜𝑜𝑜𝑜𝑜 where is the wave skewness, and are the onshore and offshore peak orbital velocity. The wave skewness varies between 0.50 and 0.75 (Grasmeijer, 2002). For skewness analysis the U 𝑆𝑆 𝑈𝑈𝑜𝑜𝑜𝑜 𝑈𝑈𝑜𝑜𝑜𝑜𝑜𝑜 1/3th values are used to determine and , so actually the significant orbital velocity.

𝑈𝑈𝑜𝑜𝑜𝑜 𝑈𝑈𝑜𝑜𝑜𝑜𝑜𝑜

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Field site and instrumentation

The wave incidence angle is determined by regression analysis of the spectrally determined gravity domain of cross-shore (U) and longshore (V) directed oscillatory velocities. So first a distinction is made between high-frequency and low-frequency oscillatory velocities and then the high-frequency velocities are used to determine the wave incidence angle. Simultaneously measured U and V oscillatory velocities are plotted in Figure 2.3.

0.2 linear 0.15 VELXY (m/s)

0.1

0.05

0

-0.05 V (m/s)

-0.1

-0.15

-0.2

-0.25

-0.3 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 U (m/s)

Figure 2.3 Velocities in X and Y direction for 256 sec. Overall wave incidence angle is given by the alpha coefficient of the linear regression.

The slope α of the linear regression gives the wave-incidence angle. Alpha is calculated each 256 seconds. Positive α (0° to 90°) values indicate a positive incidence angle and subsequently a northward ward directed longshore current. Negative α (-90° to 0°) values indicate a southward directed longshore current.

For a systemic description of the contribution of mean flows, short waves and infragravity waves to cross-shore sediment transport the oscillatory velocity signal needs decomposition into low- and high- frequency signals. The oscillatory signal is therefore low- and high pass filtered with a cut-off- frequency of 0.05 Hz. This is done by transforming the time-series signal to the frequency domain, and apply a mask which cuts off the high- and low frequencies respectively. Subsequently the inverse FFT returns a filtered time-series signal.

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Field site and instrumentation

2.5 Suspended sediment transport calculations

2.5.1 Cross-shore sediment fluxes

For cross-shore analysis of sediment fluxes frequently (Osborne & Greenwood, 1992; Ruessink et al., 1998) the time-series of instantaneous cross-shore velocity U and concentrations C are decomposed into mean and oscillating components. Net-time averaged suspended transport is decomposed into a mean and oscillating part (2.9)

= ( + )( + ) = + (2.9)

〈𝑢𝑢 𝑢𝑢〉 〈 𝑢𝑢� 𝑢𝑢� 𝑐𝑐̅ 𝑐𝑐̃ 〉 𝑢𝑢�𝑐𝑐̅ 〈 𝑢𝑢�𝑐𝑐̃〉 where denotes that the sediment flux is averaged over a 5 min period, is the time averaged mean flux computed as the product of averaged concentrations and velocities. Positive sediment fluxes 〈 〉 𝑢𝑢�𝑐𝑐̅ indicate onshore transport, whereas negative sediment fluxes indicate offshore transport.

The term is the time-averaged wave-related oscillatory flux, computed as the product of instantaneous oscillating concentrations and velocities which are subsequently averaged (Ruessink et 〈 𝑢𝑢�𝑐𝑐̃〉 al., 1998). This term is also called flux coupling in Jaffe et al., 1985 (in Osborne and Greenwood, 1992) and is a measure of correlation between velocity- and concentration fluctuations, where low values indicate random temporal fluctuations in oscillatory velocities and concentrations and high values indicate a strong degree of temporal correlation (Osborne and Greenwood, 1992). The time- averaged oscillatory flux can be further decomposed into high- and low frequency fluxes (2.10)

= ( + )( + ) = + (2.10)

〈 𝑢𝑢�𝑐𝑐̃〉 〈 𝑢𝑢�ℎ 𝑢𝑢�𝑙𝑙 𝑐𝑐ℎ̃ 𝑐𝑐𝑙𝑙̃ 〉 〈𝑢𝑢�ℎ 𝑐𝑐ℎ̃ 〉 〈𝑢𝑢�𝑙𝑙 𝑐𝑐𝑙𝑙̃ 〉 where is the time-averaged high-frequency sediment flux and is the time-averaged low- frequency sediment flux. Cross-products of high and low frequency velocities and concentration are 〈𝑢𝑢�ℎ 𝑐𝑐ℎ̃ 〉 〈𝑢𝑢�𝑙𝑙 𝑐𝑐𝑙𝑙̃ 〉 neglected because these are generally very small (Ruessink et., 1998). The low- and high frequency fluxes are calculated as the averaged product of the instantaneous high-and low pass filtered oscillatory concentrations and velocities. Eq. 2.9 and 2.10 determine the main contributing mechanisms to cross-shore sediment transport, i.e. low, high frequency- and mean sediment fluxes (2.11).

= + + (3.11)

〈𝑢𝑢 𝑢𝑢〉 𝑢𝑢�𝑐𝑐̅ 〈𝑢𝑢�ℎ 𝑐𝑐ℎ̃ 〉 〈𝑢𝑢�𝑙𝑙 𝑐𝑐𝑙𝑙̃ 〉 Mean fluxes are depth-corrected using an engineering rule (2.12) of Van Rijn (1991). It is noted that this is only done for the 5 min. averaged mean velocities, so not for oscillatory signals.

0.25 1 1 = 2 (2.12) 𝑧𝑧2 𝑢𝑢� 𝑢𝑢� �𝑧𝑧 �

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Field site and instrumentation

Where 1 (lowest) and 2 (highest) denote the height above the bed and 1 and 2 denote the corresponding velocities. Because velocities were measured at 15 cm and concentrations at 5, 10 and 𝑧𝑧 𝑧𝑧 𝑢𝑢� 𝑢𝑢� 20 cm above bed level, corresponding velocities are calculated at 76 %, 90 % and 107% of measured velocities.

To analyze effect of (non-) breaking waves on net fluxes, high-, low- and mean fluxes are plotted against the relative significant wave height, which increases for progressively smaller water depths. The contribution of suspended mean fluxes (here), high- and low frequency fluxes to the gross suspended fluxes are calculated by formula 2.13, where | | denotes absolute values.

| | (2.13) | |+| |+ | | 𝑢𝑢�𝑐𝑐̅ 𝑢𝑢�𝑐𝑐̅ 〈𝑢𝑢�ℎ 𝑐𝑐ℎ̃ 〉 〈𝑢𝑢�𝑙𝑙𝑐𝑐𝑙𝑙̃ 〉 The influence of oscillatory wave velocities on sediment concentration fields is analyzed by means of co-spectral and coherence analysis. In the frequency domain power spectral densities (Puu and Pcc) and co-spectral densities (Kuc) of velocities and concentrations are constructed. The co-spectrum shows the magnitudes and directions of sediment fluxes and is the real part of the cross-spectrum. If integrated over infragravity and gravity frequencies, the co-spectrum is equal to the time-averaged oscillatory flux (Ruessink et al., 1999).

Power and co-spectra are constructed by a Hanning-filtered 1024-points FFT with 8 50%-overlapping segments with a frequency resolution of 0.004 Hz. Additionally coherence squared diagrams and phase diagrams are constructed to indicate correlation between oscillatory velocity motions and sediment bursts and respectively to indicate whether sediment is transported with the on- or offshore phase of the oscillatory wave motion. Coherences ( ) and phase differences ( ) are calculated by formula 2.14 and 2.15. 𝑐𝑐𝑐𝑐ℎ 𝑝𝑝ℎ𝑎𝑎

( ) = (2.14) 𝑃𝑃𝑢𝑢𝑢𝑢 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑃𝑃𝑢𝑢𝑢𝑢 𝑐𝑐𝑐𝑐ℎ 𝑃𝑃𝑢𝑢𝑢𝑢 𝑃𝑃𝑐𝑐𝑐𝑐

2( , ) = 360 (2.15) 2 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐾𝐾𝑢𝑢𝑢𝑢 𝑄𝑄𝑢𝑢𝑢𝑢 where is 𝑝𝑝theℎ𝑎𝑎 complex �conjugate𝜋𝜋 of the� co-spectrum and 2 is the four quadrant arctangent of the real ( ) and imagery parts ( ) of the co-spectrum. Coherence squared diagrams 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑃𝑃𝑢𝑢𝑢𝑢 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 range from 0 (no correlation in u and c) to 1 (complete correlation in u and c). The phase diagram 𝐾𝐾𝑢𝑢𝑢𝑢 𝑄𝑄𝑢𝑢𝑢𝑢 ranges from -180 to 180° for which -90 °< phase < +90° sediment is stirred up during the onshore phase of the wave motion, whereas for phase > |90°| sediment is stirred up during the offshore phase of wave motion.

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Field site and instrumentation

2.5.2 Longshore sediment fluxes

A quantification of longshore suspended sediment fluxes is made by the calculation of depth- integrated transport rates. Suspended sediment transport profiles are constructed by the product of velocity and concentration profiles. For the velocity profile the engineering rule of Van Rijn (2.12) is again used to extrapolate a singular averaged point into a velocity profile.

Concentration profiles vary over the wave periods, but when averaged over many wave cycles they approximate an exponential shape (Aagaard and Masselink in Short, 1999), Eq. 2.16.

= 0 (2.16) 𝑤𝑤𝑠𝑠𝑧𝑧 𝑐𝑐𝑧𝑧 𝑐𝑐 𝑒𝑒𝑒𝑒𝑒𝑒 �− 𝜀𝜀𝑠𝑠 � where is the concentration at height above the bed, 0 is a reference concentration at bed level, is the particle𝑐𝑐𝑧𝑧 fall velocity and is 𝑧𝑧an eddy diffusion𝑐𝑐 coefficient. can be determined by linear𝑤𝑤𝑠𝑠 𝑤𝑤𝑠𝑠 regression of a concentration profile.𝜀𝜀𝑠𝑠 𝜀𝜀𝑠𝑠

Concentration profiles are constructed by linear regression of ln ( ) and , where a and b are subsequently plotted in an exponential profile (Eq. 2.17 and 2.18) ⁡𝑐𝑐𝑧𝑧 𝑧𝑧

ln ( ) = + (2.17)

⁡𝑐𝑐𝑧𝑧 𝑎𝑎𝑎𝑎 𝑏𝑏 = ( + ) = ( ) (2.18) 𝑧𝑧 𝑐𝑐 𝑒𝑒𝑒𝑒𝑒𝑒 𝑎𝑎𝑎𝑎 𝑏𝑏 𝑏𝑏 𝑒𝑒𝑒𝑒𝑒𝑒⁡𝑎𝑎𝑎𝑎 where = and = 0. Concentrations are averaged over 512 sec., so that each 512 sec. a 𝑤𝑤𝑠𝑠 concentration𝑎𝑎 − 𝜀𝜀profile𝑠𝑠 𝑏𝑏is calculated𝑐𝑐 with corresponding and values. Depth- and time-averaged suspended transport rates are calculated from 0.05 < < i.e. from 5 cm above bed level to the 𝑎𝑎 𝑏𝑏 surface level by multiplication of the velocity profile by Van Rijn (1993). 𝑚𝑚 𝑧𝑧 ℎ𝑤𝑤

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General observations and conditions

3 General observations and conditions

3.1 Offshore boundary conditions

Offshore boundary conditions during the fieldwork (Figure 3.1) determine the local conditions for hydrodynamics, sediment transport and morphologic change in the Slufter. The field work period is characterized by a calm weather period and by a severe storm event (7 days including a short interval) in which 2 distinct peaks can be distinguished (Table 3.1).

Storm event Hs, off max Duration (d) Wind dir (°) Wind speed Tidal range Set-up (m) (cm) (dm/s) (m) Peak 1 450 3 W (270°) 110 2 0.8 Peak 2 478 2 W (270°) 95 1.3 1.5 Table 3.1 Storm conditions near the Slufter system

During this storm period measurements were done at the beach flat which became completely inundated. Measurements in the breaker zone were restricted to the first and last periods for which smaller wave height peaks can be distinguished ranging from 200-300 cm.

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General observations and conditions

Figure 3.1 Offshore boundary conditions during the fieldwork period. Offshore data from the Eierlandsche Gat wave buoy are taken from the 30-100 MHz spectrum and involve A) The water levels determined from the frames in the breaker zone, B) The offshore tidal signal determined by T-tide C) the local set-up or set-down. D) The significant wave period E) The significant wave height, F) The wave angle relative to the North (The coastline is orientated at 303° N). G) The daily averaged wind direction measured at the KNMI station at de Kooy, Texel, H) The day averaged wind speeds (dm/s).

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General observations and conditions

3.2 Geomorphologic change

The total Slufter system can roughly be divided into an inland basin, a meandering channel and a spit- like beach flat, located between the meandering channel, the North Sea and the southward-located dunes. During the fieldwork, the Slufter system was characterized by a downdrift-located main channel. During the entire period, the main channel was characterized by two large meander bends (Figure 3.2).

Figure 3.2 3D-map of the Slufter system based upon merged AHN and DGPS data (van Puijvelde, 2009).

During the field work period significant morphological change was observed due to a severe storm event (Hs,off > 4.0 m), which occurred from 30/09- 05/10 and coincided with spring tide conditions. In this period the Slufter area (beach flat and inland basin) was completely inundated (Photo 3.1).

Photo 3.1 Merged photographs (ca 200°) of the completely inundated Slufter basin at 01/10.

The initial pre-storm situation is shown in Photo 3.2. The channel extends far downdrift and curves beyond the downdrift dune row. Also a small bar and trough system is visible on Photo 3.2b.

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General observations and conditions

Photo 3.2 Initial pre-storm situation of the Slufter channel and mouth.

During the storm the inlet channel migrated in northward direction. Photo 3.3 shows the position of the main channel relative to a fixed post. It can be seen from Figure 3.3 that the channel has migrated 10-15 m. Additionally the channel mouth has migrated southward and bends back from the northern dune row. In fact this means that the channel has become more curved. Figure 3.3 also shows that beach flat elevation remained relatively constant during the storm event, although the profile at 11/10 indicates that beach flat elevation is 10-20 cm higher with respect to 12/09 and some accretion has occurred. The Slufter inlet is located between two dune ridges respectively represented on the right and left hand side in Photo 3.3 (see also Figure 3.2).

Photo 3.3 The lateral migration of main channel.

4

3

2 29-sep 12-sep 1 2-okt 0 11-okt 584000000 584200000 584400000 584600000 584800000 -1

-2

Figure 3.3 DGPS measurements of the lateral migration of the main channel and beach flat elevation for the period of 12/09 – 11/10.

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General observations and conditions

Geomorphologic change of the coast during the storm has been twofold: 1) a cross-shore flattening of the beach profile (Figure 3.4 and Figure 3.5) and 2) the northward transport of a large sandbody (Figure 3.5). The cross-shore flattening of the beach flat occurred throughout the major part of the measured beach transect, whereas the downdrift migrating sandbody is a local phenomenon only occurring in the vicinity of the breaker zone measurement site in October shortly updrift of the inlet mouth (post-storm, Figure 3.5). Measurement stations in September (prior to storm) were located in this sheltered embayment, which was completely buried during the storm event. No measurements were done relating to the process of the downdrift migrating sand body.

1,5

1

0,5 12-sep 0 2-okt 583.800.000 584.000.000 584.200.000 584.400.000 584.600.000 584.800.000 -0,5

-1

-1,5

Figure 3.4 Coastal change in a cross-shore section close to (~ 50 m) the Slufter main channel inlet mouth in continuation of the frames location on the beach flat. At 12/09 the cross-section of the Slufter was measured from the beach (right) over the beach flat and the channel (left). At 12/09 a ridge/runnel was visible near the Slufter inlet mouth which has completely disappeared during the first storm peak.

1,000 Pre-Storm 18/09

0,500 Post-storm 07/10 1 2 0,000 584.410.000 584.420.000 584.430.000 584.440.000 584.450.000 584.460.000 584.470.000 -0,500

-1,000

-1,500

-2,000

-2,500

Figure 3.5 Coastal change close to the location of the miniframes in the breaker zone during the low-moderate wave energy period after the storm. Frames were located close to the seaward end of the 07/10 profile and are referred to as 1 (landward) and 2 (seaward).

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General observations and conditions

Sediments at the Slufter are characterized by a gradual fining land inward and are mainly composed of medium sands. In the breaker zone largest sediment diameters are found (Table 3.2) where d10, d50 and d90th refer to the nth percentile of the grain size distribution. Further in the basin sediment particle sizes reduce to alternating finer sands and clays.

Grain size (μm) Main frame Breaker zone Beach flat Upstream d10 231 250 196 210 d50 275 390 275 231 d90 390 790 370 380

Table 3.2 Sediment grain sizes at the slufter system as found by sieving in the FG lab. Grain sizes are averaged over 3 samples.

For more details on morphologic change see the MSc thesis of van Puijvelde (2009).

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Hydrodynamics results

4 Hydrodynamics results

4.1 Breaker zone

4.1.1 Spatial and temporal differences in (relative) wave heights

The wave climate over the total fieldwork period is shown in Figure 4.1 and the period used to analyze wave hydrodynamics in Figure 4.2. Hs land and sea refer to the land- and seaward frame respectively, which are located in the breaker zone. Waves measured in the breaker zone show an alternating signal modulated by the tide. Offshore wave heights, which are 10-min averages out of the 30-100 MHz spectrum are a factor 2-3 larger than wave heights in the breaker zone.

5 Hs, offshore 4.5 Hs land per 1 Hs land per 2 4 Hs sea per 1 Hs sea per 2 3.5 Hs land september Hs sea september 3

2.5 Hs (m)

2

1.5

1

0.5

0 250 255 260 265 270 275 280 285 290 295 Julian day

Figure 4.1 The significant wave heights, Hs (m) for the fieldwork period; Offshore wave heights compared to locally measured wave heights in the breaker zone shortly updrift of the Slufter inlet.

Significant wave height - last period 3.5 Hs offshore Breaking zone landwards - period 1 3 Breaking zone landwards - period 2 Breaking zone seawards - period 1 2.5 Breaking zone seawards - period 2

2 Hs (m) 1.5

1

0.5

0 280 282 284 286 288 290 292 Julian day

Figure 4.2 The significant wave heights, Hs (m) for the last part of the fieldwork period.

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Hydrodynamics results

Spatial change in wave height is related to the change in wave height when waves are propagating from the sea- to landward frame, whereas temporal change is related to two different offshore wave height regimes, i.e. low (~0.6 m) and high (3 m) waves.

• Spatial change in wave heights In period 1 - day 282-285, wave heights at the seaward frame are higher than for the landward frame during the whole tidal period. In period 2, wave heights were in the same order of magnitude for the sea- and landward frame. Waves were slightly higher at the landward frame at high tide, and slightly lower at low tide. Wave height increase during wave propagation during high tides can be related to wave shoaling, whereas at low tide dissipation can occur during wave breaking so that measured waves are generally smaller.

Based on Figure 4.3 it becomes clear that large relative significant wave heights (Hs/h) coincide with low water, and small relative significant wave heights coincide with high water.

Waves heights increase during shoaling at Hs/h > 0.3 and reach maximal wave heights at

initiation of wave breaking around Hs/h = 0.4-0.5. The landward frame is during low tides

located in fully saturated breaking conditions (Hs/h > 0.55). Figure 4.3 illustrates that when waves are fully broken wave heights rapidly decline. It should be noted that when water depth

drops below 0.2 m, measurements become unreliable, so peaks in the peaks in Hs/h of 1 could not be analyzed.

• Temporal change in wave heights (Hs, off = 0.6 – 3 m) The seaward frame measures the largest variability in wave heights (0.20 – 0.1 m).

For low wave height conditions (Hs,off < 1.0 m) the tidal-forced modulation in significant

wave height is smaller than for high wave height conditions (Hs,off > 2.0 m). Under low wave conditions, wave heights vary from 0.2-0.3 m during low tide to 0.3-0.4 m during high tide. Under high wave conditions variation is larger: 0.4 – 1.0 m from low to high tide. It must be noted that under high wave conditions the water levels will be higher than the predicted

astronomical levels due to wind- and wave set-up. This will also positively influence Hs/h under low tide situations.

Hs, h and Hs/h - Landwards 07/10 - 11/10 Hs, h and Hs/h - Landwards 11/10 - 16/10 1.8 3 relative signifcant w ave height Hs/h relative significant w ave height Hs/h w ater depth h 1.6 w ater depth h significant w ave height Hs 2.5 significant w ave height Hs

1.4

2 1.2

1 1.5

0.8 1 Hs (m), h (m) and Hs/h (-) Hs (m), h(m) and Hs/h (-) 0.6

0.5 0.4

0.2 0 281.5 282 282.5 283 283.5 284 284.5 285 286 287 288 289 290 291 Julian day Julian day

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Hydrodynamics results

Hs, h and Hs/h - Seaward 07/10 - 11/10 Hs, h and Hs/h - Seaward 11/10 - 17/10 2.5 3 relative significant w ave height Hs/h relative significant w ave height Hs/h w ater depth h w ater depth h significant w ave height Hs 2.5 signifcant w ave height Hs 2

2 1.5

1.5

1 1 Hs (m), h (m) and Hs/h (-) Hs (m), h (m) and Hs/h (-)

0.5 0.5

0 0 281.5 282 282.5 283 283.5 284 284.5 285 285.5 285 286 287 288 289 290 291 292 Julian day Julian day

Figure 4.3 The relative significant wave height Hs/h, the residual water depth (h) and the significant wave height for the landward and seaward located frame. Inconsistencies occur at the start of the measuring series, so initial values of the measurement series are omitted from analysis.

4.1.2 Mean currents

Cross-shore mean currents are frequently directed offshore (Figure 4.4). Longshore currents are mostly positive, i.e. indicating northward transport and are a factor 2-3 larger than cross-shore velocities.

0.6 V (m/s) 0.4 U (m/s) 0.2

0 Velocity (m/s) Velocity -0.2

-0.4 285 286 287 288 289 290 291 julian day

Figure 4.4 Mean cross (U) and longshore (V) currents (m/s) in the breaker zone (landward frame)

It can be seen in the cross-shore mean current signal that there is some variation in magnitude of maximum offshore directed current velocities. Around day 287-288 negative velocities are smaller than around day 290 where offshore directed velocities almost reach -0.2 m/s. This variation is caused by differences in breaker height.

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Hydrodynamics results

4.1.3 Cross-shore mean currents

In the nearshore magnitudes and direction of wave-induced cross-shore mean currents are dependent upon the breaking of waves. This is related to the relative significant wave height. Temporal variations in the cross-shore mean current are analyzed by a comparison between low- and high wave conditions to determine the effect of wave height on the cross-shore mean currents. Furthermore, spatial analysis is used to give an indication of the cross-shore distribution in mean currents. Additionally, mean current results were compared to calculated undertow (Van Rijn, 1993) based upon water depth and wave height (Eq. 4.1)

0.5 1.5 2 , = 0.15 (4.1) − 𝑈𝑈�𝑚𝑚 𝑜𝑜𝑜𝑜𝑜𝑜 𝑔𝑔 ℎ 𝐻𝐻 Where , denote offshore directed mean currents, h the water depth and H the wave height. Results are as follows: 𝑈𝑈�𝑚𝑚 𝑜𝑜𝑜𝑜𝑜𝑜

• Landward, Low wave conditions (Hs, off < 1.0 m)

The cross-shore mean current velocities are directly realted to the relative significant wave

height, i.e large relative waveheights (Hs/h > 0.3, breaking wave conditions) indicate stronger offshore directed undertow velocities, which compensate the onshore mass flux of breaking waves (Figure 4.5A). The tide shows an asymmetric pattern characterized by shorter flood duration and a longer ebb duration. During flood the relative significant wave height reduces

rapidly, suggesting a transition from breaking to non-breaking wave conditions (Hs/h < 0.3). The tidal influence on the cross-shore currents is demonstrated by a rapid reduction in cross- shore velocities to zero that coincides with maximum flood velocities. At high water the cross-shore current is relatively small and the wave-induced undertow seems to be very limited. During falling tide the off-shore directed mean current gradually increases. Peak negative current velocities occur at low water, where Hs/h > 0.3 which indicates the importance of breaking waves for the mean currents.

Comparison with calculated undertows shows reasonable agreement. Measured peak negative mean velocities are in the same order of magnitude as calculated peak undertow velocities,

both occurring at maximum Hs/h.

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Hydrodynamics results

High-wave conditions / Landward Low-wave conditions / Landward 3 3 2 2 h(m) 1 1 0 286 286.5 287 287.5 288 0 288.5 289 289.5 290 290.5 291 1 1.5

0.5 1 0.5 Hs(m) and Hs/h(-) 0 0 286 286.5 287 287.5 288 288.5 289 289.5 290 290.5 291 0.2 0.2

0 0 Umean (m/s) -0.2 286 286.5 287 287.5 288 -0.2 288.5 289 289.5 290 290.5 291 0 0 -0.1 -0.2 Ucalc (m/s) Ucalc -0.2 286 286.5 287 287.5 288 -0.4 Julian day 288.5 289 289.5 290 290.5 291 Julian day

Seaward / Low-wave conditions 3

2 h(m) 1

0 286 286.5 287 287.5 288

0.6 0.4 0.2

Hs(m) and Hs/h(-) 0 286 286.5 287 287.5 288 0.1

0 Umean (m/s) -0.1 286 286.5 287 287.5 288 0

-0.05 Ucalc (m/s) Ucalc -0.1 286 286.5 287 287.5 288 Julian day Figure 4.5 Spatial and temporal differences in mean cross-shore currents, water levels and (relative) significant wave heights. A,B) temporal differences for low and high wave conditions, A, C) Spatial differences for the land-and seaward frame.

• Landward, High wave conditions (Hs, off > 2.0 m)

The inverse Hs/h relation with mean cross-shore currents also applies to high-wave conditions (Figure 4.5B). The most important difference is that offshore directed mean current velocities are slightly larger. Secondly, a small positive peak in mean cross-shore velocity is visible for

the last tidal cycle. Finally, two distortions in the cross-shore signal occur where Hs/h reaches very high values. Since the water depth drops here below 20 cm these results are not reliable.

Under high wave conditions, mean currents are close to zero from flood to HWS (Hs/h =0.25-

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Hydrodynamics results

0.35). Under ebb mean cross-shore velocities are stronger negative and gradually decline to

0.1 m/s at low water (Hs/h =0.5-0.1).

Differences between calculated undertow and measured mean velocities are larger than for low wave conditions. The calculated negative peak shows a little more deviation from measured values. This suggests that here, the undertow formula can relatively well be used for low energetic wave conditions, but is insufficient for higher wave conditions, were also other mechanisms seem to be operating.

• Seaward, Low wave conditions (Hs, off < 1.0 m)

The seaward frame is characterized by slightly lower relative significant wave heights (Figure

4.5C) at high water Hs/h < 0.2. These conditions are not sufficient to generate a strong

undertow. Offshore directed mean currents are a factor 2-3 weaker (-0.05 < Umean < 0 m/s) than for the landward frame. The undertow formula slightly overpredicts the magnitude of the offshore directed mean current velocities.

From the spatial analysis it is concluded that offshore directed mean cross-shore currents associated with wave breaking increase from the seaward to landward frame. Minimal flows at rising tides occur at both frames. The small peak in onshore velocities during rising tide in the last tidal cycle can be caused by onshore propagating bores at Hs/h =0.5. The influence of wave breaking on cross-shore mean currents can be analyzed using the relative significant wave height as conditional parameter. Figure 4.6 plots the mean cross-shore current for increasing wave height. Also, the Van Rijn undertow relation is plotted to compare measured cross-shore mean currents to modeled undertow. Temporal analysis for low and high wave condition is done by comparing Figure 4.6 A and B, whereas spatial analysis is done for Figure 4.6 A and C.

• Landward, low wave conditions (Hs, off < 1.0 m) Mean cross-shore currents are inversely related to increasing relative significant wave heights. Positive mean current values are related to the flood-velocity induced positive peak. If these values are left out of analysis because they are not related to wave breaking, offshore mean

current velocities start to increase rapidly for Hs/h > 0.35. For non-breaking conditions Hs <

0.2 undertow velocities do not become larger than -0.05 m/s. From Hs/h > 0.35 onwards undertow velocities become 2-3 times larger (0.10-0.15 m/s). The van Rijn relation exhibits less scatter than the measured cross-shore mean currents. Scatter in the van Rijn relation occurs

because of magnitude differences in powers of h and Hs in Eq. 4.1, so that differences in

Ucalc,off can occur for the same values of Hs/h. The measured cross-shore currents seem to reach maximal values between Hs/h =0.4-0.5 at maximal wave breaking. The calculated undertow velocities in the van Rijn relation increase further for higher Hs/h values.

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Hydrodynamics results

• Landward, high wave conditions (Hs, off > 2.0 m)

For high waves the relation between Hs/h and Umean is less clear. Umean and Hs/h are still inversely related, but more scatter occurs in the relation. This especially applies to the measured mean currents, but also applies to the van Rijn relation. This indicates large variation in wave heights and water depths in this period. Offshore velocities during ebb are

higher than during low wave conditions and increases for larger Hs/h values

• Seaward, low wave conditions (Hs, off < 1.0 m)

The Hs/h relation with mean currents is less strong for the seaward than for the landward

frame. An Hs/h increase of 10% implies a decline in cross-shore velocities of 0.6%, whereas for the landward frame this is still 2.5%. This is the result of lower maximal offshore directed undertow values and indicates that mean currents at the seaward frame are less strongly influenced by wave breaking.

Landward / Low wave conditions Landward / High wave conditions 0.1 Umeasured Umeasured Ucalc, off Ucalc,off 0.1 0.05

0.05 0

0 -0.05

-0.05 -0.1 Umean (m/s) Umean (m/s)

-0.1 -0.15

-0.15 -0.2

-0.2 -0.25 0.1 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Hs/h (-) Hs/h (-)

Seaward / Low wave conditions 0.04 Umeasured Ucalc, off 0.02

0

-0.02

-0.04 Umean (m/s)

-0.06

-0.08

-0.1 0.1 0.2 0.3 0.4 0.5 0.6 Hs/h (-)

Figure 4.6 Relations between mean cross-shore currents and the relative significant wave heights. A,B) temporal differences for high and low wave conditions, A, C) Spatial differences for the land-and seaward frame.

Shortly, the undertow formula from Van Rijn does not predict the measured mean currents very well. However, mean current prediction is difficult and additionally velocity measurements have only been done at one height, whereas the undertow is actually a profile over the water column.

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Hydrodynamics results

4.1.4 Longshore mean currents

The longshore current consists of wave-driven, tide-driven and wind-driven components. In this section the influence of (breaking) waves on the longshore current will be analyzed. The magnitude and direction of the mean longshore current is related to the (relative) significant wave height and the incident wave angle. For longshore currents positive values indicate northward directed velocities and the opposite accounts for southward directed velocities. Temporal and spatial analysis on longshore mean currents will be performed by means of comparison on time-series data for the seaward and landward frame.

Relationships between the Hs/h, Hs, the wave-incidence angle and the longshore current are shown in Figure 4.7. Dominant longshore current values are positive which implies a northward transport. The general pattern is that when Hs/h > 0.3 a longshore current is generated. Longshore current velocities start to develop when 0.2

Subsequently the measured longshore current is compared to the CERC formula which uses the wave height and wave incidence angle simultaneously to calculate the longshore current. This way it can be evaluated how strong the CERC formula predicts the longshore current in the breaker zone in front of the Slufter system. The CERC formula is formulated as follows (Eq 4.2)

= 41.4 (4.2)

𝑙𝑙 𝑏𝑏 𝑏𝑏 𝑏𝑏 Where g is the gravitational𝑣𝑣̅ acceleration,𝑆𝑆�𝑔𝑔𝐻𝐻 𝑠𝑠𝑠𝑠𝑠𝑠𝛼𝛼 𝑐𝑐𝑐𝑐𝑐𝑐 is𝛼𝛼 the wave height at wave breaking, is the wave incidence angle of breaking waves and S the beach slope. The beach slope is used as calibration 𝐻𝐻𝑏𝑏 𝛼𝛼𝑏𝑏 parameter and set at S=1/75 which gave the best-fit results, because the measured beach slope exhibits strong local variation (Figure 3.5), and provides unreliable results.

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Hydrodynamics results

Low-wave conditions / Landward High-wave conditions / Landward 3 3 2 2 h(m) 1 h(m) 1

0 0 286 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8 288 288.8 289 289.2 289.4 289.6 289.8 290 290.2 290.4 290.6 290.8 1 1.5 Hs/h (-) Hs/h (-) 1 Hs ( m) Hs ( m) 0.5 0.5

0 Hs(m) and Hs/h(-) 0 Hs(m) and Hs/h(-) 286 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8 288 288.8 289 289.2 289.4 289.6 289.8 290 290.2 290.4 290.6 290.8 30 30 20 20 10 10 0 0 alpha SN) (deg -10 alpha SN) (deg -10 286 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8 288 288.8 289 289.2 289.4 289.6 289.8 290 290.2 290.4 290.6 290.8 0.5 1

0.5 0 0 Vmean (m/s) -0.5 Ymean (m/s) 286 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8 288 -0.5 288.8 289 289.2 289.4 289.6 289.8 290 290.2 290.4 290.6 290.8 0.5 1 0 0 Vcerc (m/s) Vcerc -0.5 Vcerc (m/s) Vcerc 286 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8 288 -1 Julian day 288.8 289 289.2 289.4 289.6 289.8 290 290.2 290.4 290.6 290.8 Julian day

Low-wave conditions / Seaward 3

2

h(m) 1

0 286 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8 288

Hs/h (-) 0.5 Hs ( m)

0 Hs(m) and Hs/h(-) 286 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8 288 20

0

alpha SN) (deg -20 286 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8 288 0.5

0

Ymean (m/s) -0.5 286 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8 288 0.5

0 Vcerc (m/s) Vcerc -0.5 286 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8 288 Julian day

Figure 4.7 Mean longshore currents, wave incidence angle alpha in degrees to shore normal, Hs, Hs/h and h in the nearshore for the land and seaward frame. Longshore currents increase significantly when Hs> 0.2 and Hs/h > 0.3. A,B) temporal differences for low and high wave conditions, A, C) Spatial differences for the land-and seaward frame.

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Hydrodynamics results

• (Non - ) Breaking waves Longshore mean current velocities are positively related to the relative significant waveheight

and increase rapidly for breaking conditions Hs/h > 0.3 for the seaward frame as well as for the landward frame.

For both low- and high wave conditions Hs/h peaks at low water which corresponds to three

peaks in longshore current Ymean. This illustrates the importance of Hs/h on the longshore current. Longshore current velocities are of equal magnitude for the sea- and landward frame. Highest longshore mean velocities (0.5 m/s) are attained for high wave conditions; they are a factor 2 larger than for low wave conditions.

• Wave incidence angle (α) Dominantly waves are directed from the south (positive values of α). Highest longshore velocities (0.5 m/s) are attained for steady positive alpha values from day 289.0-290.0, under breaking wave conditions. In Figure 4.7 a clear relation is not present between α and V. Peaks in α do not very well correspond to peaks in the longshore current. This could be related to

stronger influence of Hs/h over α. A general trend of positive α values corresponding to positive longshore current velocities does however exist.

• CERC modeling CERC modeled longshore currents are also shown in Fig 4.7. It can be seen that the CERC formula strongly reflects the behaviour of α. Measured longshore current velocities show a

strong connection with Hs/h. Since in the CERC formula only Hb and α are used the formula

shows less relation with Hs/h than the measured signal. The magnitude of the longshore current is slightly overpredicted for high wave conditions.

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Hydrodynamics results

4.1.5 Intra wave effects: wave skewness

Spatial and temporal variation in near-bed wave orbital skewness at 15 cm above bed level are analyzed using Hs/h as conditional parameter for wave propagation across the surfzone. Skewness ratio’s (S = Uosc,on/(Uosc,on +Uosc,off), Eq. 3.6) range generally between 0.5 and 0.75 and higher values

(Uosc,on > Uosc,off ) indicate more skewness. The skewness ratio is determined by averaged significant cross-shore oscillatory velocities (U1/3th) based upon 256 sec. of data.

To obtain the cross-shore distribution in skewness, the skewness ratio S is plotted against the relative significant wave height at the land and seaward frame simultaneously (Figure 4.8), whereas for the influence of wave height on skewness in the nearshore, the skewness ratio S is plotted for scenario A)

Hs,off < 1.0 m and B) Hs,off > 2.0 m (Figure 4.9). For both situations high and low-tides are taken into account.

0.535 0.535 Seaward, Hs,off = 1-1.5 m Landward, Hs,off = 1-1.5 m 0.53 y = 0.093*x + 0.49 linear 0.53 y = 0.082*x + 0.49 linear

0.525 0.525

0.52 0.52

0.515 0.515 S (-) S (-)

0.51 0.51

0.505 0.505

0.5 0.5

0.495 0.495 0.18 0.2 0.22 0.24 0.26 0.28 0.2 0.25 0.3 0.35 0.4 Hs/h (-) Hs/h (-) Figure 4.8 The skewness of waves for the land and seaward frame in the same period for different relative significant wave heights. A trend line is plotted which indicates a positive relation between S and Hs-h.

0.55 0.55 Seaward, Hs,off < 1.0 m 0.54 y = 0.029*x + 0.5 linear 0.54 y = 0.07*x + 0.49

0.53 0.53

0.52 0.52 S (-) S (-) 0.51 0.51

0.5 0.5

0.49 0.49 Seaward, Hs,off > 2.0 m linear 0.48 0.48 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.3 0.35 0.4 0.45 0.5 Hs/h (-) Hs/h (-) Figure 4.9 The skewness of waves for the seaward frame during two distinct wave height scenario’s for different relative significant wave heights. A trend line is plotted which indicates a positive relation between S and Hs-h.

Results are formulated as follows, bust should be taken with care since the skewness vs. Hs/h relationship exhibits significant scatter. • Spatial change in skewness Generally wave skewness increases for increasing Hs/h. Maximum skewness values amount to 0.525. In the same period, Hs/h ranges from 0.18-0.26 for the seaward frame, whereas for the

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Hydrodynamics results

landward frame Hs/h ranges from 0.23 -0.4. Shoaling waves (Hs/h < 0.3) at the seaward frame show more scatter in wave asymmetry than breaking waves at the landward frame and skewness is of somewhat smaller magnitude. Largest skewness values are observed at low

tide, which can be recognized by the highest Hs/h values at the seaward frame. Regression

coefficients are not very different which implies that if Hs/h increases by 1%, skewness changes in the same order of magnitude for both frames.

• Skewness for high- and low wave conditions For both wave conditions skewness increases with Hs/h. Maximum skewness values attained are 0.53-0.54 for low wave conditions and 0.54-0.55 for high wave conditions. For low wave

conditions Hs/h ranges from 0.1-0.6 and for high wave conditions from 0.3-0.5. Since under

low wave condition the Hs/h range is large the relation between Hs/h and skewness can be seen

more clearly. Largest skewness values are recorded at high tide and correspond to Hs/h = 0.4- 0.5. Finally it should be noted that scatter increases strongly under high-wave conditions.

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Hydrodynamics results

4.2 Beach flat (spit-like platform)

4.2.1 Mean currents

During the severe (Hs,off = 3-5 m) storm, spring tide conditions and wind/wave set-up enabled significant amounts of water to flow into the Slufter basin. The inflow of water is mainly a result of mean flows (Figure 4.10). The first two flooding events were most pronounced and are subject of analysis.

Temporal analysis on the beach flat reveals that a flooding stage can be subdivided in to three phases, A) initial flooding, the period for which water levels are rapidly rising, B) peak flooding at high water where water levels are constant and free infragravity waves are able to progress land inward and C) from basin to sea. All phases are most clearly visible in the first two flooding events at day 275.75-276 and 276.25-276.5 in Figure 4.10. It must be stressed that reliability of data rapidly reduces when the average water level drops below 0.2 m, because in this case the sensor might be elevated above the water level when the trough of a wave passes. For this reason only data is used in analysis for which hw < 0.2. Only the first two flood stages are strongly significant above the 0.2 m boundary. The high water stage can be analyzed with confidence, but results of inflow and outflow have to be taken with a grain of salt.

1 h (m) Hs (m)

0.5 h(m) and Hs(m)

0 275.6 275.8 276 276.2 276.4 276.6 276.8 277 277.2 277.4 277.6

1

0.5

0 Umean (m/s)

-0.5 275.6 275.8 276 276.2 276.4 276.6 276.8 277 277.2 277.4 277.6

0.6

0.4

0.2

0 Vmean (m/s)

-0.2 275.6 275.8 276 276.2 276.4 276.6 276.8 277 277.2 277.4 277.6 Julian day

Figure 4.10 First period of the beach flat inundation; plotted are the water depth (h), the significant wave height and the cross-shore and long-shore velocity. The black dashed line denotes the h=0.2 m boundary.

Figure 4.10 shows mean flows decomposed into flows into the basin (Umean 19.3° corrected) and parallel to the coast (Ymean 19.3° corrected). A rapid rise in water level to 0.4 m is accompanied by mean onshore

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Hydrodynamics results velocities to 0.5-0.6 m/s. After this initial flooding water levels gradually increase to 0.9 m. During ebb cross-shore velocities rapidly reverse into the offshore direction and reach magnitudes of 0.2 – 0.3 m/s. This coincides with a positive peak in the along basin velocity (0.25 m/s) at d=275.95, indicating that part of the drainage of the system occurs from the beach flat to the main channel which is very effective in transporting water offshore.

4.2.2 Intra wave effects: infragravity energy

Wave propagation into the basin mainly occurs during maximum water levels. Waves were entering the basin with a wave incidence angle of roughly 20° SW. Wave spectral density diagrams (Figure 4.11) of the oscillating term in wave height point out that for initial flooding and retreat wave energy is bound at very low frequencies, whereas for the peak flood situation a peak in spectral density can be distinguished at 0.02-0.05 Hz. Figure 4.11 also indicates that highest waves are observed for the initial and peak flood situations (0.5 and 0.44 m respectively). A typical time-series of 512 sec. (Figure 4.12) shows the presence of free infragravity waves. A free infragravity wave is characterized by significant skewness in velocities and is visible in Photo 4.1. High-frequency oscillations behave as irregularities in infragravity waves; most gravity waves have broken in the breaker zone seaward of the beach flat. Free-infragravity waves travel shoreward due to wave breaking in the nearshore and are able to propagate into the Slufter basin instead of being reflected or trapped in the nearshore.

Initial flooding (h=0.46-0.54) Peak flooding (h=0.8-0.85 m) Retreat (h=0.6-0.45 m) 0.25 0.2 0.14

0.18 0.12 0.2 0.16 /Hz) /Hz)

/Hz) 0.1 2 2 0.14 2

0.15 0.12 0.08 0.1 0.06 0.1 0.08

0.06 0.04 Wave spectral density (m Wave spectral density (m Wave spectral density (m 0.05 0.04 0.02 0.02

0 0 0 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 Frequency (Hz) Frequency (Hz) Frequency (Hz) Figure 4.11 Power spectral density of waves on the beach flat for a) initial flooding, b) peak flooding and c) water retreat based upon 512 sec. 8 halfway overlapping 1024- points Fourier transforms.

2 high freq. 1 low freq.

u (m/s) 0

-1 0 50 100 150 200 250 300 350 400 450 500 time (s)

Figure 4.12 Dominance of free infragravity waves entering the basin, high-frequency oscillations exist as infragravity wave irregularities; all gravity waves have broken in the breaker zone in the nearshore. Infragravity waves are heavily skewed (onshore directed velocities are generally higher than offshore).

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Hydrodynamics results

Photo 4.1 Infragravity waves entering the basin during a flooding event.

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Sediment transport results

5 Sediment transport results

5.1 Sediment transport in the breaker zone

5.1.1 Concentrations and cross-shore velocity time series

5-min. Averaged velocity- and sediment concentration time series are given in Figure 5.1. Concentrations at 5 cm above the bed are nearly over the whole period higher than concentrations measured at 20 cm. During low wave-condition at the landward side 5-min averaged concentrations reach maximal values of 5 kg/m3. For high wave conditions, measured concentrations are a factor 2 higher. Noticeable is a high peak in concentrations at low tide at the end of the time series simultaneously occurring with the small positive peak in mean cross-shore current velocities. Highest waves were measured at this point, which suggest increased wave-induced sediment stirring. When comparing cross-shore sediment fluxes it is striking that measured mean fluxes are roughly twice as high under high wave conditions compared to low wave conditions.

Landward / Low-wave conditions High-wave conditions / Landward 0.2 0.2

0 0 U (m/s) U (m/s)

-0.2 -0.2 286 286.5 287 287.5 288 288.5 289 289.5 290 290.5 291

6 15

) C ( 5 c m)

) C (20 cm) 3 3 4 C (5 cm) 10 C (20 cm)

2 5 C (kg/m C (kg/m

0 0 286 286.5 287 287.5 288 288.5 289 289.5 290 290.5 291

0.5 /s) 0.5 2 /s) 2 0 0 -0.5

Mean flux (kg/m -0.5 -1 286 286.5 287 287.5 288 Mean flux (kg/m 288.5 289 289.5 290 290.5 291 julian day julian day

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Sediment transport results

Seaward / Low-wave conditions 0.1

0 U (m/s)

-0.1 286 286.5 287 287.5 288

10 ) 3 5 C (kg/m

0 286 286.5 287 287.5 288

0.5 /s) 2

0

Mean flux (kg/m -0.5 286 286.5 287 287.5 288 julian day

Figure 5.1 The mean cross-shore current velocities (m/s), averaged concentrations (kg/m3) and sediment fluxes (kg/m2/s) for A,B) spatial differences in the cross shore and A,C) low-, and high-wave conditions

Besides analyzing suspended sediment transport, cross-shore transport is subdivided into net, mean, high- and low-frequency oscillatory fluxes and subjected to spatial and temporal analysis as function of the relative significant wave height. Spatial distribution (seaward and landward frame) of sediment fluxes is analyzed for low (Hs,off < 1.0 m) and high-wave (Hs,off > 2.0 m) conditions. All sediment fluxes have been averaged over 512 s.

5.1.2 Cross-shore sediment fluxes (Hs,off < 1.0 m)

Measured sediment fluxes for low wave conditions at the seaward frame are plotted in Figure 5.2 as function of Hs/h for the same period as used in the time series. In this period which lasts three tidal cycles, mean cross-shore currents are dominated by offshore directed undertow.

High-frequency fluxes were for the upper sensor positive for increasing Hs/h values. For Hs /h = 0.2- 0.4, high-frequency fluxes do not deviate significantly from zero and start to increase for breaking 2 waves to maximal values of 0.02 kg/m /s at Hs/h = 0.5. For the lowest sensor, high-frequency sediment fluxes are mainly positive, although a few large negative fluxes have been measured in the range of

Hs/h =0.2-0.4. Onshore fluxes can be related to skewness in wave orbital velocities, whereas negative sediment fluxes can be related to phase differences in velocity- and concentration fields due to the presence of bedforms. According to van Rijn (1993) ripples are frequently present for peak orbital velocities between 0.2 and 0.8 m/s. Field measurements of Osborne and Greenwood (1992b) have shown that high frequency fluxes can be reversed to offshore directions due to the presence of ripples. Sediment elevated from the bed by the positive phase of wave motion is transported backwards by the offshore directed phase of wave motion. The absence of offshore directed sediment fluxes at the highest sensor indicates that bed forms are irrelevant for sediment transport at 20 cm above bed level. Despite some negative fluxes at the lowest sensor, high-frequency fluxes are dominantly onshore

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Sediment transport results directed and increase with Hs/h and peak at Hs/h = 0.45 to values of 0.2 kg/m2/s (which is 10 times larger than for the upper sensor).

Infragravity induced low-frequency fluxes are insignificant for the sediment transport at the upper 2 sensor, although very small negative fluxes are visible at high Hs/h values (0.005 kg/m /s at Hs/h =0.5). For the lower sensor infragravity fluxes are generally negative (offshore directed) over the whole range of Hs/h. Infragravity fluxes remain relatively constant for increasing relative significant wave height, and reach maximal values of -0.05 kg/m2/s. At low Hs/h values group-bound long waves generally induce offshore transport, for higher Hs/h values gradual released long waves can cause an onshore shift in low-frequency sediment fluxes. In the range of Hs/h = 0.3-0.5 some positive sediment fluxes were measured (maximal 0.02 kg/m2/s), although negative fluxes occur more frequent and are of larger magnitude. Infragravity fluxes are far more important at the lower than for the upper sensor.

Lowest Sensor Highest Sensor

/s) 0.5 /s) 0.05 2 2

0 0

-0.5 -0.05 High freq. flux (kg/m 0.2 0.3 0.4 0.5 0.6 High freq. flux (kg/m 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-)

/s) 0.1 /s) 0.05 2 2 0.05

0 0

-0.05

Low freq.Low flux (kg/m -0.1 freq.Low flux (kg/m -0.05 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-) 0.5 0.1 /s) /s) 2 2 0.05

0 0

-0.05

Mean flux (kg/m -0.5 Mean flux (kg/m -0.1 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-) 0.5 0.1 /s) /s) 2 2 0.05

0 0

-0.05 Net flux (kg/m Net flux (kg/m -0.5 -0.1 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-) Figure 5.2 Low wave conditions (seaward frame) - Measured 256 s averaged sediment fluxes a,b) high frequency, c,d) low- frequency, e,f) mean and g,h) net fluxes for the lowest (ca 5 cm) and highest (ca 20 cm) OBS sensor related to the relative significant wave height (Hs/h).

Mean fluxes are generally negative for the highest and lowest sensor except for a few outliers at Hs/h =

0.2-03 and Hs/h= 0.4. At the upper sensor Negative mean fluxes become stronger for higher Hs/h 2 values: peak negative mean fluxes (-0.06 kg/m /s) are recorded at the far end of the Hs/h range (Hs/h >

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Sediment transport results

0.5). This result agrees with mean cross-shore current hydrodynamics for which highest mean currents coincide with largest relative significant wave heights. For the lower sensor maximal offshore directed 2 mean fluxes of -0.2 m kg/m /s are attained at wave breaking Hs/h =0.35-0.45.

High-frequency, low-frequency and mean fluxes combine to produce the net suspended sediment flux. For the upper sensor the net flux is dominated by the mean component (which can also be seen in

Figure 5.6) and becomes progressively more offshore directed for higher Hs/h values. Maximal values 2 of the net flux (-0.05 kg/m /s at Hs/h = 0.5) are somewhat lower than mean fluxes due to the onshore directed high-frequency fluxes which partly compensate the offshore directed mean component. For the lowest sensor, net offshore directed fluxes are generally stronger negative than mean fluxes for 2 Hs/h < 0.5 and stronger positive for Hs/h > 0.45 (+0.2 kg/m /s). The significant increase in offshore directed net flux is caused by a combined effect of low-frequency and mean fluxes which are negative over the complete Hs/h range and the additional contribution of some negative high-frequency fluxes.

The positive directed net flux at high Hs/h values is dominated by the onshore skewness- induced high-frequency flux.

For a better understanding of high and low-frequency motions, oscillatory velocity and concentration signals were subjected to co-spectral analysis to relate oscillations in velocity to sediment concentration bursts. Intraburst time series of 512 seconds at HWS (Hs/h = 0.30) for low wave conditions at the seaward frame are shown in Figure 5.3. Co-spectral analysis was applied under different relative significant wave height scenarios. At Hs /h is approximately 0.30, coherence in velocities and concentrations proved optimal. The velocity time-series show the following characteristics: infragravity energy is still noticeable bound to wave groups (lower during larger amplitude gravity waves and higher under lower amplitude waves), and concentration bursts take place simultaneously with passing of large wave groups. The largest peak in concentration occurs simultaneously with the passage of the largest wave group at t= 230s.

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Sediment transport results

Time series seaward - Low wave conditions at Hs/h = 0.30 1 high-freq. low-freq. 0 u (m/s)

-1 0 50 100 150 200 250 300 350 400 450 500

10

) OBS 5 cm 3

5 C (kg/m

0 0 50 100 150 200 250 300 350 400 450 500

6

) OBS 10 cm 3 4

2 C (kg/m

0 0 50 100 150 200 250 300 350 400 450 500

2

) OBS 20 cm 3

1 C (kg/m

0 0 50 100 150 200 250 300 350 400 450 500 time (s) Figure 5.3 Low wave conditions (seaward frame) – Oscillatory velocity- and concentration time series used for co-spectral analysis. a) High and low-frequency cross-shore velocity, b) suspended concentrations at the OBS at 5 cm, c) suspended concentrations at the OBS at 10 cm, d) suspended concentrations at the OBS at 20 cm.

Frequency domain analysis of the time series presented in Figure 5.3, is shown in Figure 5.4. The power spectral density spectrum of the oscillating velocity peaks at gravity wave frequencies of 0.18 and at 0.16 Hz corresponding to periods of 5-6 seconds and also shows a small peak at infragravity frequencies at 0.01 Hz. Concentrations for the lower and upper OBS peak at the same frequencies. Co- spectral results show for the lowest sensor an onshore directed sediment flux (1.5 kg/m2s/Hz) at 0.16 -0.18 Hz (5.5 s), although this positive peak is not present for the highest sensor. No second peak is visible at 0.36 Hz (2 ) besides the single peak at 0.16-0.18 Hz in the gravity domain (5-6 s) which indicates that sediment was only stirred up during the onshore phase of the wave motion. 𝑓𝑓𝑝𝑝

A negative (offshore directed) peak is present at infragravity frequencies (-0.6 kg/m2s/Hz for the lowest sensor) which gives a smaller flux as the onshore directed peak. The onshore peak at far infragravity frequencies is unreliable and is characterized by a poor coherence between u and c (Coh2 < 0.2). For peaks in the gravity frequencies Coh2 ranges from 0.6-0.8 meaning that coherence is significant. For the peak in infragravity frequencies coherence squared also proved significant with values of Coh2 = 0.8. Generally, the concentration oscillations in the gravity band were almost in phase with the velocity oscillations, which indicates that sediment is transported during onshore phase of wave orbital motion. For the upper sensor, the small negative peak at 0.18 Hz visible in the co-spectral density diagram coincides with a phase difference peak of -170°, indicating that sediment at 0.18 Hz was transported during the offshore phase of the wave motion. At infragravity frequencies the phase differences peak at -180° which implies that the low-frequency concentrations coincide with the peak offshore phase (> 90 and > -90 degrees in the phase diagram) of the low-frequency wave.

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Sediment transport results

Low wave - Hs/h = 0.30 2 10 1.5 U (15 cm) /Hz) s/Hz) 6

C (20 cm) 2

/m 1

2 C ( 5 c m) 0 10 0.5 /Hz) /kg /Hz) 2 /s

2 0

-2 10 -0.5 Energy (m Co-spectral density (kg/m -1 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 Frequency (Hz) Frequency (Hz)

1 150

0.8 100

50 0.6 0 0.4 -50 Phase (deg)

Coherence squared 0.2 -100 -150 0 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 Frequency (Hz) Frequency (Hz)

Figure 5.4 Low wave conditions (seaward frame) – Co-spectral analysis of cross-shore oscillatory velocities and sediment concentrations of frequency domain converted time-series: a) power spectral densities, b) co-spectra, c) coherence squared diagrams and d) phase diagrams.

Measured sediment fluxes for low wave conditions at the landward frame are plotted in Figure 5.5 as function of Hs/h for the same period as for the seaward frame to give an indication of cross-shore suspended sediment transport distributions.

For both sensors high-frequency fluxes generally increase sharply for Hs /h > 0.35. Maximum onshore sediment fluxes are in the order of 0.1-0.2 kg/m2/s. As for the seaward frame, a number of negative fluxes occur for low Hs/h values at the lower sensor and for high Hs/h values at the upper sensor. High frequency fluxes for the lowest sensor are in the same order of magnitude as for the seaward frame, whereas for the highest sensor, high frequency fluxes become a factor 4-5 higher when

Hs/h > 0.35.

Low-frequency fluxes are negative throughout the entire Hs/h range for the lower sensor. For the upper sensor low-frequency fluxes start to develop for Hs/h > 0.35 and are dominantly negative. For high Hs/h values (Hs/h > 0.45) a few positive values in low-frequency fluxes occur. These positive values can be attributed to onshore fluxes by released long waves. Low-frequency fluxes are overall a factor 4-5 higher for the upper sensor with respect to the seaward frame and in the same order of magnitude for the lower sensor.

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Lowest Sensor Highest Sensor /s) 0.2 /s) 0.2 2 2

0 0

-0.2 -0.2 High freq. flux (kg/m 0.2 0.3 0.4 0.5 0.6 High freq. flux (kg/m 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-)

/s) 0.1 /s) 0.1 2 2

0 0

-0.1 -0.1 Low freq.Low flux (kg/m Low freq.Low flux (kg/m 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-)

0.5 0.5 /s) /s) 2 2

0 0

Mean flux (kg/m -0.5 Mean flux (kg/m -0.5 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-) 0.5 0.5 /s) /s) 2 2

0 0 Net flux (kg/m Net flux (kg/m -0.5 -0.5 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-)

Figure 5.5 Low wave conditions (Landward frame) - Measured 256 s averaged sediment fluxes a,b) high frequency, c,d) low-frequency, e,f) mean and g,h) net fluxes for the lowest (ca 5 cm) and highest (ca 20 cm) OBS sensor related to the relative significant wave height (Hs/h).

Mean fluxes are negative for the lower sensor and start increasing from Hs/h = 0.35 and peak at -0.2 2 kg/m /s for Hs/h = 0.4-0.5. For the upper sensor, mean fluxes occur only for Hs/h > 0.38 and are subject to significant more scatter than for the lower sensor. Negative fluxes attain maximum values of -0.4 to -0.5 kg/m2/s. In comparison to the seaward frame, mean fluxes are more negatively distributed along Hs/h. Additionally mean fluxes are a factor 5-10 larger for the upper sensor for high Hs/h values and mean fluxes show a broader negative dominated pattern for the lower sensor.

For the landward frame net fluxes are dominantly offshore over the entire Hs/h range. For low Hs/h values this is due to high- and low-frequency fluxes, whereas from Hs/h > 0.35 net offshore transport is mainly caused by mean currents. In comparison to the seaward frame, net fluxes for the upper sensor are a factor 5-10 larger for the landward frame.

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Most obvious changes form seaward to landward frame in cross-shore sediment fluxes are related to the increase in sediment fluxes at the upper sensor at the landward frame for high Hs /h values. It should be noted that the upper range in Hs/h is larger for the landward frame, i.e more sediment fluxes occur for Hs /h > 0.5 (up to 4 times more occurrences). Therefore it is fair to say that sediment fluxes

(gravity, infragravity and mean) increase for higher Hs /h values. Mean fluxes increase most strongly for higher Hs/h values. This can be related to hydrodynamics, where offshore directed mean currents are a factor 2 larger (-0.1 m/s) for the landward frame at Hs/h peaks with respect to the seaward frame (-0.05 m/s) at Hs/h peaks at LWS.

The relative importance of high-, and low frequency and mean fluxes to the gross suspended transport can be made more clear by examining their relative contributions. Figure 5.6 illustrates the relative contributions of a) the sea- and b) the landward frame during low-wave conditions. At 20 cm above bed level for the seaward frame trends are summarized by a high mean current contribution (frequently exceeding 75 %). For Hs/h > 0.35 the high-frequency contribution increases to some extent (a few values above 50 %), thereby reducing the mean contribution. Infragravity fluxes remain low throughout the entire Hs/h range; the largest part of low-frequency flux contributions stays below 10% of the gross flux. At 5 cm above bed level the mean current contribution and high-frequency fluxes exhibit more scatter; contributions vary strongly. Infragravity energy contributions are higher; the majority is below 20% of the gross suspended sediment flux, although at Hs/h =0.2 -0.3 before wave- breaking initiates, infragravity energy can contribute to 50 % of the gross suspended sediment flux. Here infragravity energy is still bound to short waves and are responsible for offshore fluxes (see Figure 5.2).

Lowest Sensor Highest Sensor Lowest Sensor Highest Sensor 1 1 1 1

0.5 0.5 0.5 0.5 High freq. contribution High freq. contribution

High freq. contribution 0 High freq. contribution 0 0 0 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-) Hs/h (-) Hs/h (-) 1 1 1 1

0.5 0.5 0.5 0.5 Low freq.Low contribution freq.Low contribution Low freq.Low contribution 0 freq.Low contribution 0 0 0 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-) Hs/h (-) Hs/h (-)

1 1 1 1

0.5 0.5 0.5 0.5

0 0 Mean-flow contribution Mean-flow contribution Mean-flow contribution Mean-flow contribution 0 0 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-) Hs/h (-) Hs/h (-)

Figure 5.6 1) Low wave conditions (Seaward frame) - The relative contributions of 1 a,b) high-frequency, 1 c,d) low- frequency and 1 e,f) mean flows to net suspended sediment fluxes. 2) Low wave conditions (landward frame) - The relative contributions of 2 a,b) high-frequency, 2 c,d) low-frequency and 2 e,f) mean flows to net suspended sediment fluxes.

For the upper sensor at the landward frame, high-frequency contributions peak at Hs/h =0.25-0.4 (>

50% ) and decline afterwards for Hs/h > 0.4. For higher Hs/h values wave-breaking becomes saturated

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Sediment transport results and high frequency contributions stay below 50%. For the upper sensor high-frequency fluxes peak at

Hs/h is 0.4-0.5 and diminish afterwards. For the lower sensor, infragravity fluxes are relatively constant over the Hs/h range although maximum contributions (10-20 %) are realized at the onset of breaking at Hs/h =0.3. For the upper sensor infragravity energy increases from Hs/h> 0.35 and the transport contribution remains relatively constant at 10%.

5.1.3 Cross-shore sediment fluxes (Hs,off = 2-3 m)

The measured sediment fluxes for high wave conditions at the landward frame are plotted in Figure

5.7 as function of Hs/h. The period analyzed corresponds to the high-wave period at day 290.

For high-wave conditions, the high frequency fluxes are generally positive. High-frequency fluxes are substantially larger for the lower sensor than for the upper sensor. Maximal onshore gravity fluxes 2 (+0.02 kg/m /s) are reached at Hs/h = 0.3-0.4. With respect to low wave conditions, high frequency fluxes are more strongly skewed to onshore transport and of larger magnitude. Low frequency fluxes are for the lowest sensor a factor 2 larger. Infragravity fluxes demonstrate a peak in the offshore 2 direction at -0.04 kg/m /s for Hs/h = 0.3 at the onset of wave breaking. Low frequency fluxes are very small at the upper sensor.

From the hydrodynamics section it follows that during high-wave conditions mean currents are of larger magnitude than for low wave conditions. In Figure 5.7 largest negative mean fluxes (-0.6 2 kg/m /s) are found at Hs/h=0.4 for the lowest sensor. The upper sensor shows the same pattern with 2 fluxes up to -0.5 kg/m /s. Net fluxes are dominantly offshore directed, except at wave breaking (Hs/h =0.4), where the onshore directed high-frequency contribution is larger. Mean flows are the most strongly contributing mechanisms.

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Lowest Sensor Highest Sensor /s) /s)

2 0.4 2 0.2

0.2 0.1 0 0 -0.2 -0.1

High freq. flux (kg/m 0.2 0.4 0.6 0.8 High freq. flux (kg/m 0.2 0.4 0.6 0.8 Hs/h (-) Hs/h (-) /s) /s) 2

0.05 2 0.05

0 0

-0.05 -0.05 Low freq.Low flux (kg/m

0.2 0.4 0.6 0.8 freq.Low flux (kg/m 0.2 0.4 0.6 0.8 Hs/h (-) Hs/h (-)

/s) 0.5 /s) 0.5 2 2

0 0

-0.5 -0.5 Mean flux (kg/m Mean flux (kg/m 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 Hs/h (-) Hs/h (-) 0.5 0.5 /s) /s) 2 2

0 0

-0.5 -0.5 Net flux (kg/m Net flux (kg/m 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 Hs/h (-) Hs/h (-)

Figure 5.7 High wave conditions (Landward frame) - Measured 256 s averaged sediment fluxes a,b) high frequency, c,d) low-frequency, e,f) mean and g,h) net fluxes for the lowest (ca 5 cm) and highest (ca 20 cm) OBS sensor related to the relative significant wave height (Hs/h).

Co-spectral analysis of oscillatory velocities and concentrations at an HWS situation with local significant wave heights of 1 m and Hs/h = 0.3 (same as for the co-spectral results of the low-wave situation), show a positive peak in the high-frequency spectrum (0.18 Hz) and a negative peak in the infragravity at < 0.05 Hz up to -5 kg/m2s/Hz (Figure 5.8). The high-wave situation is subject to short waves with peak periods of 5.5 s with an offshore directed flux of about 10 kg/m2s/Hz (a factor 6-7 higher compared to 1.5 kg/m2s/Hz for the low-wave situation) for the lower sensor. Whereas no co- spectral peak was visible for the upper sensor under low-wave conditions, under large waves a peak of 1 kg/m2s/Hz is visible at 0.18 Hz. The coherence squared is significant for the peaks in gravity and infragravity frequencies. Phase differences for the offshore peak in the co-spectral density for low frequencies are found to be around 180° for both the sensors. Sediment concentrations are still within phase of the high-frequency wave motion of although phase differences range from -50 to 50°.

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High wave - Hs/h= 0.3

U (15 cm) /Hz) 2 10 s/Hz) 6

10 2 C (20 cm) /m 2 C (5 cm) 5 0

/Hz) /kg /Hz) 10 2 /s 2 0 -2 10 Energy (m Co-spectral density (kg/m -5 0 0.1 0.2 0.3 0 0.1 0.2 0.3 Frequency (Hz) Frequency (Hz)

1 150 0.8 100 50 0.6 0 0.4 -50 Phase (deg)

Coherence squared 0.2 -100 -150 0 0 0.1 0.2 0.3 0 0.1 0.2 0.3 Frequency (Hz) Frequency (Hz)

Figure 5.8 High wave conditions (landward frame) – Co-spectral analysis of cross-shore oscillatory velocities and sediment concentrations of frequency domain converted time-series: a) power spectral densities, b) co-spectra, c) coherence squared diagrams and d) phase diagrams.

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5.1.4 Depth-integrated longshore sediment fluxes

Measured concentrations at respectively 0.05, 0.10 and 0.20 m are used to construct exponential concentration profiles, which are multiplied by calculated velocity profile to obtain transport profiles. Figure 5.9 gives an example how concentration, velocity and transport profiles are constructed.

Concentration profiles Velocity profiles Transport profiles 0.7 0.7 0.7

0.6 0.6 0.6

0.5 0.5 0.5

0.4 0.4 0.4

0.3 0.3 0.3 Height above bed (m) Height above bed (m) Height above bed (m) 0.2 0.2 0.2

0.1 0.1 0.1

0 0 0 0 0.5 1 1.5 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 3 2 5 min-averaged concentration (kg/m ) 5 min-averaged velocities (m/s) 5 min-averaged sediment transport (kg/m /s)

Figure 5.9 a) Concentration, b) velocity and c) suspended transport profile for a depth of z= 0.05 m – Hw and a mean longshore velocity of 0.15 m/s.

Depth-integrated suspended transport is calculated by the integration over depth of the 5 min averaged transport profiles presented in Figure 5.10 and Figure 5.11. The figures indicates that sediment concentrations reach maximally 2 kg/m3 at z = 0.05 m for low wave conditions, whereas for high wave conditions sediment concentration reach maximally 6.2 kg/m3 at z = 0.05 m.

The resultant transport profiles range from -0.05 kg/m2/s to 0.2 kg/m2/s at z = 0.05 m for low wave conditions and -0.25 kg/m2/s to 1.25 kg/m2/s at z = 0.05 m for high wave conditions. Transport profiles decline less rapidly than sediment concentration profiles because velocities increase with height above the bed in the used logarithmic velocity profile. For larger heights above the bed, the inaccuracy of the logarithmic profile is less relevant due to sharply declining concentrations.

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Concentration profiles Velocity profiles Transport profiles 2.5 2.5 2.5

2 2 2

1.5 1.5 1.5

1 1 1 Height above bed (m)

0.5 0.5 0.5

0 0 0 0 1 2 3 -0.2 0 0.2 0.4 0.6 -0.1 0 0.1 0.2 0.3 3 5 min averaged velocities (m/s) 2 5 min averaged concentration (kg/m ) 5 min averaged sediment transport (kg/m /s) Figure 5.10 a) Concentration, b) velocity and c) suspended transport profiles used for depth-integrated suspended longshore transport rates for low wave conditions.

Concentration profiles Velocity profiles Transport profiles 3 3 3

2.5 2.5 2.5

2 2 2

1.5 1.5 1.5

Height above bed (m) 1 1 1

0.5 0.5 0.5

0 0 0 0 2 4 6 -0.5 0 0.5 1 -0.5 0 0.5 1 1.5 5 min averaged concentration (kg/m3) 5 min averaged sediment transport (kg/m2/s) 5 min averaged velocities (m/s) Figure 5.11 a) Concentration, b) velocity and c) suspended transport profiles used for depth-integrated suspended longshore transport rates for high wave conditions.

Depth-integrated concentration fields and sediment transport rates are calculated by integrating both the concentration and sediment transport profiles, and plotted in Figure 5.12. Each point in Figure 5.12 below denotes the integrant of a concentration/transport profile from z = 0.05 – hw. Such a point gives the total depth-integrated concentration and longshore sediment flux in the water column. Under low wave conditions, depth-integrated transport ranges from -0.18 - + 0.08 kg/m2/s, corresponding to maximal longshore velocities up to ca 0.2 m/s. Although an occasional peak in measured sediment fluxes in southern direction is observed, transport is mainly in northern direction and the time- integrated flux is positive (in northern direction). Under high wave conditions, larger fluxes (-0.3 – 0.8 kg/m/s) are the result of both increased concentrations in the water column (more intense wave

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Sediment transport results breaking) and higher longshore current velocities. This results in a longshore sediment transport which is for dominant northern direction 10 times higher compared to low-wave conditions.

Landward / Low-wave conditions Landward / High wave conditions Longshore depth-integrated suspended sediment transport rates (z > 0.05 cm) Longshore depth-integrated suspended sediment transport rates (z > 0.05 cm) 1 0.6

0.4 0.5

0.2 0 0 -0.5 Longshore velocity V (m/s)

Longshore velocity V (m/s) -0.2 289 289.5 290 290.5 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8

1.5 2

1.5

1 and V) (m/s) ) and V) (m/s) 2 2 1

0.5 0.5

0 0 289 289.5 290 290.5 Depth-int (kg/m C 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8 Depth-int (kg/m C

0.2 1

0.1 0.5

0 0 -0.1

-0.2 -0.5 289 289.5 290 290.5

Depth-int sed. transport (kg/m/s) 286.2 286.4 286.6 286.8 287 287.2 287.4 287.6 287.8 Depth-int sed. transport (kg/m/s) Julian day Julian day

Figure 5.12 The cross-shore distribution of depth-integrated suspended and time-averaged longshore transport rates constructed for part of the period used in cross-shore analysis, constructed by the product of depth-integrated transport profiles: a) landward frame and b) seaward frame

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5.2 Sediment transport on the beach flat (Hs,off = 4-5 m)

5.2.1 Concentrations and cross-shore velocity time series

The time series of averaged sediment concentrations on the beach flat show that concentrations are large during the initial flooding and during ebb (Figure 5.13). In Figure 5.13 only data is analyzed for which the water level is higher than 0.2 m. During the major part of the inundation, cross-shore mean fluxes are positive and thus directed into the basin. 5-Min averaged fluxes are calculated to be around 0.6 kg/m2/s for the lowest sensor and 0.3 kg/m2/s for the upper sensor. Compared to the breaker zone conditions, this is comparable to the mean offshore transport fluxes which are attained under offshore significant wave height conditions of 3 m. It should be stressed onshore sediment transport during the initial incoming tide and peak flood conditions occurs over the whole beach flat. Although not everywhere the same fluxes will be attained, sediment import due to mean currents is significant.

1

0.5

U (m/s) 0

-0.5 275.6 275.8 276 276.2 276.4 276.6 276.8 277 277.2 277.4 277.6

10 C (20 cm) )

3 5 C (5 cm)

C (kg/m 0

-5 275.6 275.8 276 276.2 276.4 276.6 276.8 277 277.2 277.4 277.6

2 /s)

2 Flux (20 cm) 1 Flux (5 cm) 0

-1 Mean flux (kg/m -2 275.6 275.8 276 276.2 276.4 276.6 276.8 277 277.2 277.4 277.6 Julian day

Figure 5.13 Cross-shore mean velocities over the beach flat and measured concentrations to obtain the mean fluxes during the flooding events. Mean velocities were measured at 15 cm; for mean flux calculation the Van Rijn velocity profile calculation (chapter 2 is used) to plot fluxes at 5 and 20 cm depth.

During the first flooding event a very large concentration peak is observed during ebb flow. This peak is not present in the subsequent flooding events. Overall time-integrated mean fluxes are directed land inward.

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5.2.2 Cross-shore sediment fluxes

Measured sediment fluxes for the first inundation of the beach flat at day 275.8 are plotted in Figure

5.14 as function of Hs/h; water levels varied during this period from 0.5-0.8 m and measurements include the initial incoming tide, peak flood flow and ebb flow. High frequency fluxes for the lower sensor are onshore directed and are in the order of 0.01 – 0.02 kg/m2/s. For the highest sensor high 2 frequency fluxes scatter from Hs/h > 0.3 but are generally offshore directed (maximal -0.05 kg/m /s).

2 Low frequency fluxes are over the entire Hs/h range positive and peak at Hs/h =0.3 to 0.08 kg/m /s for the lower sensor. For the upper sensor, infragravity fluxes increase from Hs/h = 0.3 and are generally 2 negative (0.06 kg/m /s). Mean fluxes are positive for both sensors over the whole Hs/h range and peak at 0.35 kg/m2/s for the lower sensor and at 0.55 kg/m2/s for the upper sensor. It should be noted that mean fluxes are ‘velocity-depth’ corrected, which results in smaller velocities for the lowest sensor. Nonetheless, larger transport fluxes for the upper sensor indicate high concentrations throughout the water column. The mean flux is most important for the net transport. Net fluxes are therefore positive over the entire Hs/h range.

Relative contributions are plotted in Figure 5.15. Except for one outlier mean fluxes contribute 75 % to the gross suspended transport for the lowest sensor. High frequency fluxes are restricted to 5-10% and low-frequency fluxes form the remaining 15-20 % of the gross cross-shore suspended transport. The highest sensor shows some more scatter in measured values. Most values are even more dominated by the mean current. There are however a number of net sediment fluxes that are significantly influenced by gravity and infragravity fluxes.

The same sediment flux patterns are observed during the second inundation event (Figure 5.16). Generally, mean current fluxes contribute most strongly to sediment import into the system. As measured during the first inundation, the lowest sensor indicates onshore (infra-) gravity transport. Fluxes are during the second inundation event about a factor 2 lower. Contributions of the individual low-, high-frequency and mean fluxes seem to be equally important for net transport.

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Lowest Sensor Highest Sensor

/s) 0.1 /s) 0.1 2 2

0 0

-0.1 -0.1 High freq. flux (kg/m 0.2 0.25 0.3 0.35 0.4 0.45 High freq. flux (kg/m 0.2 0.25 0.3 0.35 0.4 0.45 Hs/h (-) Hs/h (-)

/s) 0.2 /s) 0.2 2 2

0 0

-0.2 -0.2 Low freq.Low flux (kg/m 0.2 0.25 0.3 0.35 0.4 0.45 freq.Low flux (kg/m 0.2 0.25 0.3 0.35 0.4 0.45 Hs/h (-) Hs/h (-)

0.5 1 /s) /s) 2 2 0.5 0 0

Mean flux (kg/m -0.5 Mean flux (kg/m -0.5 0.2 0.25 0.3 0.35 0.4 0.45 0.2 0.25 0.3 0.35 0.4 0.45 Hs/h (-) Hs/h (-)

0.5 1 /s) /s) 2 2 0.5 0 0 Net flux (kg/m Net flux (kg/m -0.5 -0.5 0.2 0.25 0.3 0.35 0.4 0.45 0.2 0.25 0.3 0.35 0.4 0.45 Hs/h (-) Hs/h (-)

Figure 5.14 First beach flat largest inundation - Measured 5-min averaged sediment fluxes a,b) high frequency, c,d) low- frequency, e,f) mean and g,h) net fluxes for the lowest (ca 5 cm) and highest (ca 20 cm) OBS sensor related to the relative significant wave height (Hs/h).

Lowest Sensor Highest Sensor 1 1

0.5 0.5

0 0 High freq. contribution High freq. contribution 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-) 1 1

0.5 0.5

Low freq.Low contribution 0 freq.Low contribution 0 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-) 1 1

0.5 0.5

0 0 Mean-flow contribution 0.2 0.3 0.4 0.5 0.6 Mean-flow contribution 0.2 0.3 0.4 0.5 0.6 Hs/h (-) Hs/h (-)

Figure 5.15 Beach flat largest inundation - The relative contributions of a,b) high-frequency, c,d) low-frequency and e,f) mean flows to gross suspended sediment fluxes.

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Lowest Sensor Highest Sensor

/s) 0.05 /s) 0.05 2 2

0 0

-0.05 -0.05 High freq. flux (kg/m 0.2 0.25 0.3 High freq. flux (kg/m 0.2 0.25 0.3 0.35 Hs/h (-) Hs/h (-) /s) /s) 0.1 0.1 2 2

0 0

-0.1 -0.1 Low freq.Low flux (kg/m Low freq.Low flux (kg/m 0.2 0.25 0.3 0.2 0.25 0.3 0.35 Hs/h (-) Hs/h (-)

0.2 0.2 /s) /s) 2 2

0 0 Mean flux (kg/m -0.2 Mean flux (kg/m -0.2 0.2 0.25 0.3 0.2 0.25 0.3 0.35 Hs/h (-) Hs/h (-)

0.2 0.2 /s) /s) 2 2

0 0 Net flux (kg/m Net flux (kg/m -0.2 -0.2 0.2 0.25 0.3 0.2 0.25 0.3 0.35 Hs/h (-) Hs/h (-)

Figure 5.16 Second beach flat largest inundation - Measured 5-min averaged sediment fluxes a,b) high frequency, c,d) low- frequency, e,f) mean and g,h) net fluxes for the lowest (ca 5 cm) and highest (ca 20 cm) OBS sensor related to the relative significant wave height (Hs/h).

In the oscillatory velocity and concentration time series at the peak flood (Figure 5.17) on the beach flat the form of the infragravity wave is clearly visible. Infragravity waves reach current speeds up to +1 and -0.5 m/s and are strongly skewed and asymmetric. Gravity waves are very small and not well developed; they look more like infragravity wave irregularities. Concentration bursts seem to coincide with the largest amplitude infragravity waves. Figure 5.18 represents the peak-flood time-series of the second inundation event and shows a similar pattern of skewed infragravity dominance.

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2 high freq. 1 low freq.

u (m/s) 0

-1 0 50 100 150 200 250 300 350 400 450 500

4 OBS 5 cm ) 3

2 C (kg/m

0 0 50 100 150 200 250 300 350 400 450 500

2

) OBS 10 cm 3

1 C (kg/m

0 0 50 100 150 200 250 300 350 400 450 500 2

) OBS 20 cm 3

1 C (kg/m

0 0 50 100 150 200 250 300 350 400 450 500 time (s)

Figure 5.17 First inundation - Peak flood condition (h = 0.8 and Hs/h = 0.3) - Velocity- and concentration time series used for co-spectral analysis. a) High and low-frequency fluxes of the cross-shore velocity, b) suspended concentrations at the OBS at 5 cm, c) suspended concentrations at the OBS at 10 cm, d) suspended concentrations at the OBS at 20 cm.

1 high-freq. low -freq. 0 u (m/s)

-1 0 50 100 150 200 250 300 350 400 450 500 3

) OBS 5 cm 3 2

1 C (kg/m

0 0 50 100 150 200 250 300 350 400 450 500

1.5

) OBS 10 cm 3 1

0.5 C (kg/m

0 0 50 100 150 200 250 300 350 400 450 500 1

) OBS 20 cm 3

0.5 C (kg/m

0 0 50 100 150 200 250 300 350 400 450 500 time (s)

Figure 5.18 Second inundation - Peak flood condition (h = 0.6 and Hs/h = 0.3) - Velocity- and concentration time series used for co-spectral analysis. a) High and low-frequency fluxes of the cross-shore velocity, b) suspended concentrations at the OBS at 5 cm, c) suspended concentrations at the OBS at 10 cm, d) suspended concentrations at the OBS at 20 cm.

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Spectral analysis of the time series above is presented in Figure 5.19 (first inundation) and Figure 5.20 (second inundation). The power spectral density diagram of the first inundation series shows a velocity peak at 0.02 Hz and a smaller peak at 0.05 Hz which are probably not significant. Sediment concentrations peak at far infragravity frequencies. Because the sediment concentrations are relatively in phase (-90° < phase < +90°) with the infragravity wave orbital velocities, the infragravity sediment flux is onshore directed. This is illustrated in the co-spectral diagram which shows an onshore peak of 1.75 kg/m2s/Hz at 0.02 Hz for the lowest sensor and 0.5 kg/m2s/Hz for the highest sensor. The smaller peak at 0.05 Hz reaches flux densities of 0.25 kg/m2s/Hz for the lower sensor. The coherence squared is significant for infragravity frequencies.

2 10 2 u 1 /Hz) 1.5

C 20 cm s/Hz) 6 10 2

/m C 5 cm 2 0 1 10

/Hz) /kg /Hz) 0.5 2 -1 /s 10 2 0 -2 10 -0.5 Energy (m Co-spectral density (kg/m -3 10 -1 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3 Frequency (Hz) Frequency (Hz)

1 150

0.8 100

50 0.6 0 0.4

Phase (deg) -50 Coherence squared 0.2 -100 -150 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3 Frequency (Hz) Frequency (Hz)

Figure 5.19 First inundation - Peak flood condition (h = 0.8 m , Hs/h = 0.3) – Co-spectral analysis of cross-shore oscillatory velocities and sediment concentrations of to frequency domain converted time-series: a) power spectral densities, b) co- spectra, c) coherence squared diagrams and d) phase diagrams.

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Sediment transport results

2 10 1.5 /Hz)

U 15 cm s/Hz) 6 2

/m C (20 cm)

2 1 C ( 5 c m) 0 10

/Hz) /kg /Hz) 0.5 2 /s 2

-2 0 10 Energy (m Co-spectral density (kg/m -0.5 0 0.1 0.2 0.3 0 0.1 0.2 0.3 Frequency (Hz) Frequency (Hz)

1 150 0.8 100 50 0.6 0 0.4 -50 Phase (deg)

Coherence squared 0.2 -100 -150 0 0 0.1 0.2 0.3 0 0.1 0.2 0.3 Frequency (Hz) Frequency (Hz)

Figure 5.20 Second inundation - Peak flood condition (h = 0.8 m , Hs/h = 0.3) – Co-spectral analysis of cross-shore oscillatory velocities and sediment concentrations of to frequency domain converted time-series: a) power spectral densities, b) co- spectra, c) coherence squared diagrams and d) phase diagrams.

Co-spectral results of the second inundation event are very similar: a small peak at 0.05 Hz which is in the same order of magnitude (0.5 kg/m2s/Hz – lowest sensor) as during the first inundation and a large peak at 0.02 Hz (0.8 kg/m2s/Hz – lowest sensor), which is of subordinate magnitude compared to the first inundation. Infragravity transport occurs dominantly during the onshore phase of wave motions, which implies that infragravity fluxes are onshore directed.

Additional co-spectral analysis was done during the first inundation event for the initial flood (Figure 5.21) conditions and when water retreated from the beach flat flowing back to the sea (Figure 5.22). Boundary conditions for the initial flooding were confined at h= 0.5 m and Hs/h = 0.35, water depth was still increasing until HWS at 0.8 m. Co-spectra show a significant peak in infragravity energy at positive flux densities of 0.5 kg/m2s/Hz for the lowest sensor and 0.2 kg/m2s/Hz for the highest sensor at 0.02 Hz (the same 50 second periods as for the peak flooding situations). Maximal sediment fluxes are reached at infragravity frequencies up to 1.8 kg/m2s/Hz for the highest sensor. The coherence is strong for the infragravity 0.02 Hz peak (0.8), but is relatively low (0.3) although still significant for infragravity frequencies.

During outflow/ falling tide boundary conditions were h = 0.55 m and Hs/h = 0.22 m. Only very small peaks remain in the co-spectra of oscillatory velocity and concentration signals. For the 0.02 Hz signal sediment flux density is only 0.28 kg/m2s/Hz compared to 1.75 kg/m2s/Hz for the peak situation indicating diminishing influence of oscillatory fluxes on net suspended sediment transport in

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Sediment transport results comparison to peak flood conditions. Finally, it must be noted that because boundary conditions change co-spectral results have to be interpreted with care.

Initial flooding: h=0.50, Hs/h =0.35 2 10 2 U 15 cm /Hz) s/Hz) 6 C 10 cm 2 1.5 /m

2 C 5 c m 0 1 10

/Hz) /kg /Hz) 0.5 2 /s 2 0 -2 10 -0.5 Energy (m Co-spectral density (kg/m -1 0 0.1 0.2 0.3 0 0.1 0.2 0.3 Frequency (Hz) Frequency (Hz)

1 150

0.8 100

50 0.6 0 0.4 -50 Phase (deg)

Coherence squared 0.2 -100 -150 0 0 0.1 0.2 0.3 0 0.1 0.2 0.3 Frequency (Hz) Frequency (Hz)

Figure 5.21 First inundation - Initial flood (h = 0.5 m , Hs/h = 0.35) – Co-spectral analysis of cross-shore oscillatory velocities and sediment concentrations of to frequency domain converted time-series: a) power spectral densities, b) co-spectra, c) coherence squared diagrams and d) phase diagrams.

Retreat h = 0.55, Hs/h = 0.22 2 10 2 U 15 cm 1 C 5 c m /Hz) 1.5 s/Hz) 6

10 2 C 10 cm /m 2 1 0 10 0.5 /Hz) /kg /Hz) 2 -1 /s

2 10 0

-2 10 -0.5 Energy (m Co-spectral density (kg/m -3 10 -1 0 0.1 0.2 0.3 0 0.1 0.2 0.3 Frequency (Hz) Frequency (Hz)

Figure 5.22 First inundation – Falling tide and outflow (h = 0.55 m , Hs/h = 0.22) – Co-spectral analysis of cross-shore oscillatory velocities and sediment concentrations of to frequency domain converted time-series: a) power spectral densities, b) co-spectra.

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Discussion

6 Discussion

6.1 Transport for moderate wave energy conditions (Hs,off < 3 m)

6.1.1 Cross-shore sediment transport in the breaker zone

Field measurements on wave driven transport processes in the breaker zone at the Slufter, Texel demonstrate that low-, high-frequency and mean fluxes were important in determining the cross-shore net-transport rate for high wave conditions. High-frequency and mean fluxes were often higher than low-frequency fluxes but opposed in direction so that low-frequency can be important for the net cross-shore transport under low- moderate wave energy conditions.

During low wave-conditions (Hs,off < 1 m) net suspended transport rates were distributed in the range of -0.3 - +0.1 kg/m2/s, mainly offshore directed. High-frequency fluxes were found to be in the same order of magnitude as the mean fluxes although of opposite sign. Thereby they often cancel each other out. General trends indicate that offshore calculated mean current velocities by equation 4.1 (Van Rijn, 1993) seem to agree reasonable well with measured mean velocities.

Low-frequency fluxes were of smaller magnitude (-0.05 kg/m2/s) and directed offshore. In Ruessink et al. (1998) contributions of high-, low- frequency and mean fluxes to cross-shore transport at depths of 3-9 m at Terschelling are analyzed. They observe a balance between offshore directed mean currents and onshore directed high-frequency fluxes was observed. Infragravity fluxes, although significantly smaller, were however steadily offshore directed and did have significant influence on net transport rates and directions. Although the research at Terschelling was subject to significantly larger water depths, results are in line with the low wave situation at the Slufter system where infragravity waves have a 10-20% contribution to the gross suspended transport and seem to be important for offshore transport.

For more energetic conditions (Hs,off = 2-3 m) generally offshore directed net suspended transport fluxes are observed. Although generally onshore directed gravity fluxes increased during high wave conditions, net fluxes were dominated by mean fluxes over the whole Hs/h range. Measured infragravity fluxes were relatively low and seem to be less important for cross-shore transport.

One peak in onshore directed mean fluxes is observed and associated with onshore directed mean currents during the last part of the tidal cycle. It should be noted that based on visual observations, the field side was characterized by a downdrift migrating sand body. Onshore directed mean fluxes were in earlier research reported by Aagaard et al. (1998) and Aagaard et al. (2006) related to onshore bar

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Discussion migration. Onshore directed mean fluxes were induced by cell circulation. Under these conditions, fluxes of waves at (infra)-gravity frequencies were found of subordinate magnitude to the mean transport. In Aagaard (2006) an onshore migrating bar in three-dimensional bar settings filled up a runnel. Onshore directed mean currents were found here for high-wave conditions. For low-wave conditions (weakly breaking or shoaling) suspended sediment transport was consistently directed offshore mainly due to the mean component.

6.1.2 Longshore sediment transport in the breaker zone

The longshore current is generated by wind- tidal and wave-drive components. Measurements were done at a site far shoreward which was frequently in the breaker zone. Here, the wave-driven longshore current should be the dominant process. The magnitude of the wave-induced longshore current is mainly determined by the wave height and the angle of incidence at wave breaking. Here it is found that the relative significant wave height is the most significant parameter in explaining the fluctuations in magnitude of the longshore current. The anticipated relation with the wave incidence angle is less evident. Close to the beach substantial refraction of the wave field has already occurred and thereby also local morphology influences this parameter.

According to theory (Grasmeijer, 2002), highest longshore current velocities should be observed for maximal wave breaking and decline further shoreward. In the Slufter breaker zone it is found that longshore currents are generated shortly before wave breaking and reach maximal velocities for Hs/h > 0.3. Hydrodynamic results point out that longshore current velocities are a factor 2 higher for high wave conditions (Hs,off = 2-3 m) than for low wave conditions (Hs, off < 1 m). CERC modeling provides a viable approach to longshore currents in the breaker zone, but does not account for the Hs/h dependence and overpredicts magnitudes.

Sediment transport results indicate that longshore fluxes however are a factor 5-10 higher for high wave conditions (Hs,off = 2-3 m) than for low wave conditions (Hs, off < 1 m). These results are in line with Yu et al., 1993 who found much higher longshore fluxes during higher wave conditions. Maximal suspended sediment longshore fluxes are found to be larger than maximal cross-shore fluxes (1.2 - 1.3 kg/m2/s with respect to 0.5 - 0.6 kg/m2/s). This indicates that longshore transport is generally of larger magnitude than cross-shore transport. Hydrodynamic results indicate that higher longshore fluxes are caused by the higher mean velocities in the longshore direction ( - 0.5 m/s max. with respect to - 0.2 m/s) and higher concentrations in the water column during intensified wave 𝑣𝑣̅ breaking. 𝑢𝑢�

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Discussion

6.2 Inundation beach flat (Hs,off > 4 m)

During the severe storm events (Hs, off = 4-5 m) the beach flat was completely inundated. Water levels reached heights of 0.8-0.9 m above the bed during the largest flooding event. This main event is used for process based sediment transport analysis. Cross-shore sediment flux results point out that the mean component is most significant in determining inland sediment fluxes.

To gain insight in to the dimensions over which sediment transport occurs during the storm a simple calculation of sediment transport is extrapolated over dimension and time. The Slufter cross-section measures 400 m, for which the beach flat stretches 340 m. The water level during strongest onshore fluxes (0.4 kg/m2/s) is roughly 0.6 m. Furthermore it is assumed that the beach flat slopes over the cross-section (0-340 m) from 0-0.6 m water depth in a straight line.

1 = 2 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑡𝑡𝑡𝑡𝑡𝑡 𝑤𝑤ℎ𝑤𝑤 ∗ 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓

Where w is the width of the beach flat (340 m), hw is the water depth and flux is the flux measured at 5-20 cm above the bed level. For simple calculation purposes the flux is assumed to be constant over the entire water column. This is a strong assumption, although sediment transport results indicate that measured sediment transport fluxes from 5-20 cm are in the same order of magnitude. The calculated total flux is then ca. 50 kg/s. So a rough estimate on sediment import indicates that during peak flooding each second 50 kg of sediment is imported over the beach flat, neglecting the transport which occurs in the main channel. For total transport over the beach during one tidal cycle additional assumptions have to be made on average flow velocity and concentrations. For simplicity the time- averaged total flux during the flooding is assumed to be 1/4th of the total flux, because of time (flux increase from zero to peak and back over time) and scale reasons (flooding occurs over increasing cross-sectional area and back). Then the total import of sediment during one tidal cycle which lasts 3 roughly 6 hours is in the order of 250000 kg (100 m ), leaving alone import/export in the main channel.

Mean fluxes contribute for 80-90 % to the net suspended sediment transport over the beach flat. Infragravity waves are second important contributors to net transport rates. Co-spectral results show that the largest infragravity wave energy enters when the beach flat is completely inundated (peak flooding). For initial flooding infragravity energy is less important and mean flows are most important for sediment transport. At falling tide low infragravity peaks are found in co-spectral analysis indicating that infragravity wave propagation is minimal.

The falling tide situation is not used for high-, low-, and mean flux analysis because the period is very short and results are unreliable. Sediment fluxes are approximately zero with a tendency to become negative. According to hydrodynamic results peak offshore velocities are attained for very low water depths (h < 0.3 m) which casts some doubt on the quality of data. The peak in outflow velocities is according to the cross-shore corrected mean velocities -0.3 m/s. The peak in outflow coincides with a

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Discussion positive peak in the original Y direction (0.35 m/s), which indicates that outflow occurs from the beach flat to the main channel because the channel acts as efficient drainage system

International literature on overwash and basin inundation has not been extensively documented. Ongoing research on wave propagation is carried out by the US Army Corps of Engineers for lowland areas at islands sheltered by coral reefs (Demirbilek and Nwogu, 2007). During typhoons the water levels are elevated above coral reef level by surges and waves are able to propagate inland. Co-spectral results at Ipan, Guam (Micronesia) show a gradual cross-shore shift to far lower frequencies. Co- spectral results of the Slufter beach flat show a similar co-spectral pattern during the initial flooding situation. Although far infragravity waves are of significant magnitude in the Slufter basin during the semi-severe storm / spring tide event, the major part of cross-shore suspended sediment transport is determined by mean fluxes. Simultaneously with transport over the beach flat sediment is transported through the main channel. During falling tide the main channel is important for the seaward transport of water/ sediment. For more information on sediment transport in the main channel see the thesis of Kramer (2009).

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Discussion

6.3 Wave-driven influence on the Slufter system

Under low-moderate wave energy conditions, tidal exchange between sea and adjacent Slufter basin is restricted to the main channel, whereas under storm and/or spring tide conditions tidal exchange also occurs over the spit-like platforms (beach flat) between the northern and southern dune rows. For wave-driven influence on the dynamics of the Slufter, this implies that under normal conditions wave influence is restricted to the surf zone, whereas under storm and/or spring tide conditions waves are able to propagate into the system and are important for sediment transport patterns within the system.

Cross-shore transport is relatively balanced compared to longshore sediment transport which is not only of larger magnitude than cross-shore transport, but also has a steady direction. For cross-shore transport high-frequency and mean fluxes often are of opposed sign and lead to a reduction of net cross-shore transport. Often this implies that opposite infragravity fluxes, although of smaller magnitude, become of importance for cross-shore transport.

Longshore sediment fluxes are found to be generally a factor 2-3 higher than cross-shore sediment fluxes, which implies that under normal conditions it are mainly longshore currents which affect sediment transport patterns in the nearshore. According to theory, the longshore current imposes a constant downdrift forcing on channel mouth migration which involves the process of sediment bypassing. Sediment bypassing (Gerritsen et al., 2003; Castelle et al., 2003 and Fitzgerald and Pendleton, 2002) is the process by which sediment moves from the up- to downdrift side of the inlet, thereby interacting with the inlet channel and ebb-tidal delta. For the Slufter, under low-moderate wave energy conditions there is no interaction between inlet and wave-driven transport. This situation changes substantially under storm conditions.

Under storm and/or spring tide conditions beach flat inundation can occur. During these conditions the entire Slufter basin is inundated. Gravity waves break offshore in the breaker zone and probably generate strong longshore currents. During the flood event mean fluxes on the beach flat were dominantly directed onshore which implies sediment import into the system. Additionally, skewed and asymmetric free infragravity waves were able to propagate over the beach flat into the basin and caused additional inland transport. During beach flat inundation onshore transport is fully dominant in the system, although during ebb, very high offshore directed sediment fluxes were measured in the main channel (see thesis Kramer, 2009). Ebb-tidal flow in the channel can transport sediment to the outside of the delta where longshore currents can transport the available sediment past the inlet. In conclusion, currents, fluxes and spatial scale of sediment transport patterns are of a much higher order under storm and/or spring tide conditions making inland flooding of Slufters a viable subject for future research.

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Discussion

6.4 Future recommendations

The Slufter fieldwork campaign 2008 is until now the most extensive university organized campaign for this system. Miniframes were used which have proven their value over years, complemented by a Truc Vert frame which is capable of processing and storing more data.

Velocity and concentration measurements generated interesting results for the breaking zone and especially for the beach flat. In literature (Fitzgerald, 2000; Balouin and Howa, 2002), longshore current is often found important for sediment bypassing. Therefore additional longshore current measurement and modeling near the main channel inlet mouth could yield new insights into system dynamics.

Beach flat inundation measurements provide relatively new information on small tidal inlet system dynamics. For future research it would be desirable to have a cross-shore line of measurement frames located from breaking zone to beach flat to measure wave spectrum deformation to analyze the shift to lower frequencies. Finally, this thesis treats suspended sediment transport. Bed load transport modeling can add significant value to research on Slufter dynamics.

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Conclusions

Conclusions

During a measurement campaign of 6 weeks at the Slufter system it was found that the morphodynamic behaviour of the system is very different under low-moderate wave energy and storm conditions. Under low-moderate wave energy conditions measurement were done in the breaker zone, whereas during the storm measurements were performed on the spit-like platform (beach flat) inside the system.

Hydrodynamics • Low-moderate wave energy conditions Mean currents in the breaking zone show an alternating signal with the tide and become

increasingly negative for Hs/h > 0.3 for low wave conditions . During ebb mean cross-shore currents are offshore directed. Modeled offshore mean current velocities by the formula of van Rijn (1993) show a similar pattern. For high wave conditions offshore mean currents are

stronger. Wave skewness increases for higher Hs/h ratios and higher asymmetry ratios are found for high wave conditions. Measured longshore mean currents were found to be strongly influenced by the relative significant wave height and reached velocities up to 0.5 m/s.

• Storm conditions During flooding of the Slufter system 5-min averaged mean onshore velocities reached 0.5 m/s on the beach flat. Under ebb conditions cross-shore velocities declined rapidly to negative values of 0.2 – 0.3 m/s. Highest waves entering the beach flat were in the infragravity region for the initial and peak flood situations and oscillatory velocities reached up to + 0.8 / -0.5 m/s. During ebb, the wave-influence is rather small.

Sediment transport • Low-moderate wave energy conditions Although the contribution to the gross suspended sediment transport does not exceed 20 %, infragravity waves were important for net offshore transport in the breaking zone during low wave conditions. Mean fluxes (generally offshore) and high-frequency (generally onshore) fluxes contributed stronger to the net transport, but frequently were of opposite sign. The

consistent negative infragravity signal over the whole Hs/h range is important for net offshore transport. For high wave conditions, net suspended transport was dominated by the mean flux component which was dominantly directed offshore, partly compensated by higher onshore high-frequency fluxes. Low-frequency fluxes were only a fraction higher for high wave conditions. Mean sediment fluxes reached maximal offshore directed values at wave breaking

(0.3 < Hs/h < 0.55) whereas high-frequency sediment fluxes reached maximal onshore

directed values wave breaking. At very high Hs/h values (0.6-0.8) some indication of infragravity wave release is visible as onshore directed low frequency fluxes. Longshore fluxes were consistently larger than cross-shore fluxes and dominantly northward directed.

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Conclusions

• Storm conditions Flooding events of the beach flat are dominated by onshore directed mean fluxes. Average mean fluxes contributed to more than 75% of the net suspended sediment transport. Infragravity fluxes were dominant in the oscillatory velocity signal and are also mainly onshore directed contributing 15- 20% to the gross suspended transport. Strongest fluxes at infragravity frequencies occurred during the peak flooding situations. During falling tide, wave influence is very small.

Morphodynamics

• When only the main channel is used for tidal exchange between sea and inland basin, wave- influence on the Slufter system is restricted to the nearshore and the main channel inlet mouth. Under low-moderate wave energy conditions net cross-shore fluxes were found generally offshore directed. Longshore fluxes are higher than cross-shore fluxes and are therefore determining sediment transport patterns in the nearshore. Under storm and/or spring tide conditions the complete inland basin of the Slufter is inundated. Strong onshore mean current velocities combined with skewed infragravity waves generate strong sediment fluxes over the beach flat into the Slufter basin. More sediment import occurs over the beach flat during flooding than sediment export during ebb. Where under normal conditions wave influence is restricted to the breaker zone and channel mouth interaction, wave driven influence on the Slufter system increases spatially under storm conditions as infragravity waves are able to intrude over the beach flat into the adjacent basin.

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References

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Appendix

1 Field work program

day date julian Main Frame Breaking zone Upstream Beach flat Mon 08/09/2008 252 Truc Vert Frame 16 landward seaward seaward landward landward seaward Tue 09/09/2008 253 17:00 17:00 Wed 10/09/2008 254 11:00 Thur 11/09/2008 255 11:00 Fri 12/09/2008 256 Sat 13/09/2008 257 Sun 14/09/2008 258 Mon 15/09/2008 259 Tue 16/09/2008 260 Wed 17/09/2008 261 21:00 08:00 Thur 18/09/2008 262 Fri 19/09/2008 263 12:00 Sat 20/09/2008 264 Sun 21/09/2008 265 16:00 16:00 Mon 22/09/2008 266 16:00/18:00 18:00/20:00 Tue 23/09/2008 267

Wed 24/09/2008 268 10:00/13:00 09:00/11:00 change program

Thur 25/09/2008 269 Fri 26/09/2008 270 13:00/15:30 11:00/13:30 Sat 27/09/2008 271 15:00 13:30/23:00 Sun 28/09/2008 272 Mon 29/09/2008 273 12:30 Tue 30/09/2008 274 Wed 01/10/2008 275 16:00 18:00 Thur 02/10/2008 276 Fri 03/10/2008 277 13:00/15:00 13:00 Sat 04/10/2008 278 16:00 22:30 Sun 05/10/2008 279 11:00/ Mon 06/10/2008 280 18:00 16:30 16:30 16:00 16:00 Tue 07/10/2008 281 16:30/19:30 15:30/19:00 Wed 08/10/2008 282 Thur 09/10/2008 283 8:30/ Fri 10/10/2008 284 11:00 08:30 Sat 11/10/2008 285 14:30 10:30 Sun 12/10/2008 286 13:30 Mon 13/10/2008 287 13:30 Tue 14/10/2008 288 Wed 15/10/2008 289 Thur 16/10/2008 290 17:00 15:30 Fri 17/10/2008 291 15:00 Table A1 The time and location schedule of the measurement program. Gray blocks indicate that measurements have been done for this location from denoted start to end time.

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2 Correction beach flat data

The data available for the beach flat frequently gives values which are not possible, although patterns which do contain valuable information can be distinguished. Figure A1 gives the original water height data. To correct the water depths for the negative values the assumption is made that if cross-shore current velocities are present, a positive water level should also be present. An additional assumption is taken that the peaks in water level are in the right order of magnitude. By making use of these assumptions, the water level is shifted upwards, and a new zero-water level reference is chosen.

Figure A1 Original data on water depth for a) the first period and b) the second period.

The data from the landward frame in the first period and the seaward frame in the second period is not taken into consideration because water pressure values are unrealistic. Frame Landward period 1 gives a negative water depth alternating signal between -1.1065 and -1.1045 m, and the sensor of Frame Seaward indicates water depths of 3 m (a 3-fold increase relative to maximum attained water level on the beach flat) when the storm was already declining. These unrealistic values could be related to the burial of the pressure sensors under extreme sediment transport rates.

3 DVD Slufter 2008 data

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