Downstream Fining in Sand-Bed Rivers

River Flow 2010 - Dittrich, Koll, Aberle & Geisenhainer (eds) - © 2010 Bundesanstalt für Wasserbau ISBN 978-3-939230-00-7 Downstream fining in sand-bed rivers R.M. Frings Inst. of Hydraulic Engineering and Water Resources Management, RWTH Aachen University, Germany W. Ottevanger & C.J. Sloff1 Dept. of Hydraulic Engineering, Delft University of Technology, Delft, The Netherlands 1 also at Deltares, Delft, The Netherlands ABSTRACT: Downstream fining of river bed sediments is well-known for gravel-bed rivers, but also oc- curs in sand-bed rivers, where it has a major influence on sediment-transport dynamics, bed-form dimensions and hydraulic roughness. The objective of this study was to determine the effects of dune sorting, overbank deposition and river bifurcations on downstream fining in sandy lowland rivers. The time-scale of interest was 10-1800 years. For the analysis, a numerical simulation model was developed using Delft3D software. The model shows that dune sorting increases fining rates, whereas overbank deposition has the opposite effect. River bifurcations affect the fining rate because of their effect on the sediment supply to bifurcating lowland rivers. Downstream fining development can take several centuries, but in situations with sudden changes in river geometry (exemplary for bank erosion) a strong downstream fining trend can develop within decades. A comparison of the modeled fining rates with those observed in the Dutch part of the river Rhine, the prototype for the model, shows reasonable agreement. KEYWORDS: downstream fining, sand-bed river, dune sorting, river bifurcation, overbank deposition 1 INTRODUCTION river may react to this by taking new fine grains from the river bed into suspension, thus prevent- Characteristic for many rivers is a downstream ing a rapid downstream fining of bed sediments. decrease in bed grain size, a phenomenon known River bifurcations control the sediment supply as ‘downstream fining’ (e.g. Morris & Williams, to the downstream river branches. It has been 1999). The causes of downstream fining have shown that differences in supply between the been subject of study for decades, because branches lead to a discontinuity in downstream changes in grain size affect sediment dynamics, fining trend at the bifurcation (Frings & Klein- bed-form dimensions and hydraulic roughness. hans, 2008). The sediment supply also determines Most studies focused on gravel-bed rivers (e.g. the aggradation rate of the downstream branches. Knighton, 1982; Paola et al., 1992; Kodama, This, in turn, may affect the concavity of their 1994; Ferguson et al., 1996; Hoey & Bluck, longitudinal profile, and hence the selectivity of 1999). Sand-bed rivers have received much less the transport process and the degree of down- attention, although the causes of downstream fin- stream fining (Wright & Parker, 2005a,b). ing in these rivers differ from those in gravel-bed The objective of this study was to determine rivers (Frings, 2008). Three processes that are of the effects of dune sorting, overbank deposition minor importance in gravel-bed rivers, but are and river bifurcations on the downstream fining thought to significantly influence downstream fin- trend of sand-bed rivers. The time period of inter- ing in sand-bed rivers are: dune sorting, overbank est was 10-1800 years. In order to investigate the deposition and river bifurcation (Frings, 2008). bed level development and the downstream fining Dune sorting concentrates coarse grains in development simultaneously, we used the numeri- deep bed layers which are immobile during low cal modeling system Delft3D and adapted it to flows. These grains become permanently unavail- meet the requirements of this study. The model able for downstream transport if the river ag- was applied to a 1D hypothetical sand-bed river in grades. This must increase the degree of down- an aggrading delta. The river characteristics were stream fining. as much as possible based on the present-day river Overbank deposition causes a net extraction of Rhine, just downstream of the Pannerdensche Kop fine grains from the river’s sediment load. The bifurcation in the Netherlands (Figure 1). 831 sponding to the average dune height during flood conditions in the Rhine. The substrate consisted of 14 bookkeeping layers of 10 cm thickness and a base layer of 5 m thickness. The sediment mixture was divided into seven grain-size classes, ranging from 0.125 to 16 mm. Bed-load transport was calculated with the Van Rijn (1984a) formula, which we adapted for the transport of multiple grain-size fractions according to Kleinhans & Van Rijn (2002). The stochas- tic method to calculate the shear stress proposed by Kleinhans & Van Rijn (2002) was not adopted here. The size-selectivity of the bed-load transport depends on the hiding-exposure correction (ξi), for which a simple power function was used: ξi = -m (Di/D50) , with Di the representative grain size of size fraction i, D50 the median grain size of the local sediment mixture and m the hiding-exposure exponent, for which a value of 0.9 was used. Sus- pended-load transport was calculated with the ad- vection-diffusion equation, with the transport capacity (equilibrium suspension) calculated with the Van Rijn (1984b) predictor. A comparison of the transport rates predicted with the Van Rijn formulae to measured transport rates in the River Rhine (data from Frings & Kleinhans, 2008) shows acceptable agreement. If, after calculating the sediment fluxes into a Figure 1. Study area: (a) location, (b) median bed-surface cell and out of a cell, sedimentation was predicted sediment diameter in 1995 AD (after Ten Brinke, 1997). for a cell, the deposited sediment was mixed with the active layer sediment, after which the excess sediment in the active layer was passed down to 2 THE NUMERICAL MODEL the substrate. This method to calculate the composition of the sedimentation was also used by 2.1 Basic equations Wright & Parker (2005a,b) and is assumed to be Delft3D (Lesser et al., 2004) solves the unsteady realistic for sand-bed rivers. In case of erosion, the Navier-Stokes equations for an incompressible eroded part of the active layer was replenished fluid, under the shallow-water and Boussinesq as- from the substrate. sumptions. Here, the model was used in 1D mode (depth and width averaged). To close the set of 2.2 Initial and boundary conditions flow equations, the Chezy roughness formula was used, for which the Chezy value was calculated The initial bed profile was straight with a slope of according to White-Colebrook from a constant 1x10-4 m/m and an initial water depth of 6.2 m. user-specified roughness height (ks=0.25 m). This The initial bed sediment composition was constant value corresponds to ks-values derived from over the study reach with a D50 of 1.2 mm and a measured velocity profiles and dune heights gravel percentage of 38%. The porosity of the (Frings & Kleinhans, 2008). The grain roughness river bed was estimated to be 34% and the sedi- 3 was taken equal to the D90 of the local river bed. ment density was taken equal to 2650 kg/m . To calculate morphological changes, a continu- The upstream model boundary was situated at ity equation was used that schematises the river the gravel-sand transition, the downstream bound- bed in two layers: the active (transport) layer and ary at the transition to the estuarine area with a the substrate beneath it (Hirano’s approach; Hi- mixed clay-sand bed. The imposed boundary con- rano, 1971). The active layer thickness in sand- ditions were the upstream flow discharge, the bed rivers is usually assumed to scale with the downstream water level and the upstream sedi- dune height and the water depth (e.g. Deigaard, ment input. The flow discharge was held constant 1980). Here, the active layer thickness was taken at a value of 1700 m3/s. The downstream water equal to 11% of the water depth. For the initial level was initially set at 0.8 m above sea level. A model conditions it was 68 cm, roughly corre- sea level rise of 2 mm/year was applied, as well as 832 a diurnal tidal water level variation with harmonic amplitudes (M2-S2) of 16 and 3.5 cm. The upstream sediment input was equal for all model runs, constant in time, and equal to the initial transport capacity at the upstream boundary. The incoming sediment concentration was 22.7 mg/l, partly supplied as bed load and partly as sus- pended load. These boundary conditions resemble the present-day situation in the river Rhine. 2.3 Spatial and temporal resolution After specifying the initial and boundary conditions, the flow and transport equations were solved on a staggered finite-difference grid with Figure 2. Bed schematization in model scenarios with dune an orthogonal curvilinear co-ordinate system. The sorting. modelling grid was straight and one-dimensional and had a length of 93 km divided into 93 cells of mode (constant b equal to 0), which results in a 1 km length. The grid width exponentially in- linear sorting profile. For constant a (the dune creased from 260 to 416 m in the downstream di- sorting intensity) values between 0 and 0.45 were rection, just as in the prototype. chosen. After integration of the sorting function The flow was assumed to be concentrated in a over the depth, a simple linear formulation for the single, rectangular channel without tributaries or sediment concentration of a size fraction in the floodplains. The time step of the flow (Δt) was 20 exchange layer and active layer was obtained: minutes. In order to reduce simulation time, the morphological change in each time step was mul- f i, E 1 1.67aG L tiplied with a factor (F) of 100, which means that f i 4 years of flow simulation were enough to simu- i, av late 400 years of morphological evolution (e.g.

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