A model of equilibrium bed topography for meander bends with erodible banks

Channel curvature produces secondary currents and a transverse sloping channel bed, along which the depth increases towards the outer bank. As a result deep pools tend to form adjacent to the outer bank, promoting bank collapse. The interaction of sediment grains with the primary and secondary flow and the transverse sloping bed also causes meanders to move different grain sizes in different proportions and directions, resulting in a consistent sorting pattern. Several models have been developed to describe this process, but they all have the potential to over-predict pool depth because they cannot account for the influence of erodible banks. In reality, bank collapse might lead to the development of a wider, shallower cross-section and any resulting flow depth discrepancy can bias associated predictions of flow, sediment transport, and grain-size sorting. While bed topography, sediment transport and grain sorting in bends will partly be controlled by the sedimentary characteristics of the bank materials, the magnitude of this effect has not previously been explored. This paper reports the development of a model of flow, sediment transport, grain-size sorting, and bed topography for river bends with erodible banks. The model is tested via intercomparison of predicted and observed bed topography in one low-energy (5·3 W m-2 specific stream power) and one high-energy (43·4 W m-2) study reach, namely the River South Esk in Scotland and Goodwin Creek in Mississippi, respectively. Model predictions of bed topography are found to be satisfactory, at least close to the apices of bends. Finally, the model is used in sensitivity analyses that provide insight into the influence of bank erodibility on equilibrium meander morphology and associated patterns of grain-size sorting. The sensitivity of meander response to bank cohesion is found to increase as a function of the available stream power within the two study bends.