Concave-upward composite river bank profile shape at migrating meander bends

In this investigation, we performed an analytical treatment of the sediment mass conservation equation applied to bank material mobilized as bedload (the non-cohesive coarse-grained lower layer of the composite river bank) to ascertain details about bank profile shape. The bank profile has a significant influence on meander migration rates when implementing a parallel migration assumption in physically-based erosion algorithms in meandering river migration models. However, such profiles are not readily specified a priori, as they are part of the solution of the problem. The analysis revealed that a straight-forward analytical function to express the shape for a parallel-migrating bank was not tractable; however, the necessity of the bank profile to be concave-upwards to satisfy the simplified governing equations was demonstrated. This contradicts predictions made by commonly used models that implement an excess shear stress formulation for entrainment rate without incorporating sediment flux divergence terms in the mass conservation equation.