Numerical assessment of the interactions between hydrodynamics, bed morphodynamics and bank erosion

For the meandering Beatton River, Canada, Nanson and Hickin (1983) demonstrated that short-term meander migration rates are not representative of the long-term averages, as two almost identical bends had very different short-term migration rates but similar long-term migration rates. They postulated that this was caused by the asynchronous interactions between erosion of the cut bank along the outside of a bend (or bank pull) and accretion on the point bar along the inside of a bend (or bar push). The findings of Nanson & Hickin (1983) have important implications for modeling the morphodynamics of meandering streams. For example, most widely-used models of river meandering assume a temporally and spatially constant channel width ( Ikeda et al. 1981 & Seminara et al. 2001 ), and therefore cannot be used to simulate the shortterm planform dynamics. In addition, the role of bank pull on scroll-bar formation indicates the importance of incorporating cut-bank erosion processes in numerical models of river meandering to improve the simulation of long term (geologic scale) planform dynamics ( Van de Lageweg et al. 2014 ). Numerical assessment of river planform morphodynamics requires at least a two-dimensional (2D) depth-averaged model that can adequately simulate the governing processes and their interactions. At present, the simulation of hydrodynamics and river bed morphodynamics using 2D models is relatively straightforward. However, unlike onedimensional computer models, the implementation of bank erosion processes in multi-dimensional computer models is rather complicated. One-dimensional computer models simulate river morphodynamics using a series of cross sections, and adjust the cross-sectional profile where erosion and deposition occur. These models can handle complex geometry including steep bank sections. Such sections cannot be represented adequately by 2D models, which divide the computational domain into a mesh of elements on which the topography is described. As cut-bank profiles are very steep due to basal erosion, near-bank mesh elements may become too small to perform efficient and numerically stable simulations. Furthermore, the subgrid scale bank topography cannot be represented as modeled bank profiles generally comprise a single, linear segment (or planar surface). A novel approach to simulate bank erosion in 2D models is presented that combines the TELEMAC2D/SISYPHE computer models of river bed morphodynamics of the TELEMAC-MASCARET Suite of Solvers ( EDF-R&D 2015 ) and the CONCEPTS riverbank erosion algorithms ( Langendoen & Simon 2008 ). The subgrid scale riverbank geometry is represented using a depth-dependent porosity formulation. The new model is used to examine the interactions between hydrodynamics, point bar accretion (bar push) and bank erosion (bank pull) of a bendway on the Goodwin Creek, Mississippi, USA between 1996 and 2007. For this period, a seasonal-resolution time series of detailed bend topography is available.

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