Mechanistic 2D flow-erosion modelling of vegetated river banks

We present a simple, vertically-explicit 2D model of river bank erosion that also takes the effect of sediment stabilization by plant roots into account. The model is solved in quasi-analytical form for an exemplary non-stationary hydrograph temporal signal representing a typical flood event. The modelling framework considers that hydraulic erosion at each water elevation lasts for a different time because of the non-stationary nature of the flood wave and the threshold imposed by the critical shear stress. In order to proceed analytically, we assume a local 1D framework for calculating the bank shear stress and then obtain the corresponding erosion rate by appealing to the well-known Partheniadis formula. The correction for the effect of stream curvature is also in terms of excess velocity at the outer bank, i.e. following classical meandering model’s theories. The solution of the model is semi analytical and provides the formula in closed form for the erosion times at each bank elevation and the shape of the resulting vertical profile starting from a generic cross section. Despite originating from a simplified modelling framework, this approach provides realistic qualitative results and a tool for assessing the role of vegetation roots in bank erosion as flow level changes during hydrologic events.