A reduced complexity model of a gravel-sand river bifurcation: Equilibrium states and their stability

Abstract

We derive an idealized model of a gravel-sand river bifurcation and analyze its stability properties. The model requires nodal point relations that describe the ratio of the supply of gravel and sand to the two downstream branches. The model predicts changes in bed elevation and bed surface gravel content in the two bifurcates under conditions of a constant water discharge, sediment supply, base level, and channel width and under the assumption of a branch-averaged approach of the bifurcates. The stability analysis reveals more complex behavior than for unisize sediment: three to five equilibrium solutions exist rather than three. In addition, we find that under specific parameter settings the initial conditions in the bifurcates determine to which of the equilibrium states the system evolves. Our approach has limited predictive value for real bifurcations due to neglecting several effects (e.g., transverse bed slope, alternate bars, upstream flow asymmetry, and bend sorting), yet it provides a first step in addressing mixed-size sediment mechanisms in modeling the dynamics of river bifurcations.