Coupling of sediment transport phenomena with turbulent surface flows: mathematical modeling, finite volume approximation and test simulations

Abstract

Several sediment transport models coupled with shallow water equations have been developed in the literature over the past few decades. The water flow in the presence of abrupt bottom slopes distorts and cause turbulence. This phenomenon is well-known in the sediment transport theory. Sediment transport models based on shallow water equations do not include turbulence effects or the phase-lag between water velocity and bottom velocity. In this study, we consider a one-dimensional free surface turbulent water flow with sediment and morphodynamic. We propose a new one-dimensional acceleration-dissipation mathematical sediment transport model that considers the distortion of horizontal profile velocity in transport. The model is an improved version of existing averaged sediment transport models. In the new model, there is a distinction between fluid velocity and bottom velocity through a new bedload equation. The mathematical model is a system of nonlinear hyperbolic partial differential equations that are approximated by a stable and robust finite volume scheme presented in the path-conservative framework. Numerical tests are performed to demonstrate the efficiency of the developed theory.