One-dimensional modelling of fluvial bed morphodynamics

Abstract

An understanding of fluvial processes is vital for river management systems. This paper describes a one-dimensional model of fluvial bed morphodynamics, with the flow hydrodynamics represented by the hyperbolic nonlinear shallow water equations and the bed morphodynamics by the bed deformation equation, with an empirical formula used for the bed load. Suspended sediment transport is not considered. The model uses a deviatoric form of the nonlinear shallow water equations that mathematically balances the source and flux gradient terms at equilibrium, and inherently caters for non-uniform bed topography. The governing equations are solved in an uncoupled way, using a Godunov-type finite volume solver for the nonlinear shallow water equations and second-order finite differences for the bed deformation equation. Generalised approximate analytical solutions and numerical predictions are presented for the evolution of a hump in an open channel. The numerical model predictions on converged grids are found to be in excellent agreement with the approximate analytical solutions within the range of validity of the approximate analytical model. It is demonstrated that uncoupling the shallow flow and bed morphodynamics calculations is computationally efficient and accurate. Results from a detailed parameter study are presented in order to interpret further the underlying physics of hump migration, and the influence studied of a morphodynamic time-scale related to the speed of bed change.