On an evolution equation for sand dunes

Abstract

We propose a model for aeolian or fluvial dune formation in which the turbulent flow of air or water is described by a constant eddy viscosity model. Asymptotic methods are used to derive an expression for the basal shear stress and this is used in the Exner equation to describe a nonlinear model for the evolution of dunes. The model is then extended to allow for the existence of separation bubbles in a self-consistent way, and computational results of the consequent model are presented.