On a Mathematical model for traveling sand dune

Abstract

Our aim in this note is to introduce and study a mathematical model for the description of traveling sand dunes. We use surface flow process of sand under the effect of wind and gravity. We model this phenomena by a non linear diffusion-transport equation coupling the effect of transportation of sand due to the wind and the avalanches due to the gravity and the repose angle. The avalanche flow is governed by the evolution surface model and we use a nonlocal term to handle the transport of sand face to the wind.