On a Mathematical model for traveling sand dune

TL;DR

This paper introduces a mathematical model for traveling sand dunes that combines nonlinear diffusion-transport equations with surface flow dynamics, capturing the effects of wind and gravity on sand movement.

Contribution

It develops a novel coupled nonlinear diffusion-transport model incorporating nonlocal terms and avalanche dynamics for sand dune behavior.

Findings

Model effectively describes sand dune traveling phenomena.

Incorporates wind and gravity effects in a unified framework.

Provides a basis for further analytical and numerical studies.

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.