Towards theoretical modeling of the sand dunes motion

Abstract

The transport of sand by wind is a potent erosion force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols. This article presents a short review of the physics of wind-driven sand. Specifically, we review the physics of saltation, the formation and development of sand dunes and ripples. We also discuss some classes of the governing equations which describe the physics of wind-driven sand and dune formation. We describe selected types of dunes and conditions under which they occur, and also some features of dunes as well as processes that they are involved in. We show that the normalized dunes height collapses using a simple product of the Froude and Reynolds numbers. This would obscure the effects of frictional dissipation, which clearly plays an important role in all mentioned upper process. Ignoring friction, one can construct a simple energy balance between the kinetic energy of the impacting and the potential energy of the dunes, where we assume the dunes thickness is proportional to d_s. This produces the following scaling. In other words, was one to increase the grain diameter d_s by a factor of 10 ~ i.e., reduce Re by 100! for the same impact conditions, then the frictionless flow would predict a 10-fold reduction in , whereas the experiments suggest a 100-fold reduction. This shows clearly that viscous forces play a role in the granular dunes formation (and their relevant dynamics), as well as gravity and inertia.

These circumstances move us to conclude   the vide range of (non-dissipative) hydrodynamic approaches to describe dunes formation and their dynamics just as a robust model approaches.