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 ds. This produces the following scaling. In other words, was one to increase the grain diameter ds 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.
Highlights
Dunes are found wherever a fluid interacts with an erodible bed beneath it, whether this is in the familiar context of sand in a desert blown by the force of the wind, the silt on the bed of a river being eroded by the water flowing over it, or drifts formed by the action of wind on powdery snow
We address the question: do exist the scaling of the objects which is of the height of a dune? The relevant calculations performed in case of typical sand dunes leads to a high Reynolds number of about 6000 [2]
The effective viscosity of flowing granular media remains an active topic of research and is far from fully characterized. Particular study of this subject shows that phenomena governed more by compressive rather than shear stresses, the relevant model for sand motion can be only a rough approximation
Summary
Dunes are found wherever a fluid interacts with an erodible bed beneath it, whether this is in the familiar context of sand in a desert blown by the force of the wind, the silt on the bed of a river being eroded by the water flowing over it, or drifts formed by the action of wind on powdery snow The ubiquity of these repetitive, wavelike features suggests that there is an inherent instability making it impossible for a horizontal bed to stay horizontal, and that there is an underlying reason, predictable by analytic study of the processes involved, that causes such features to form in a wide variety of circumstances, and on a number of different scales. The behavior of granular flow is complex and only partially understood These two mechanisms in turn affect each other, since the fluid exerts a force on the substrate, causing it to be eroded, and thereby changing its shape, whereas the shape of the bed in turn influences the characteristics of the flow of the fluid over it. The shear stress changes the profile of the underlying surface, but the shear stress itself depends on the bed profile, so there is a feedback mechanism between the two
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