Aeolian transport layer

We investigate the airborne transport of particles on a granular surface by the saltation mechanism through numerical simulation of particle motion coupled with turbulent flow. We determine the saturated flux $q_{s}$ and show that its behavior is consistent with a classical empirical relation obtained from wind tunnel measurements. Our results also allow to propose a new relation valid for small fluxes, namely, $q_{s}=a(u_{*}-u_{t})^{\alpha}$, where $u_{*}$ and $u_{t}$ are the shear and threshold velocities of the wind, respectively, and the scaling exponent is $\alpha \approx 2$. We obtain an expression for the velocity profile of the wind distorted by the particle motion and present a dynamical scaling relation. We also find a novel expression for the dependence of the height of the saltation layer as function of the wind velocity.Comment: 4 pages, 4 figure

Minimal model for aeolian sand dunes

We present a minimal model for the formation and migration of aeolian sand dunes. It combines a perturbative description of the turbulent wind velocity field above the dune with a continuum saltation model that allows for saturation transients in the sand flux. The latter are shown to provide the characteristic length scale. The model can explain the origin of important features of dunes, such as the formation of a slip face, the broken scale invariance, and the existence of a minimum dune size. It also predicts the longitudinal shape and aspect ratio of dunes and heaps, their migration velocity and shape relaxation dynamics. Although the minimal model employs non-local expressions for the wind shear stress as well as for the sand flux, it is simple enough to serve as a very efficient tool for analytical and numerical investigations and to open up the way to simulations of large scale desert topographies.Comment: 19 pages, 22 figure

A Continuum Saltation Model for Sand Dunes

We derive a phenomenological continuum saltation model for aeolian sand transport that can serve as an efficient tool for geomorphological applications. The coupled differential equations for the average density and velocity of sand in the saltation layer reproduce both known equilibrium relations for the sand flux and the time evolution of the sand flux as predicted by microscopic saltation models. The three phenomenological parameters of the model are a reference height for the grain-air interaction, an effective restitution coefficient for the grain-bed interaction, and a multiplication factor characterizing the chain reaction caused by the impacts leading to a typical time or length scale of the saturation transients. We determine the values of these parameters by comparing our model with wind tunnel measurements. Our main interest are out of equilibrium situations where saturation transients are important, for instance at phase boundaries (ground/sand) or under unsteady wind conditions. We point out that saturation transients are indispensable for a proper description of sand flux over structured terrain, by applying the model to the windward side of an isolated dune, thereby resolving recently reported discrepancies between field measurements and theoretical predictions.Comment: 11 pages, 7 figure

Corridors of barchan dunes: stability and size selection

Barchans are crescentic dunes propagating on a solid ground. They form dune fields in the shape of elongated corridors in which the size and spacing between dunes are rather well selected. We show that even very realistic models for solitary dunes do not reproduce these corridors. Instead, two instabilities take place. First, barchans receive a sand flux at their back proportional to their width while the sand escapes only from their horns. Large dunes proportionally capture more than they loose sand, while the situation is reversed for small ones: therefore, solitary dunes cannot remain in a steady state. Second, the propagation speed of dunes decreases with the size of the dune: this leads -- through the collision process -- to a coarsening of barchan fields. We show that these phenomena are not specific to the model, but result from general and robust mechanisms. The length scales needed for these instabilities to develop are derived and discussed. They turn out to be much smaller than the dune field length. As a conclusion, there should exist further - yet unknown - mechanisms regulating and selecting the size of dunes.Comment: 13 pages, 13 figures. New version resubmitted to Phys. Rev. E. Pictures of better quality available on reques