Analytical model for flux saturation in sediment transport

The transport of sediment by a fluid along the surface is responsible for dune formation, dust entrainment and for a rich diversity of patterns on the bottom of oceans, rivers, and planetary surfaces. Most previous models of sediment transport have focused on the equilibrium (or saturated) particle flux. However, the morphodynamics of sediment landscapes emerging due to surface transport of sediment is controlled by situations out-of-equilibrium. In particular, it is controlled by the saturation length characterizing the distance it takes for the particle flux to reach a new equilibrium after a change in flow conditions. The saturation of mass density of particles entrained into transport and the relaxation of particle and fluid velocities constitute the main relevant relaxation mechanisms leading to saturation of the sediment flux. Here we present a theoretical model for sediment transport which, for the first time, accounts for both these relaxation mechanisms and for the different types of sediment entrainment prevailing under different environmental conditions. Our analytical treatment allows us to derive a closed expression for the saturation length of sediment flux, which is general and can thus be applied under different physical conditions

The physics of wind-blown sand and dust

The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols. This article presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars. Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices. We also discuss the physics of wind-blown sand and dune formation on Venus and Titan.Comment: 72 journal pagers, 49 figure

Calculation of the separation streamlines of barchans and transverse dunes

We use FLUENT to calculate the wind profile over barchans and transverse dunes. The form of the streamlines of flow separation at the lee side of the dunes is determined for a symmetric barchan dune in three dimensions, and for the height profile of a measured transverse dune field in the Len\c{c}\'ois Maranhenses.Comment: 6 pages including 5 figures. Proceedings of PSIS 200

Sliding susceptibility of a rough cylinder on a rough inclined perturbed surface

A susceptibility function ${\chi}(L)$ is introduced to quantify some aspects of the intermittent stick-slip dynamics of a rough metallic cylinder of length $L$ on a rough metallic incline submitted to small controlled perturbations and maintained below the angle of repose. This problem is studied from the experimental point of view and the observed power-law behavior of ${\chi}(L)$ is justified through the use of a general class of scaling hypotheses.Comment: 14 pages including 5 figure

Transverse instability of dunes

The simplest type of dune is the transverse one, which propagates with invariant profile orthogonally to a fixed wind direction. Here we show numerically and with a linear stability analysis that transverse dunes are unstable with respect to along-axis perturbations in their profile and decay on the bedrock into barchan dunes. Any forcing modulation amplifies exponentially with growth rate determined by the dune turnover time. We estimate the distance covered by a transverse dune before fully decaying into barchans and identify the patterns produced by different types of perturbation.Comment: 4 pages, 3 figures; To appear in Physical Review Letter

Minimal size of a barchan dune

Barchans are dunes of high mobility which have a crescent shape and propagate under conditions of unidirectional wind. However, sand dunes only appear above a critical size, which scales with the saturation distance of the sand flux [P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002); B. Andreotti, P. Claudin, and S. Douady, Eur. Phys. J. B {\bf{28,}} 321 (2002); G. Sauermann, K. Kroy, and H. J. Herrmann, Phys. Rev. E {\bf{64,}} 31305 (2001)]. It has been suggested by P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002) that this flux fetch distance is itself constant. Indeed, this could not explain the proto size of barchan dunes, which often occur in coastal areas of high litoral drift, and the scale of dunes on Mars. In the present work, we show from three dimensional calculations of sand transport that the size and the shape of the minimal barchan dune depend on the wind friction speed and the sand flux on the area between dunes in a field. Our results explain the common appearance of barchans a few tens of centimeter high which are observed along coasts. Furthermore, we find that the rate at which grains enter saltation on Mars is one order of magnitude higher than on Earth, and is relevant to correctly obtain the minimal dune size on Mars.Comment: 11 pages, 10 figure

Numerical modeling of the wind flow over a transverse dune

Transverse dunes, which form under unidirectional winds and have fixed profile in the direction perpendicular to the wind, occur on all celestial objects of our solar system where dunes have been detected. Here we perform a numerical study of the average turbulent wind flow over a transverse dune by means of computational fluid dynamics simulations. We find that the length of the zone of recirculating flow at the dune lee --- the {\em{separation bubble}} --- displays a surprisingly strong dependence on the wind shear velocity, $u_{\ast}$: it is nearly independent of $u_{\ast}$ for shear velocities within the range between $0.2\,$ms and $0.8\,$ms but increases linearly with $u_{\ast}$ for larger shear velocities. Our calculations show that transport in the direction opposite to dune migration within the separation bubble can be sustained if $u_{\ast}$ is larger than approximately $0.39\,$ms, whereas a larger value of $u_{\ast}$ (about $0.49\,$ms) is required to initiate this reverse transport.Comment: 11 pages, 8 figure