A Model for the Threshold of the Rolling Transition

A dynamic transition has been identified recently by numerical simulations in the case of a granular flow along a rotating boundary (Rioual and Le Quiniou (2011)). We showed that this transition appears above a certain critical microscopic friction coefficient particle/boundary µ* from which the particles roll without any sliding. We propose here a model at the scale of the microstructure which aimes to be close to the physical process considered and predicts also a threshold for the apparition of this dynamic transition. We discuss the discrepancy on a quantitative level in terms of friction properties at the contact

Dynamics of aeolian sand ripples

We analyze theoretically the dynamics of aeolian sand ripples. In order to put the study in the context we first review existing models. We argue on the local character of sand ripple formation. Using a hydrodynamical model we derive a nonlinear equation for the sand profile. We show how the hydrodynamical model may be modified to recover the missing terms that are dictated by symmetries. The symmetry and conservation arguments are powerful in that the form of the equation is model-independent. We then present an extensive numerical and analytical analysis of the generic sand ripple equation. We find that at the initial stage the wavelength of the ripple is that corresponding to the linearly most dangerous mode. At later stages the profile undergoes a coarsening process leading to a significant increase of the wavelength. We find that including the next higher order nonlinear term in the equation, leads naturally to a saturation of the local slope. We analyze both analytically and numerically the coarsening stage, in terms of a dynamical exponent for the mean wavelength increase. We discuss some future lines of investigations.Comment: 22 pages and 10 postscript figure

An analytical analysis of vesicle tumbling under a shear flow

Vesicles under a shear flow exhibit a tank-treading motion of their membrane, while their long axis points with an angle < 45 degrees with respect to the shear stress if the viscosity contrast between the interior and the exterior is not large enough. Above a certain viscosity contrast, the vesicle undergoes a tumbling bifurcation, a bifurcation which is known for red blood cells. We have recently presented the full numerical analysis of this transition. In this paper, we introduce an analytical model that has the advantage of being both simple enough and capturing the essential features found numerically. The model is based on general considerations and does not resort to the explicit computation of the full hydrodynamic field inside and outside the vesicle.Comment: 19 pages, 9 figures, to be published in Phys. Rev.

A two-species continuum model for aeolian sand transport

Starting from the physics on the grain scale, we develop a simple continuum description of aeolian sand transport. Beyond popular mean-field models, but without sacrificing their computational efficiency, it accounts for both dominant grain populations, hopping (or "saltating") and creeping (or "reptating") grains. The predicted stationary sand transport rate is in excellent agreement with wind tunnel experiments simulating wind conditions ranging from the onset of saltation to storms. Our closed set of equations thus provides an analytically tractable, numerically precise, and computationally efficient starting point for applications addressing a wealth of phenomena from dune formation to dust emission.Comment: 23 pages, 9 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

A comprehensive numerical model of steady state saltation (COMSALT)

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95613/1/jgrd15469.pd