A model for ripple instabilities in granular media

We extend the model of surface granular flow proposed in \cite{bcre} to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We discuss in detail how this mechanism can be described in a phenomenological way, and show that a flat bed is linearly unstable against ripple formation in a certain region of parameter space. We focus in particular on the (realistic) case where the migration velocity of the instability is much smaller than the grains' velocity. In this limit, the full dispersion relation can be established. We find that the critical wave vector is of the order of the saltation length. We provide an intuitive interpretation of the instability.Comment: 11 pages, latex, 2 encapsulated postscript figure

Selection of dune shapes and velocities. Part 1: Dynamics of sand, wind and barchans

Almost fifty years of investigations of barchan dunes morphology and dynamics is reviewed, with emphasis on the physical understanding of these objects. The characteristics measured on the field (shape, size, velocity) and the physical problems they rise are presented. Then, we review the dynamical mechanisms explaining the formation and the propagation of dunes. In particular a complete and original approach of the sand transport over a flat sand bed is proposed and discussed. We conclude on open problems by outlining future research directions.Comment: submitted to Eur. Phys. J. B, 20 pages, 20 figure

Direct numerical simulations of aeolian sand ripples

Aeolian sand beds exhibit regular patterns of ripples resulting from the interaction between topography and sediment transport. Their characteristics have been so far related to reptation transport caused by the impacts on the ground of grains entrained by the wind into saltation. By means of direct numerical simulations of grains interacting with a wind flow, we show that the instability turns out to be driven by resonant grain trajectories, whose length is close to a ripple wavelength and whose splash leads to a mass displacement towards the ripple crests. The pattern selection results from a compromise between this destabilizing mechanism and a diffusive downslope transport which stabilizes small wavelengths. The initial wavelength is set by the ratio of the sediment flux and the erosion/deposition rate, a ratio which increases linearly with the wind velocity. We show that this scaling law, in agreement with experiments, originates from an interfacial layer separating the saltation zone from the static sand bed, where momentum transfers are dominated by mid-air collisions. Finally, we provide quantitative support for the use the propagation of these ripples as a proxy for remote measurements of sediment transport.Comment: 21 pages, 12 figure

Active dry granular flows: rheology and rigidity transitions

The constitutive relations of a dense granular flow composed of self-propelling frictional hard particles are investigated by means of DEM numerical simulations. We show that the rheology, which relates the dynamical friction $\mu$ and the volume fraction $\phi$ to the inertial number $I$, depends on a dimensionless number $\mathcal{A}$, which compares the active force to the confining pressure. Two liquid/solid transitions -- in the Maxwell rigidity sense -- are observed. As soon as the activity is turned on, the packing becomes an `active solid' with a mean number of particle contacts larger than the isostatic value. The quasi-static values of $\mu$ and $\phi$ decrease with $\mathcal{A}$. At a finite value of the activity $\mathcal{A}_t$, corresponding to the isostatic condition, a second `active rigidity transition' is observed beyond which the quasi-static values of the friction vanishes and the rheology becomes Newtonian. For $\mathcal{A}>\mathcal{A}_t$, we provide evidence for a highly intermittent dynamics of this 'active fluid'.Comment: 7 pages, 7 figures, final version, accepted for publication in Europhys. Let

Transition from viscous to inertial regime in dense suspensions

Non-Brownian suspensions present a transition from Newtonian behavior in the zero-shear limit to a shear thickening behaviour at a large shear rate, none of which is clearly understood so far. Here, we carry out numerical simulations of such an athermal dense suspension under shear, at an imposed confining pressure. This set-up is conceptually identical to the recent experiments of Boyer and co-workers [Phys. Rev. Lett. 107,188301 (2011)]. Varying the interstitial fluid viscosities, we recover the Newtonian and Bagnoldian regimes and show that they correspond to a dissipation dominated by viscous and contact forces respectively. We show that the two rheological regimes can be unified as a function of a single dimensionless number, by adding the contributions to the dissipation at a given volume fraction.Comment: 4 pages, 3 figure