Modelling formation and evolution of transverse dune fields

We model formation and evolution of transverse dune fields. In the model, only the cross section of the dune is simulated. The only physical variable of relevance is the dune height, from which the dune width and velocity are determined, as well as phenomenological rules for interaction between two dunes of different heights. We find that dune fields with no sand on the ground between dunes are unstable, i.e. small dunes leave the higher ones behind. We then introduce a saturation length to simulate transverse dunes on a sand bed and show that this leads to stable dune fields with regular spacing and dune heights. Finally, we show that our model can be used to simulate coastal dune fields if a constant sand influx is considered, where the dune height increases with the distance from the beach, reaching a constant value.Comment: 18 pages including 9 figure

Modelling a Dune Field

We present a model to describe the collective motion of barchan dunes in a field. Our model is able to reproduce the observation that a typical dune stays confined within a stripe. We also obtain some of the pattern structures which ressemble those observed from aerial photos which we do analyse and compare with the specific field of La\^ayounne.Comment: 15 pages, 13 figure

The fluctuation energy balance in non-suspended fluid-mediated particle transport

Here we compare two extreme regimes of non-suspended fluid-mediated particle transport, transport in light and heavy fluids ("saltation" and "bedload", respectively), regarding their particle fluctuation energy balance. From direct numerical simulations, we surprisingly find that the ratio between collisional and fluid drag dissipation of fluctuation energy is significantly larger in saltation than in bedload, even though the contribution of interparticle collisions to transport of momentum and energy is much smaller in saltation due to the low concentration of particles in the transport layer. We conclude that the much higher frequency of high-energy particle-bed impacts ("splash") in saltation is the cause for this counter-intuitive behavior. Moreover, from a comparison of these simulations to Particle Tracking Velocimetry measurements which we performed in a wind tunnel under steady transport of fine and coarse sand, we find that turbulent fluctuations of the flow produce particle fluctuation energy at an unexpectedly high rate in saltation even under conditions for which the effects of turbulence are usually believed to be small

Jump at the onset of saltation

We reveal a discontinuous transition in the saturated flux for aeolian saltation by simulating explicitly particle motion in turbulent flow. The discontinuity is followed by a coexistence interval with two metastable solutions. The modification of the wind profile due to momentum exchange exhibits a second maximum at high shear strength. The saturated flux depends on the strength of the wind as $q_s=q_0+A(u_*-u_t)(u_*^2+u_t^2)$

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

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

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 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

Wnt5a induces ROR1 to complex with HS1 to enhance migration of chronic lymphocytic leukemia cells.

ROR1 (receptor tyrosine kinase-like orphan receptor 1) is a conserved, oncoembryonic surface antigen expressed in chronic lymphocytic leukemia (CLL). We found that ROR1 associates with hematopoietic-lineage-cell-specific protein 1 (HS1) in freshly isolated CLL cells or in CLL cells cultured with exogenous Wnt5a. Wnt5a also induced HS1 tyrosine phosphorylation, recruitment of ARHGEF1, activation of RhoA and enhanced chemokine-directed migration; such effects could be inhibited by cirmtuzumab, a humanized anti-ROR1 mAb. We generated truncated forms of ROR1 and found its extracellular cysteine-rich domain or kringle domain was necessary for Wnt5a-induced HS1 phosphorylation. Moreover, the cytoplamic, and more specifically the proline-rich domain (PRD), of ROR1 was required for it to associate with HS1 and allow for F-actin polymerization in response to Wnt5a. Accordingly, we introduced single amino acid substitutions of proline (P) to alanine (A) in the ROR1 PRD at positions 784, 808, 826, 841 or 850 in potential SH3-binding motifs. In contrast to wild-type ROR1, or other ROR1P→︀A mutants, ROR1P(841)A had impaired capacity to recruit HS1 and ARHGEF1 to ROR1 in response to Wnt5a. Moreover, Wnt5a could not induce cells expressing ROR1P(841)A to phosphorylate HS1 or activate ARHGEF1, and was unable to enhance CLL-cell motility. Collectively, these studies indicate HS1 plays an important role in ROR1-dependent Wnt5a-enhanced chemokine-directed leukemia-cell migration

Formation of aeolian ripples and sand sorting

We present a continuous model capable of demonstrating some salient features of aeolian sand ripples: the realistic asymmetric ripple shape, coarsening of ripple field at the nonlinear stage of ripple growth, saturation of ripple growth for homogeneous sand, typical size segregation of sand and formation of armoring layers of coarse particles on ripple crests and windward slopes if sand is inhomogeneous.Comment: 37 pages, 10 figures, revised versio