Alexandre Valance

Saltating particles in a turbulent boundary layer: experiment and theory

The work presented here focuses on the analysis of a turbulent boundary layer saturated with saltating particles. Experiments were carried out in a wind tunnel 15 m long and 0.6 m wide at the University of Aarhus in Denmark with sand grains 242 μm in size for wind speeds ranging from the threshold speed to twice its value. The saltating particles were analysed using particle image velocimetry (PIV) and particle-tracking velocimetry (PTV), and vertical profiles of particle concentration and velocity were extracted. The particle concentration was found to decrease exponentially with the height above the bed, and the characteristic decay height was independent of the wind speed. In contrast with the logarithmic profile of the wind speed, the grain velocity was found to vary linearly with the height. In addition, the measurements indicated that the grain velocity profile depended only slightly on the wind speed. These results are shown to be closely related to the features of the splash function that characterizes the impact of the saltating particles on a sandbed. A numerical simulation is developed that explicitly incorporates low-velocity moments of the splash function in a calculation of the boundary conditions that apply at the bed. The overall features of the experimental measurements are reproduced by simulation.

Dynamics of aeolian sand ripples

Abstract:We analyze theoretically the dynamics of aeolian sand ripples. In order to put the study in the context, we first review existing models. This paper is a continuation of two previous papers (Z. Csahók et al., Physica D 128, 87 (1999); A. Valance et al., Eur. Phys. J. B 10, 543 (1999)), the first one is based on symmetries and the second on a hydrodynamical model. 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.

Barchan dune mobility in Mauritania related to dune and interdune sand fluxes

[1] We present a 1 year study of 50 dunes in a small field of barchan dunes in Mauritania. We documented the morphological evolution of the dunes and their migration rates and measured at 10 min intervals the interdune sand transport, the wind strength, and its direction for the same interval of time. The dune heights H 0 range between 2 and 5 m, and their celerity c is found to be well approximated by the standard migration law: c = Q 0 /H 0 , with Q 0 ≈ 50 m 3 /m yr. From both the interdune sand flux and the migration rate of the dunes we were able to estimate the spatially averaged sand flux at the dune crest as well as the bulk sand flux associated with the mass of sand transported by the dune. We found that the sand flux at the crest was about 3 times greater than the interdune mass transport rate, whereas the bulk sand flux was surprisingly of the same order as the interdune flux. Moreover, we analyzed carefully the interdune sand transport data, which can be well described by the Sorensen law. The cumulative mass of sand transported during moderate wind events within 1 year was much greater than that transported during strong wind events.

Granular and particle-laden flows: from laboratory experiments to field observations

This review article provides an overview of dry granular flows and particle fluid mixtures, including experimental and numerical modeling at the laboratory scale, large scale hydrodynamics approaches and field observations. Over the past ten years, the theoretical and numerical approaches have made such significant progress that they are capable of providing qualitative and quantitative estimates of particle concentration and particle velocity profiles in steady and fully developed particulate flows. The next step which is currently developed is the extension of these approaches to unsteady and inhomogeneous flow configurations relevant to most of geophysical flows. We also emphasize that the up-scaling from laboratory experiments to large scale geophysical flows still poses some theoretical physical challenges. For example, the reduction of the dissipation that is responsible for the unexpected long run-out of large scale granular avalanches is not observed at the laboratory scale and its physical origin is still a matter of debate. However, we believe that the theoretical approaches have reached a mature state and that it is now reasonable to tackle complex particulate flows that incorporate more and more degrees of complexity of natural flows.

Periodic trajectories in aeolian sand transport

We develop a simple model for steady, uniform transport in aeolian saltation over a horizontal bed that is based on the computation of periodic particle trajectories in a turbulent shearing flow. The wind and the particles interact through drag, and the particles collide with the bed. We consider collisions with both rigid and erodible beds. The impact velocity in a periodic trajectory over a rigid bed is unconstrained, while that over an erodible bed must have a value that produces a single rebounding particle. The difference in the nature of the collisions results in qualitative differences in the nature of the solutions for the periodic trajectories and, in particular, to differences in the dependence of the particle flow rate on the strength of the turbulent shearing.

Experimental study of two-dimensional, monodisperse, frictional-collisional granular flows down an inclined chute

In this study, positions, velocities, and rotations of monodisperse disks confined two-dimensionally in a glass-walled chute are measured using a high-speed camera. Steady, fully developed granular flows (SFD) down bumpy inclines are systematically investigated in the frictional-collisional (dense, rapid) regime. Three bottoms with different effective roughness heights and roughness distributions are studied to evaluate the influence of the bottom condition. The granular flows are shallow, having a typical depth of ten disk diameters. In the range of flow rates and inclination angles where SFD flows occur, the mean discharge velocity is approximately proportional to the flow depth. The surfacesolid fractions slightly decrease from the bottom to the free surface. The streamwise velocity profiles are close to the linear profile at small inclination angles, whereas at large inclination angles, they are best approximated by the Bagnold profile. The mean angular velocity is equal to the half shear rate everywhere in the flow except near the free surface and the bottom. At large inclination angles, relatively deep SFD flows exhibit an S-shaped granular temperature profile, but in the core, the temperature is far from scaling linearly with the square shear rate. The streamwise and crosswise translational temperatures are slightly different from each other, whereas the rotational temperature is only half of the crosswise translational temperature. The rough bottoms have complex influences on the granular flows as revealed by the velocity and temperature profiles.

Two- and three-dimensional confined granular chute flows: experimental and numerical results

We present experimental and numerical results on 2D and 3D confined granular chute flows. We address the issue of the role of the lateral boundaries. In particular, we find that the presence of flat frictional lateral walls greatly alters the flow features as soon as the width of the flowing layer is of the order of the spacing between the walls or greater. First, steady and fully developed (SFD) flows are observed up to very large inclination angles where accelerated flows would have been expected. Second, at given inclination angle, there exists an upper bound on the flow rate for SFD flows to occur. When one approaches this critical flow rate, a static heap forms along the chute base, on which is the flowing layer. The heap is stabilized by the flow atop it and was named a sidewall-stabilized heap (SSH) since its angle is much greater than those usually exhibited by granular heaps. Both kinds of flow have been studied in 2D and 3D confined configurations. In particular, it is found that these flows exhibit either a Bagnold velocity profile or an exponential one. Moreover, we identify a dimensionless parameter, depending crucially on the sidewall friction, that is expected to drive the transition between these two regimes. We also point out the differences between purely 2D flows and 3D confined flows.

A class of nonlinear front evolution equations derived from geometry and conservation

Abstract Based on geometry, conservation, and scaling arguments we derive a class of nonlinear front evolution equations that govern various physical systems. We exemplify the analysis on some specific systems ranging from crystal growth to sand ripples. We also show numerical results of strongly curved fronts exhibiting new patterns.

Granular medium impacted by a projectile: Experiment and model

We present a minimal discrete model for the propagation of energy through a 3D granular medium impacted by a particulate projectile. In this model, energy is transferred from grain to grain via binary collision events. This description can be successfully applied to the analysis of the collision process of a single spherical particle (of diameter donto a half space of granular medium composed of similarly sized particles. The model reproduces remarkably well the experimental observations. Besides, the present model provides a clear picture of the mechanism of energy propagation. A continuum version of the model, where the energy propagation from bead to bead is characterized by a diffusion equation, is derived. The diffusion coefficient is found to be proportional to the ratio of d2 to the characteristic collision time

Model for surface packing and aeolian transport on sand ripples

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