Sand flux over a barchan dune under a water flow

Abstract

The modelling of sand transport by uid ows is crucial in many environmental as well as industrial problems. The present work investigates an important and yet unsolved issue: the relationship between the particle ux and the shear stress exerted by the uid ow at the bed surface. It is now recognized that over a spatially varying bottom, the particle ux is not in equilibrium with the shear stress: there is some lag related to the particle inertia or particle settling. However, a confident modelling of these relaxation phenomena, and the corresponding length scales, is still lacking. We report experiments on the determination of the sand ux at the surface of a barchan dune sheared by a water ow in a closed-conduit water ow (Fig. 1a). The evolution of the dune is visualized with a high-speed camera allowing the tracking of a small fraction of marked particles. A tracking algorithm has been developed, which then allows the local particle velocity, particle ux, and particle trajectories to be determined over the dune surface (Fig. 1b). From these measurements, the relationship between the measured ux at the dune brink and the dune velocity can be assessed, in connection with Bagnold's theory (1941). Second, the relationship between the local particle ux and local shear stress (estimated from previous studies) can be analyzed, as well as the relaxation length that emerges from this analysis.