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Alexandre Valance

Sand Ripples formation in a laminar boundary layer flow

Abstract: We investigate the process of ripple formation when a sand bed is submitted to a laminar boundary layer flow. The sand transport is described in terms of a phenomenological model inspired from the BCRE approach [Bouchaud et al, Phys. Rev. Lett. 74, 1982 (1995)]. The grain transport rate results from the competition between erosion and deposition process. Both processes are evaluated taking into account local bed shear stress --which is calculated from the resolution of the flow over the sand bed--, grain inertia and gravity. The evolution of the bed profile is then deduced from mass conservation of the grain. The mechanisms of the sand bed instability are analyzed in the framework of this model. It is found that the instability results from the competition between the destabilizing effect of fluid inertia and the stabilizing ones of grain inertia and gravity. At small particle Reynolds number $Re_p$ ($Re_p <1$), the most amplified wavelength scales as the viscous length $l_\nu$ defined as $\sqrt{\gamma/\nu}$ (where $\gamma$ is the shear rate and $\nu$ the fluid viscosity) and at large $Re_p$ ($Re_p \gg 1$) it scales as the equilibrium length $l_{eq}$ associated to the distance needed for an immobile grain to equilibrate its velocity with that of the fluid. Our results are compared with available experimental data.