Evolution of a model dune in a shear flow

We present a simplified model for the displacement of a model dune in a constant viscous shear flow over a non-erodible soil. A simplified linear law with a threshold effect (in shear stress) and saturation is used to link the flux of sediments to the shear stress. The asymptotic framework of “Double Deck” (large Reynolds number laminar flow theory) is used for the flow. This method allows the computation of boundary layer separation, and the flow may be further simplified with an analytical relation linking the dune shape to the skin friction. For a given shape, the asymptotic solutions give a good agreement with Navier Stokes computations. Examples of displacement of model dunes are presented. We then obtain a selfsimilar coupled problem, predicting that the velocity of the dune is proportional to m−1/4. Computations indicate that there is no dune if the mass of the dune is too small, or if the saturation length is too large, or if the threshold is too small.