A linear stability analysis of tidally generated sand waves

A linear stability analysis is carried out to examine the initial stage of sand-wave growth under tidal flows and the occurrence of a preferred length scale. The fact that these bedforms typically have length scales small compared to the tidal excursion is exploited by adopting an asymptotic approach to solve the hydrodynamic part of the problem, i.e. to find the hydrodynamic response to an initially small bed perturbation. This method is shown to have important advantages over previously used methods, since it allows an exploration of the complete sand-wave regime (whereas other methods fail for short sand waves), and in general it is also more accurate. It is found that the selection of a preferred length scale depends mainly on only two parameters (the bed-slope coefficient, and the ratio of friction velocity to eddy viscosity), whereas there appears to be almost no dependence on the water depth.