Wave Boundary Layer over a Rough Bottom at Moderate Reynolds Numbers

We make use of the partial slip boundary condition, commonly introduced to investigate steady flows, to evaluate the oscillatory flow generated close to a rough sandy bottom by propagating surface waves. Moderate values of the Reynolds number are considered such that the flow regime is laminar. However, an eddy viscosity is introduced to take into account the momentum transfer induced by the small vortices shed by the roughness/grain elements and the effect that these vortices have on the mixing processes. Because of the oscillatory forcing, the slip velocity at the bottom turns out to be characterized by both an amplitude and a phase that are evaluated by fitting the model results to experimental measurements. Moreover, a reasonable form of the 'eddy viscosity' is chosen on the basis of physical arguments. A comparison between the model predictions and the experimental measurements supports the proposed approach.