Internal gravity waves feedback on a parallel mean flow: modelling of a boundary layer above a sinusoidal topography

Abstract

We consider a boundary layer flow horizontally homogeneous in the presence of a vertical stratification and of a sinusoidal topography. We present a simple model describing the interaction between the mean flow and the packet of internal waves emitted at the bottom, assuming that it obeys to the laws of the refraction. We focus on the configurations where no critical layers develop and where the waves propagate upward. We show that an equilibrium state exists when the bottom boundary conditions are stationary. With numerical simulations and considering the analytical expression of equilibra, we show that the presence of the waves amplifies the mean flow evolutions.