Quasilinear model of deformation of a stratified three-dimensionally inhomogeneous flow above a randomly inhomogeneous surface

Abstract

We study the deformation of the wind velocity profile due to resonant interactions with waves radiated by the flow over a statistically homogeneous topography. The wind whose velocity vector changes its direction within a layer of finite thickness is considered. Quasilinear equations for the velocity components of the mean flow are derived under large Richardson, numbers and small Froude numbers. It is shown that the modulus of the wind velocity is constant in time and its direction angle satisfies the Riemann equation for simple waves. The flow deformation is determined by the average wave resistance force per unit square. The deformation of the wind velocity profile takes place within the layer between the Earth’s surface and the level where the wind change its direction to the opposite one. At large time scales, the wind velocity vector in this layer approaches the direction opposite to the near-surface one.