The structure of the Ekman layer for geostrophic flows with lateral shear

A generalized Ekman flow is obtained for the boundary layer of a semi-infinite, rotating homogeneous fluid with lateral variation in the horizontal velocity components far from the boundary surface. The fields of motion considered include uni-directional motion with lateral shear, symmetric and elongated eddies, and cols. A solution for the first of these cases is obtained to fifth order; for the others, to second order. In all cases the magnitude of the vertical velocities induced by convergence in the boundary layer is greater for systems with negative relative vorticity than for systems with positive relative vorticity. The result differs substantially from first-order theory, for which the magnitude of the vertical velocity is proportional to the relative vorticity. A number of meteorological applications are considered.