Ekman Pumping for Stratified Planetary Boundary Layers Adjacent to a Free Surface or Topography

Abstract

In this paper, the classic Ekman pumping formulas for the vertical flow out of a boundary layer are generalized for both the layer above a rigid surface of variable slope and also for the boundary layer underneath a moving free surface. The assumptions that the density is constant and the geostrophic velocity does not vary with height in the boundary layer are relaxed without compromising the simplicity of the final approximation. Similarly, it proves to be unnecessary to assume a specific eddy viscosity law. The pumping formulas obtained here are compared with the old ones and significant differences are found.