Ekman pumping ($w_E$)

Spatial convergence or divergence of Ekman transport drives vertical motion at the base of the Ekman layer. With upward vertical coordinate,

Bottom Ekman pumping damps a horizontal quasi-geostrophic Fourier mode while its influence penetrates vertically only over $|f|/(Nk)$. For a half-space with a vertically uniform initial mode, the boundary amplitude decays exponentially while the remote interior remains unchanged.