Ekman pumping on the β -plane

Abstract

The convergence of a cluster of water columns at the ocean surface subject to a zonal wind stress on the β-plane is studied analytically by substituting the pseudo angular momentum for the zonal velocity in the Lagrangian dynamical equations. The horizontal convergence at the surface is a primary driver of Ekman pumping that connects the surface of the ocean with its deeper layers. The derived analytical expressions are verified by numerical simulations of the nonlinear equations. Both direct simulations and analysis show that, in contrast to the f-plane, for a uniform wind stress, water columns on the β-plane in the northern hemisphere always converge (diverge) when the overlying wind is directed westward (eastward). For a zonal wind stress that is westward directed at low latitudes and eastward directed at high latitudes, the β-effect mitigates (enhances) the f-plane convergence toward the latitude of vanishing wind stress for water columns located north (south) of the latitude at which the stress vanishes. For the same zonal wind stress field, the β induced convergence is of the order of 25% of that on the f-plane.