On nonlinear Ekman surface-layer pumping

Abstract

Simple expressions are presented for the corrections to the classic Ekman pumping law We = ẑ·curl(τ0/f) due to nonlinear advection effects in the surface boundary layer. These involve products of the surface Reynolds stress τ0 and the underlying ocean currents v0(x, y, t) and their derivatives, and products of τ0(x, y, t) and its own derivatives. The former interaction is independent of the turbulence closure, while the latter is obtained using solutions for a constant eddy viscosity. The corrections are usually small, as is assumed when the linear Ekman pumping relation is applied in ocean modeling. However, they can become significant in circumstances involving very high wind stresses (e.g., a hurricane), or in situations where a strong narrow oceanic current flows under a region of moderate but perhaps relatively uniform surface stress.