Ekman pumping induced by geostrophic stress under nonlinear turbulent thermal wind balance

Abstract

The Ekman pumping is one of the fundamental mechanisms via which the inviscid ocean interior is driven into motion. The classical Ekman pumping theory and its later extensions consider the Ekman pumping induced by wind stress, whereas abundant density fronts embedded in the surface boundary layer generate geostrophic stress comparable in magnitude to wind stress. In this study, we theoretically investigate the Ekman pumping induced by the geostrophic stress under the nonlinear turbulent thermal wind balance, assuming a small Rossby number but a finite Ekman number. An asymptotic analytical solution reveals that the geostrophic stress alone can drive a nonzero Ekman pumping velocity with downwelling at the front center but upwelling on the both sides. This Ekman pumping can be understood based on the combined effects of the advection of vertical relative vorticity, the stretching of vertical relative vorticity and the titling of horizontal relative vorticity caused by the ageostrophic secondary circulation under the turbulent thermal wind balance. These processes lead to a net tendency of the vertical relative vorticity, which is balanced by the vertical stretching of the vertical planetary vorticity via a nonzero Ekman pumping. Numerical simulations suggest that our theory also holds qualitatively in the finite Rossby number regime and for a temporally evolving front.