Ekman transport in balanced currents with curvature

Abstract

kman transport, the horizontal mass transport associated with a wind-stress applied on the ocean surface, is modified by the vorticity of ocean currents, leading to what has been termed the nonlinear Ekman transport. In this article we extend earlier work on this topic by deriving solutions for the nonlinear Ekman transport valid in currents with curvature, such as a meandering jet or circular vortex, and for flows with Rossby number approaching unity. Tilting of the horizontal vorticity of the Ekman flow by the balanced currents modifies the ocean response to surface forcing, such that, to leading order, winds parallel to the flow drive an Ekman transport that depends only on the shear vorticity component of the vertical relative vorticity, whereas across-flow winds drive transport dependent on the curvature vorticity. Curvature in the balanced flow field thus leads to an Ekman transport that differs from previous formulations derived under the assumption of straight flows. Notably, the theory also predicts a component of the transport aligned with the surface wind-stress, contrary to classic Ekman theory. In the case of the circular vortex, the solutions given here can be used to calculate the vertical velocity to a higher order of accuracy than previous solutions, extending possible applications of the theory to strong balanced flows. The existence of oscillations, and the potential for resonance and instability, in the Ekman flow at a curved jet are also demonstrated.