A two-dimensional, numerical circulation model is used to study the response of a stratified, f-plane ocean current to wind stress forcing at the surface. Nonhydrostatic, primitive equations are integrated on a 3 m vertical and 400 m horizontal grid in a periodic domain perpendicular to the ocean current. Initially, a geostrophically balanced current [Vi(x, z)] with a maximum Rossby number of 0.16–0.8 is maintained against horizontal and vertical diffusion by a body force. A spatially uniform wind is applied along and across this jet. A secondary circulation is created as a result of the nonlinear interaction between the jet and wind-driven flow in the Ekman layer. We present results from seven numerical experiments. When the wind blows in the direction of the jet (against the jet), a narrow upwelling (downwelling) area and broad downwelling (upwelling) area are formed. This secondary circulation pattern extends well below the mixed layer. When the wind blows perpendicular to the jet, the secondary circulation does not extend below the mixed layer. The fully nonlinear secondary circulation is 50% weaker than the circulation produced by the semi-linearized calculation around the basic state, Vi. Near-inertial fluctuations appear and are confined to the negative relative vorticity side of the circulation (dV/dx < 0). The time-averaged vertical velocity can be as high as 1.5 m/day with a wind stress of 1 dyne/cm2 over a jet and a maximum Rossby number of 0.16. The magnitude of the vertical circulation in this symmetric basic state is dependent on the Rossby number and the horizontal and vertical mixing coefficients.
Lee, Dong-Kyu, Peter Niiler, Alex Warn-Varnas, and Steve Piacsek. 1994. "Wind-driven secondary circulation in ocean mesoscale." Journal of Marine Research 52, (3). https://elischolar.library.yale.edu/journal_of_marine_research/2100