A Thickness-Weighted Average Perspective of Force Balance in an Idealized Circumpolar Current
Abstract The exact, three-dimensional, thickness-weighted averaged (TWA) Boussinesq equations are used to diagnose eddy–mean flow interaction in an idealized circumpolar current (ICC). The force exerted by mesoscale eddies on the TWA velocity is expressed as the divergence of the Eliassen–Palm flux tensor. Consistent with previous findings, the analysis indicates that the dynamically relevant definition of the ocean surface layer is composed of the set of buoyancy coordinates that ever reside at the ocean surface at a given horizontal position. The surface layer is found to be a physically distinct object with a diabatic and force balance that is largely isolated from the underlying adiabatic region in the interior. Within the ICC surface layer, the TWA meridional velocity is southward/northward in the top/bottom half and has a value near zero at the bottom. In the top half of the surface layer, the zonal forces due to wind stress and meridional advection of potential vorticity act to accelerate the TWA zonal velocity; equilibrium is obtained by eddies decelerating the zonal flow via a downward flux of eastward momentum that increases with depth. In the bottom half of the surface layer, the accelerating force of the wind stress is balanced by the eddy force and meridional advection of potential vorticity. The bottom of the surface layer coincides with the location where the zonal eddy force, meridional advection of potential vorticity, and zonal wind stress force are all zero. The net meridional transport Sf within the surface layer is a small residual of its southward and northward TWA meridional flows. The mean meridional gradient of the surface layer buoyancy is advected by Sf to balance the surface buoyancy flux.