An explicit analytical model of the Antarctic Circumpolar Current (ACC) is presented in which the key feature is the balance between the Eulerian circulation acting to overturn the isopycnals and geostrophic eddies which tend to flatten them. Solutions for the stratification and overturning circulation are obtained by expanding the governing residual mean equations of motion in a small parameter (ε) which measures the relative strength of the surface buoyancy flux and mechanical forcing by winds. Our balanced asymptotic model extends and reconciles the earlier views on the dynamics of the (streamwise-averaged) ACC by demonstrating that the zero order balance between the eddy-induced circulation and the mean flow determines gross features of the buoyancy distribution in the interior of the ACC. The diabatic buoyancy fluxes are essential in driving the secondary (residual) circulation which is, however, largely steered along the pathways set by the dominant adiabatic balance. Model assumptions are supported by a close agreement of the analytical solutions and fully nonlinear numerical calculations.
Radko, Timour. 2005. "Analytical solutions for the ACC and its overturning circulation." Journal of Marine Research 63, (6). https://elischolar.library.yale.edu/journal_of_marine_research/112