An analytic model of the Antarctic Circumpolar Current (ACC) is presented in which information contained in a hydrographic section is propagated along characteristics. The characteristics are obtained by assuming that potential vorticity is uniform on density surfaces: they lie between the f/H contours found in a homogeneous ocean and the f contours found in a strongly stratified ocean. Solutions describe an inviscid, adiabatic circulation in which fluid parcels negotiate a variable bottom topography while conserving density and conserving potential vorticity.
A family of solutions are obtained for a realistic spherical geometry including coastlines and major topographic features. In the limit of weak bottom currents, the ACC transports 160 Sv (Sv ≡ 106 m3 s−1) of fluid around Antarctica, with circumpolar flow in the upper three kilometers and abyssal gyres bounded by the bottom topography. In the limit of large bottom currents, the ACC exhibits increased sensitivity to the topograph; streamlines resemble f/H contours and do not pass through the Drake Passage.
Arbitrary parameters in the purely inviscid and adiabatic solution, such as the potential vorticity distribution, the cross-stream surface density profile, and the strength of the abyssal currents, can be constrained through the study of integral balances of momentum and buoyancy. In particular, a balanced momentum budget for the ACC demands the existence of closed gyres within the abyssal layers. Integral constraints along time-mean streamlines also demonstrate the importance of transient eddies in the general maintenance of the current.