The linear models of the ACC

Abstract

Discussions of the dynamics of the Antarctic Circumpolar Current (ACC) generally focus on eddies. The linear, analytical models are discussed only infrequently, and none of these models has gained widespread acceptance. These models nevertheless exist and exhibit interesting, and often realistic, features. We revisit those models, to understand their dynamics and to assess their relevance to the ACC. We focus specifically on the steady, linear, wind-driven models, and those with either a barotropic or equivalent barotropic vertical structure. The most important feature distinguishing them is their choice of geostrophic contours ( f / H or the equivalent), whether closed or blocked. We first examine the flat bottom models. With closed geostrophic contours, the solutions have a flow which is primarily along the contours and a transport which is inversely proportional to the bottom drag coefficient. For realistic parameters, this transport is excessively large. Solution with blocked contours instead exhibit gyres, with cross-contour flow and western boundary currents. But they also have one or more circumpolar jets, which follow the geostrophic contours over most of the domain. In contrast to the closed contour models, these jets have a transport which asymptotes to a constant value when the bottom drag is vanishingly weak. We then discuss solutions with bottom topography, focusing in particular on the equivalent barotropic solution. The central parameter here is the vertical scale of the current, which determines the extent of the interaction with topography and the degree to which the geostrophic contours are blocked. The solutions with a shallow current are less affected by topography and have closed geostrophic contours and large transports. Solutions with too large vertical extent are overly-controlled by topography and exhibit only weak circumpolar transport. Solutions with an intermediate vertical scale have blocked contours and also reasonable circumpolar transport. Furthermore, these solutions exhibit strikingly realistic surface height fields. As in the flat bottom case, the solutions have an interior in Sverdrup balance and a circumpolar transport which asymptotes with vanishing bottom friction. We demonstrate that this transport can be estimated via a contour integral; the result agrees well with the full equivalent barotropic solution. Both are nevertheless roughly 50% larger than observed in Drake Passage. However, the transport can be reduced to realistic values by adding lateral dissipation to the model. Thus the equivalent barotropic model is successful at capturing the steering of the ACC by topography, given the vertical scale of the current. However, it remains to understand what determines that scale. Thermohaline forcing and lateral mixing by eddies are likely to be important.