Two Sverdrup-like theories of the Antarctic Cirumpolar Current (ACC) have been proposed, due to Stommel and Webb, both of which assume an idealized geometry for the Southern Ocean in which all latitudes are blocked by either continents or "effective continents" consisting of major topographic features. However, the two models predict quite different dependencies of the ACC transport on wind stress: Stommel's model predicting transport proportional to wind stress curl, and Webb's model predicting transport proportional to the zonal wind stress. A generalization of Webb's model is shown to be equivalent to Godfrey's Island Rule, applied to an island straddling the South Pole. With realistic geometry, the strength of the ACC cannot be calculated, but a relationship can be derived which involves the transport in the western boundary current east of South America. It is shown that, if zonal wind stress is entirely balanced by form stress in Drake Passage, this transport is determined by wind stress curl as in Stommel's model. If there is no form stress supported by topography in Drake Passage, then a version of Webb's model applies, and the boundary current transport is determined by zonal wind stress. In the real Southern Ocean, neither of these extreme cases can be expected to apply, and the boundary current transport will, therefore, depend on both wind stress and distribution of form stress. The latter can only be calculated diagnostically from a more complete solution.
Hughes, Chris W.. 2002. "Sverdrup-like theories of the Antarctic Circumpolar Current." Journal of Marine Research 60, (1). https://elischolar.library.yale.edu/journal_of_marine_research/2421