The results from the homogeneous channel model discussed by Wang and Huang (1994) is extended to a model whose geometry consists of a zonal channel and two partial meridional barriers along each boundary at the same longitude. Both the model transport and especially the model circulation are significantly affected by the presence of the two meridional barriers. There is a critical height of the ridge between the two partial meridional barriers, above which all geostrophic contours in the channel are blocked. In the case with a subcritically high ridge, the Sverdrup balance does not apply and there is no finite solution in the inviscid limit. In the case with a supercritically high ridge, however, an explicit form for the through-channel transport is obtained in the inviscid limit. In the case with a uniform wind stress, the transport is independent of the width of either the ridge or the channel, and is linearly proportional to the wind stress and the length of the channel, while inversely proportional to the ridge height. In the case with a nonuniform wind stress τx = τ0(1 − cos πy/D), the relation between the transport and model parameters is more complicated. It is also related to the width of both the ridge and the channel, and the lengths of the two partial meridional barriers. The presence of the northern barrier always leads to a decrease in the transport. The presence of the southern barrier, however, increases the transport for a narrow ridge. The model demonstrates the importance of the topographic form-drag generation via the Sverdrup flow forced by the wind stress curl. In terms of the circulation structure, the presence of a southern barrier has a far more profound influence than that of a northern one. The northern barrier only has a localized influence on the circulation pattern, while the southern barrier has a global influence in the channel. In addition, the model demonstrates that most of the potential vorticity dissipation occurs around the northern barrier.
Wang, Liping. 1994. "A linear homogeneous model for topographic control of the Antarctic Circumpolar Current." Journal of Marine Research 52, (4). https://elischolar.library.yale.edu/journal_of_marine_research/2109