A Two-Layer Wind-Driven Ocean Model in a Multiply Connected Domain with Bottom Topography

Abstract

The behavior of the solution to a two-layer wind-driven model in a multiply connected domain with bottom topography imitating the Southern Ocean is described. The abyssal layer of the model is forced by interfacial friction, crudely simulating the effect of eddies. The analysis of the low friction regime is based on the method of characteristics. It is found that characteristics in the upper layer are closed around Antarctica, while those in the lower layer are blocked by solid boundaries. The momentum input from wind in the upper layer is balanced by lateral and interfacial friction and by interfacial pressure drag. In the lower layer the momentum input from interfacial friction and interfacial pressure drag is balanced by topographic pressure drag. Thus, the total momentum input by the wind is balanced by upper-layer lateral friction and by topographic pressure drag. In most of the numerical experiments the circulations in the two layers appear to be decoupled. The decoupling can be explained by the JEBAR term, whose magnitude decreases as interfacial friction increases. The solution tends toward the barotropic one if the interfacial friction is large enough to render the JEBAR term to be no larger than the wind stress curl term in the potential vorticity equation. The change of regimes occurs when the value of the interfacial friction coefficient ? equals ?0 = H1f0(Ly/Lx)(A/H0), where f0 is the mean value of the Coriolis parameter; Ly and Lx are the meridional and zonal domain dimensions; H0 and H1 are the mean depths of the ocean and of the upper layer; and A is the amplitude of topographic perturbations. Note that ?0 does not depend on the strength of the wind stress. The magnitude of the total transport is found to depend crucially on the efficiency of the momentum transfer from the upper to the lower layer, that is, on the ratio ?/ε, where ε is the lateral friction coefficient. If ε and ? are assumed to be proportional, the upper-layer transport and total transport vary as ε?5/6.