In the additional boundary condition of wind-driven ocean models on the eastern coast

In the homogeneous model of the wind-driven ocean circulation, the dynamics of the basin interior is basically governed by the Sverdrup bilance and the related no mass-flux condition on the eastern boundary of the basin, which we assume to be square for conceptual simplicity. In the presence of lateral diffusion of relative vorticity, the additional condition on the eastern boundary (like the conditions on the other boundaries) is not demanded on physical grounds but it is arbitrary to a large extent. Hence, certain choices of such boundary conditions can produce overall solutions which are “far” from that of Sverdrup in the eastern part of the domain, without any physical reason. In the present note we show that this discrepancy can be strongly reduced if the adopted boundary conditions has the same form as that implicitly satisfied by the Sversrup solution. Unlike the common approach, a criterion is thus derived which selects a suitable partila slip boundary condition according to the specific wind-stress field which is taken into account.