An inner additional condition for solving Munk-like ocean circulation models

The problem of determining the additional boundary conditions, in the framework of the wind-driven single-gyre ocean circulation with lateral diffusion of relative vorticity, is explored with reference to the western boundary and in the context of the classical linear Munk model. As, of necessity, each model solution satisfies a certain inner additional condition, the latter is used to select special kinds of partial-slip boundary conditions, one of which assures the dynamic stability of the linear solution. Moreover, as the boundary conditions are left unaffected by nonlinearity, the same condition can be applied also to the nonlinear model. In particular, an open question about the flow energetics, reported in the literature, is solved by using the present results.