On the inertial motion of a homogeneous ocean

An investigation of properties of the solutions of the steady state inviscid barotropic vorticity equation in a rectangular basin was performed for various functional relationships between potential vorticity and the streamfunction. All computed solutions which have slow interior flow and satisfy Arnol'd-Blumen condition are qualitatively similar to Fofonoff's inertial gyre. A new class of solutions with a small vortex near the boundary current is described. Such solutions are not stable under finite amplitude perturbations and instability is manifested in the drift of the vortex. It is shown that the vortex is robust and decays only after collision with the boundary or under the influence of very large perturbations. We also show that the inertial boundary current may be much wider than in Fofonoff's model due to the appearance of a countercurrent on its seaward side.