Dynamically Equilibrium Shape of Intrusive Vortex Formations in the Ocean

The problem of finding the dynamically equilibrium shape of a rotating mass of liquid with homogeneous density (lens) submerged in a stratified ocean at rest on the rotating Earth is formulated. An equation for the shape of the interface between water masses is derived. An exact solution of the problem for an anticyclonically rotating lens in a linearly stratified ocean in the neighborhood of the lens depth shows that the dynamically equilibrium shape of the interface is a triaxial ellipsoid inclined with respect to the horizon and similar to an ellipsoid of revolution for real parameters of the phenomenon. The limiting values of the latitudes at which these formations can exist are determined. Degeneration of the shape with decrease in the intrinsic lens angular rate is investigated.