The equilibrium shapes of non-uniform vortices in the ocean

The problem of the equilibrium shapes of rotating vortices in a stratified ocean, which is in a statically stable state, is considered within the framework of the model of an ideal incompressible fluid. An equilibrium shape is a surface on which the pressures in the vortex and in the ocean are equal, in which case, on this surface the normal components of the velocities of the media are equal to zero, but a discontinuity of the tangential components is allowed. The case of stratification of the media along the local vertical is considered. The external medium (the ocean) may consist of several layers, differing sharply in density.