Variational problem for vortices attached to seamounts Original Research Article

The existence of an energy maximizer relative to a class of rearrangements of a given function is proved. The maximizers are stationary and stable solutions of the two-dimensional barotropic vorticity equation, governing the evolution of geophysical flow over a surface of variable height. The theorem proved implies the existence of a family of stable vortices with anticyclonic potential vorticity over a seamount, and a similar family of vortices with cyclonic potential vorticity over a localized depression.