Existence of energy minimizing vortices attached to a flat-top seamount

The existence of an energy minimizer relative to a class of rearrangements of a given function is proved. The minimizers 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 anticyclonic vortices with cyclonic potential vorticity over a seamount, and a corresponding family of cyclonic vortices with anticyclonic potential vorticity over a localized depression. The seamount is described by a characteristic function (corresponding to a flat top) with arbitrary shape.