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| Paper IPM / M / 2342 |
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| Abstract: | |||||
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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.
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