Nonlinear adjustment of a heavy rotating fluid to equilibrium

We consider the problem of geostrophic adjustment of nonlinear axially symmetric formations in a two-layer fluid with infinitely deep lower layer and demonstrate the existence of a new integral of motion, which enables us to determine the final equilibrium state of perturbations without analyzing the transient (wave) stage of the process. It is shown that the final motions caused by initial perturbations of the opposite signs are not equivalent. Translated by Peter V. Malyshev and Dmitry V. Malyshev