On the role of angular momentum conservation in the formation and evolution of frontal vortices

The classical Rossby problem of the adjustment of a layer of a free-surface heavy fluid to equilibrium, which was previously considered in a linear ap proximation, is solved for an axisymmetric initial disturbance of arbitrary form and amplitude. This solution turns out to be feasible due to the cons ervation of axial symmetry in the course of disturbance evolution and due t o the ensuing conservation of angular momentum in a fluid particle. The con servation of a fluid volume and angular momentum enables one to construct a n integral dependent on the initial conditions for the system of equations of axisymmetric motion of a continuously stratified fluid. This additional integral of motion makes it possible to calculate the three-dimensional str ucture of an axisymmetric vortex in a stratified fluid at equilibrium witho ut solving the nonstationary problem. The theory developed describes the di stribution of velocity observed in a Gulf Stream warm-core ring with high a ccuracy.