On the Role of Angular Momentum Conservation
in the Formation and Evolution of Frontal Vortices

G. K. Korotaev

Marine Hydrophysical Institute, National Academy of Sciences of Ukraine, Kapitanskaya ul. 2, Sevastopol, 335000 Ukraine

Received April 20, 1998

Abstract—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 approximation, is solved for an axisymmetric initial disturbance of
arbitrary form and amplitude. This solution turns out to be feasible due to the conservation of axial symmetry in
the course of disturbance evolution and due to the ensuing conservation of angular momentum in a fluid particle.
The conservation of a fluid volume and angular momentum enables one to construct an integral dependent on the
initial conditions for the system of equations of axisymmetric motion of a continuously stratified fluid. This addi-
tional integral of motion makes it possible to calculate the three-dimensional structure of an axisymmetric vortex
in a stratified fluid at equilibrium without solving the nonstationary problem. The theory developed describes the
distribution of velocity observed in a Gulf Stream warm-core ring with high accuracy.

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