Multipetal vortex structures in two-dimensional models of geophysical fluid dynamics and plasma

Abstract

A new class of strongly nonlinear steadily rotating vortices is found. The Hamiltonian contour dynamics is proposed as a new approach for their study in some models of geophysical fluid dynamics and plasma. Using the Euler description as a starting point, we present a systematic procedure to reduce the two-dimensional dynamics of constant-vorticity and constant-density patches to the Hamiltonian dynamics of their contours for various parametrizations of the contour. The special Dirac procedure is used to eliminate the constraints arising in the Hamiltonian formulations with the Lagrangian parametrization of the contour. Numerical estimations illustrating the physical significance of the results and the range of model parameters where these results can be applicable are presented. Possible generalizations of the approach based on the application of the Hamiltonian contour dynamics to nonplanar and 3D flows are discussed.