Abstract
An ellipsoidal vortex model is developed in order to investigate the dynamics of vortex interactions in a quasigeostrophic turbulence. Each coherent vortex is modeled by an ellipsoid of uniform potential vorticity. It is assumed that each vortex remains to be an ellipsoid, although its principal axes and inclination angles change under the influence of the strain field induced by other vortices. The dynamics of ellipsoidal vortices are shown to be a Hamiltonian system of finite degree of freedom extracted from the partial differential equations that describe quasigeostrophic vortex dynamics. The center of vorticity and the angular momentum are conserved, besides the total energy and Casimirs of the system, such as the vortex height and the vortex volume. Chaotic motions are observed even in a two-body system.
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