Refinements on the quasi-geostrophic ellipsoidal vortex model

Abstract

Refinements on the quasi-geostrophic ellipsoidal moment model are proposed, where each coherent vortex is modeled by an ellipsoid of uniform potential vorticity. The dynamics of N ellipsoidal vortices can be described by a canonical Hamiltonian system of 3N degrees of freedom. We introduce a new set of “nearly” canonical variables in addition to those from the refined wire-vortex (spheroidal) model with 2N degrees of freedom. We replace the moment expansions used in the previous ellipsoidal moment model by the Gaussian integration method in the evaluation of the mutual interaction energy integrals. The refined model describes the interaction of two vortices very well and predicts the critical merger distance that was observed by direct simulation more accurately than the refined wire-vortex (spheroidal) model.