Refinements on the Quasi-geostrophic Wire-Vortex Model

Abstract

Refinements on the quasi-geostrophic wire-vortex model are proposed. Each coherent vortex is modeled by a straight wire of finite length. The dynamics of N wire-vortices is a canonical Hamiltonian system of 2 N degrees of freedom. We adapt the Gaussian integration method in the evaluation of the mutual energy integrals, instead of the moment approximation used in the previous wire model. The accuracy of integration is improved drastically, even if two wire-vortices are placed very close. The refined model can circumvent the singular behavior of a counter-rotating vortex pair, predicted by the previous wire moment model. We also introduce a realistic relation between the inclination angle and the vortex-slenderness parameter, assuming that each wire-vortex is a prolate spheroid. The latter refinement enables us to model fatter vortices more accurately.