Quasigeostrophic Wire-Vortex Model

Abstract

A wire-vortex model is developed in order to investigate the dynamics of vortex interactions in a quasigeostrophic turbulence. Each coherent vortex is modeled by a straight wire of finite length. A tilted wire-vortex rotates around the vertical axis steadily by its self-induction in an otherwise quiescent fluid, whereas its inclination angle changes if it is embedded in a local strain field induced by other vortices. The dynamics of wire-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.