Abstract
In geophysical flows, coherent vortex structures persist and their interactions dominate the scalar transport as well as the dynamics of turbulence. Meacham (1992) and Meacham et al. (1994) obtained exact unsteady solutions of the quasi-geostrophic equation, which represent an ellipsoidal vortex patch of uniform potential vorticity. In this paper, we investigate the scalar transport around the ellipsoidal vortex patch, both theoretically (based on the Melnikov analysis) and numerically. An inclined spheroidal vortex rotates steadily around the vertical axis, and any fluid particle moves along a closed trajectory in the coordinates rotating with the spheroidal vortex. There are heteroclinic orbits in the plane of symmetry and homoclinic orbits in other horizontal planes. We can observe chaotic mixing in the vicinity of these orbits, if the spheroid is deformed slightly.
