Vortex methods for bounded motion on a spherical surface

We discuss the motion of both point vortices and uniform vortex patches in bounded domains on a spherical surface. The fluid domains are taken to be ``basins'' having solid walls which act as impenetrable barriers for the flow. A theoretical formulation for the general N point vortex problem will be given. In addition, we describe a versatile numerical algorithm (a generalized ``contour dynamics'' scheme) to compute the motion of vortex patches in domains of arbitrary geometrical complexity on a sphere.