Finite area vortex motion on a sphere with impenetrable boundaries

Abstract

Techniques based on conformal mapping and the numerical method of contour dynamics are presented for computing the motion of a finite area patch of constant vorticity on a sphere with impenetrable boundaries. Several examples of impenetrable boundaries are considered including a spherical cap, longitudinal wedge, half-longitudinal wedge, and a thin barrier. Finite area patch motion is compared to exact point vortex trajectories and good agreement is found between the point vortex trajectories and the centroid motion of finite area patches when the patch remains close to circular. More exotic motion of the finite area patches, particularly in the thin barrier case, is then examined. In the case when background flow owing to a dipole located on the barrier is present, the vortex path is pushed close to one of the barrier edges, leading to vortex shedding and possible splitting and, in certain cases, to a quasisteady trapped vortex. A family of vortex equilibria bounded between the gap in the thin barrier is also computed.