Dynamics of uniform vortex patch with a point vortex

Abstract

Vortex dynamics in two-dimensional inviscid, incompressible fluids are isomorphic to the dynamics of strongly magnetized guiding center plasmas restricted to E x B motion. In this paper, we exploit this analogy and study the dynamics of a uniform vortex patch with a point-like vortex using a particle-in-cell code. While the results show qualitative agreement with previous works in the linear regime when the normalized point vortex charge Gamma is small, the dynamics shows many new features in the nonlinear regime: the point vortex "fangs" out the patch and moves toward the center, wrapping the patch around itself while setting up regions of zero vorticity as it moves.