Chaotic motions of inviscid point vortices around rigid obstacles

Abstract

The planar motion ofN inviscid point vortices in the presence of a fixed rigid obstacle is described by an autonomous Hamiltonian set of differential equations. For circular and rectilinear boundary of the obstacle the two-vortex system is integrable. Numerical simulations suggest that the perturbation of the circular boundary into an ellypse causes homoclinic bifurcation in the restricted two-vortex system and transition to chaotic motion. This may be compared with the case of systems of free vortices (no obstacle) where chaotic motion first appears atN=4.