Long-range interaction and elastic collisions of isolated vortices

Abstract

This study explores the interaction of two nearly axisymmetric two-dimensional vortices using a combination of numerical simulations and analytical arguments. We consider isolated or ‘shielded’ eddies, characterized by zero net vorticity. The ability of such vortices to propagate and interact is associated with the small dipolar component that is introduced initially. Numerical contour dynamics experiments indicate that the interaction of shielded eddies takes one of two forms, depending on their initial separation and on the relative orientation of their dipolar components. Eddies can influence each other by remotely modifying the dipolar moments of partner vortices, an effect manifested in a gentle deflection of their trajectories from a straight course. Strong interactions occur when eddies collide and rebound. The remote interaction is explained by weakly nonlinear theory in which the basic state consists of identical circularly symmetric eddies and the perturbation is assumed to be small. It is argued that the elastic rebounds observed during direct collisions are induced by the exchange of fluid between colliding vortices.