Dynamics of a vortex pair interacting with a fixed point vortex

¹ V. I. Il'ichev Pacific Oceanological Institute - 43, Baltiyskaya Street, Vladivostok, 690041, Russia
² Far Eastern Federal University - 8, Sukhanova Street, Vladivostok, 690950, Russia

Received: 15 April 2013
Accepted: 15 May 2013

Abstract

The dynamics of a vortex pair consisting of two counter-rotating point vortices encountering a fixed point vortex in a uniform medium is addressed. This problem is of interest in part because such an interaction occurs frequently in geophysical flows. The vortex pair is shown to exhibit two different regimes of motion. First, the localized motion (entrapping of the vortex pair), when the pair moves periodically in the vicinity of the fixed vortex. Second, the unrestricted motion, when the pair moves unrestrictedly to infinity. The realization of one of the regimes is demonstrated to be conditional on parameters determined by the asymmetry in the initial positions of the pair's vortices, and the ratio of the fixed vortex's strength and the pair's strength. We show, that unlike the classical three-vortex problem, the regime of unrestricted motion appears even if the net strength of the vortex system is not equal to zero.