Relative equilibria of singly periodic point vortex arrays

Abstract

This paper presents a systematic investigation of singly periodic discrete vortex configurations that move uniformly without change of shape or size. The general condition for existence of such equilibria is that SV̄=O, where S=Σ is the net circulation within a single period and V̄ is (the complex conjugate of) the vortex velocity. Those configurations that satisfy this condition are determined for two and three vortices per period. © 2003 American Institute of Physics.