Families of translating neutral vortex street configurations

Abstract

Translating point vortex street configurations model asymptotic states of wakes in a two-dimensional fluid. In this paper such configurations are found with the aid of a multilinear differential equation analogous to the one used in the non-periodic case. Arrangements of point vortex streets with circulations +1/ - 1 or +1/ - 2, arbitrary translation velocity and arbitrary numbers of vortex streets (consistent with zero total circulation) are found; the polynomials describing these arrangements have free complex parameters and hence describe a continuum or family of translating states. A similar family with three circulation values is also exhibited. © 2008 Springer.