Method for finding stationary states of point vortices

Abstract

The condition for stationary configurations of point vortices (or screw dislocations, line charges, etc.) having arbitrary strengths embedded in an external flow field is expressed as a differential equation for functions whose zeros are the vortex positions. For vortices of unit strength but mixed sign the stationary states are closely related to both the rational and the N-soliton solutions of the Korteweg--de Vries equation. Examples are given for no external flow, uniform flow, and quadrupole flow.