On the structure of the set of self-similar quadruples of point vortices in the plane

TL;DR

This paper investigates the structure of self-similar configurations of four point vortices in the plane, revealing new configurations beyond previously known elliptical solutions through numerical methods.

Contribution

It introduces a numerical procedure to find zeros of a vector field representing self-similar vortex configurations, discovering new solutions beyond classical ones.

Findings

Identified new components of self-similar vortex configurations.

Extended the understanding of vortex configuration sets.

Numerically verified the existence of configurations different from Novikov's ellipse.

Abstract

It has been shown that the set of self-similar configurations of point vortices in the plane is the set of zeros of a vector field. A numerical procedure for seeking the zeros has been proposed. By using this procedure, for the circulation used by Novikov, new components of the set of self-similar configurations of fours vortices, different from the ellipse identified by Novikov, have been found numerically.