Non-self-similar, partial, and robust collapse of four point vortices on a sphere

Abstract

This paper gives numerical examples showing that non-self-similar collapse can occur in the motion of four point vortices on a sphere. It is found when the four-vortex problem is integrable, in which the moment of vorticity vector is zero. The non-self-similar collapse has significant properties. It is partial in the sense that three of the four point vortices collapse to one point in finite time and the other one moves to the antipodal position to the collapse point. Moreover, it is robust with respect to perturbation of the initial configuration as long as the system remains integrable.