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

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 4-vortex problem is integrable, in which the moment of vorticity vector is zero. The non self-similar collapse has signi¯cant properties. It is partial in the sense that three of the four point vortices collapse to one point in ¯nite 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 con¯guration as long as the system remains integrable. The non self-similar, robust and partial collapse of point vortices is a new phenomenon that has not yet been reported.