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

Preprint Series # 904
SAKAJO, Takashi Non self-similar, partial and robust collapse of four point vortices on sphere. (2008);

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## 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 $4$-vortex problem is integrable, in which the moment of vorticity vector is zero. The non self-similar collapse has significant properties. It is \textit{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 \textit{robust} with respect to perturbation of the initial configuration 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.

Item Type: Preprint 10 Copies 76-xx FLUID MECHANICS 1845