open access

https://doi.org/10.14943/84054

https://hdl.handle.net/2115/69712

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

英語

2008

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

904

1-25

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.

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