Non selfsimilar, partial and robust collapse of four point vortices on sphere
Preprint Series # 904 SAKAJO, Takashi Non selfsimilar, partial and robust collapse of four point vortices on sphere. (2008); AbstractThis paper gives numerical examples showing that non selfsimilar 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 selfsimilar 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
selfsimilar, robust and partial collapse of point
vortices is a new phenomenon that has not yet been reported.
