Self-Similar Collapse of n Point Vortices

A system of a finite number of linear vortices in self-similar motion and under suitable conditions that are related to the initial positions and circulations of the vortices can collapse to the point with finite time. It is shown how the initial positions that lead to the collapse can be found numerically. An explicit solution for the self-similar collapse of the trajectories is derived. Examples of a collapsing system of 3, 7, and 30 vortices are given. A description is given of how to obtain the curves of collapsing positions of vortices if one particular system of vortices has already been found. Examples of such curves are given.