A system of point vortices constitute a simple model for the dynamics of an ideal fluid, where each vortex
moves in the velocity field induced by the other vortices. The field from the vortices does also induce a motion
of the ambient fluid. To characterize the topology of a flow field, the number and positions of the stagnation
points, i.e. the points where the velocity vanishes, is of key importance.
It turns out there is a beautiful geometrical characterization of the stagnation points in point vortex flows. The
theorem is illustrated in the figure for the case of three identical vortices. Consider the triangle with vertices at
the vortices. There is a unique ellipse which touches the sides of the triangle at their midpoints. This ellipse has two foci.
These are the stagnation points. In the picture, the dividing treamlines (sepatratrices) for the stagnation points
are also shown. The theorem can be generalized to any number of vortices of arbitrary strengths, see H. Aref
and M. Brøns: On stagnation points and streamline topology in vortex flows, Journal of Fluid Mechanics 370(1998), 1-27.
Link to article in Journal of Fluid Mechanics.