ON STAGNATION POINTS AND STREAMLINE TOPOLOGY IN VORTEX FLOWS

The problem of locating stagnation points in the flow produced by a sy stem of N interacting point vortices in two dimensions is considered, The general solution follows from an 1864 theorem by Siebeck, that the stagnation points are the foci of a certain plane curve of class N - 1 that has all lines connecting vortices pairwise as tangents. The cas e N = 3, for which Siebeck's curve is a conic, is considered in some d etail. It is shown that the classification of the type of conic coinci des with the known classification of regimes of motion for the three v ortices. A similarity result for the triangular coordinates of the sta gnation point in a flow produced by three vortices with sum of strengt hs zero is found, Using topological arguments the distinct streamline patterns for flow about three vortices are also determined. Partial re sults are given for two special sets oi. vortex strengths on the chang es between these patterns as the motion evolves. The analysis requires a number of unfamiliar mathematical tools which are explained.