1 Department of Mathematics, Technical University of Denmark2 University of Illinois at Urbana-Champaign3 Department of Applied Mathematics and Computer Science, Technical University of Denmark4 University of Illinois at Urbana-Champaign
The problem of locating stagnation points in the flow produced by a system of N interacting point vortices in two dimensions is considered. The general solution, which 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, is stated and proved. Specific results for the case N=3 are proved. The related problem of the location of stagnation points in a frame of reference moving with the vortices, when these are translating uniformly, is considered and an extension of Siebeck's theorem to this case is stated.