On Stagnation points and streamline topology in vortex flows

Hassan Aref, Morten Brøns

    Research output: Book/ReportReportResearchpeer-review


    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.
    Original languageEnglish
    Publication statusPublished - 1997


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