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Title:On stagnation points and streamline topology in vortex flows
Author(s):Aref, Hassan; Brons M
Subject(s):Stagnation Points
Streamline Topology
Vortex Flows
Abstract: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. This necessitates developing some of the mathematical apparatus of algebraic geometry. The case N=3, for which Siebeck's curve is a conic, is considered in some detail. In particular, it is shown that the classification of the type of conic coincides with the general classification of regimes of motion of the three vortices. A similarity result for the triangular coordinates of the stagnation point in a flow produced by three vortices with sum of strengths zero is found. The topologically distinct streamline patterns for the flow about three vortices are also determined, and partial results are given on the changes between these patterns as the motion evolves for two special sets of vortex strengths. 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.
Issue Date:1997-03
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 848
Genre:Technical Report
Sponsor:National Science Foundation 97/03 CTS 93 11545 97/03
Rights Information:Copyright 1997 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04

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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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