University of Illinois Urbana-Champaign

On stagnation points and streamline topology in vortex flows

Aref, Hassan; Brons M

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https://hdl.handle.net/2142/112551

Description

Title
On stagnation points and streamline topology in vortex flows
Author(s)
  • Aref, Hassan
  • Brons M
Issue Date
1997-03
Keyword(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.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 848
  • 1997-6009
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112551
Sponsor(s)/Grant Number(s)
National Science Foundation 97/03 CTS 93 11545 97/03
Copyright and License Information
Copyright 1997 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
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.