University of Illinois Urbana-Champaign

On motion of three point vortices in periodic strip

Aref, Hassan; Stremler, Mark A.

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https://hdl.handle.net/2142/112492

Description

Title
On motion of three point vortices in periodic strip
Author(s)
  • Aref, Hassan
  • Stremler, Mark A.
Issue Date
1995-06
Keyword(s)
  • Motion Of Three Point Vortices
  • Periodic Strip
Abstract
"Motivated by observations of Williamson and Roshko of the wake of an oscillating cylinder with three vortices per cycle, and by the analyses of Rott and Aref of the motion of three vortices with vanishing net circulation on the unbounded plane, the integrable problem of three interacting, periodic vortex rows is solved. The problem is ""mapped"" onto a problem of advection of a passive particle by a certain set of fixed point vortices. The results of this ""mapped"" problem are then re-interpreted in terms of the motion of the vortices in the original problem. A rather complicated structure of the solution space emerges with a surprisingly large number of regimes of motion, some of them somewhat counter-intuitive. Representative cases are analyzed in detail, and a general procedure is indicated for all cases. For rational ratios of the vortex circulations all motions are periodic. For irrational ratios this is no longer true. The point vortex results are compared to the aforementioned wake experiments and appear to shed light on the experimental observations. Many additional possibilities for the wake dynamics are suggested by the analysis."
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 795
  • 1995-6017
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112492
Sponsor(s)/Grant Number(s)
National Science Foundation 95/06 CTS 93 11545 95/06
Copyright and License Information
Copyright 1995 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.