University of Illinois Urbana-Champaign

On equilibrium and stability of row of point vortices

Aref, Hassan

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https://hdl.handle.net/2142/112470

Description

Title
On equilibrium and stability of row of point vortices
Author(s)
Aref, Hassan
Issue Date
1994-11
Keyword(s)
  • Equilibrium
  • Stability
  • Row Of Point Vortices
Abstract
The equilibrium and stability of a single row of equidistantly spaced, identical point vortices is a classical problem in vortex dynamics, that has been addressed h:- several investigators in different ways for at least a century. Aspects of the history and the essence of these treatments are traced, stating some in more accessible form, and pointing out interesting and apparently new connections between them. For example, it is shown that the stability problem for vortices in an infinite row and the stability problem for vortices arranged in a regular polygon are solved by the same eigenvalue problem for a certain symmetric matrix. This result also provides a more systematic enumeration of the basic instability modes. The less familiar theory of equilibria of a finite number of vortices situated on a line is also recalled.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 776
  • 1994-6032
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112470
Sponsor(s)/Grant Number(s)
National Science Foundation 94/11
Copyright and License Information
Copyright 1994 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.