University of Illinois Urbana-Champaign

Topological fluid mechanics of point vortex motions

Boyland, Philip L.; Stremler, Mark A.; Aref, Hassan

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https://hdl.handle.net/2142/112625

Description

Title
Topological fluid mechanics of point vortex motions
Author(s)
  • Boyland, Philip L.
  • Stremler, Mark A.
  • Aref, Hassan
Issue Date
1999-07
Keyword(s)
  • Topological Fluid Mechanics
  • Point Vortex Motions
Abstract
Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. The reduction of each system using its symmetries is described in detail. Restricting to three vortices with zero net circulation, each reduced system is described by a one degree of freedom Hamiltonian. The phase portrait of this reduced system is subdivided into regimes using the separatrix motions, and a braid representing the topology of all vortex motions in each regime is computed. This braid also describes the isotopy class of the advection homeomorphism induced by the vortex motion. The Thurston-Nielsen theory is then used to analyse these isotopy classes, and in certain cases strong conclusions about the dynamics of the advection can be made.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 917
  • 1999-6019
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112625
Copyright and License Information
Copyright 1999 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.