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Title:Topological fluid mechanics of point vortex motions
Author(s):Boyland, Philip L.; Stremler, Mark A.; Aref, Hassan
Subject(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.
Issue Date:1999-07
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 917
1999-6019
Genre:Technical Report
Type:Text
Language:English
URI:http://hdl.handle.net/2142/112625
ISSN:0073-5264
Rights Information:Copyright 1999 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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