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/2142/279

Description

Title
Topological fluid mechanics of point vortex motions
Author(s)
  • Boyland, Philip L.
  • Stremler, Mark A.
  • Aref, Hassan
Issue Date
2002-10
Keyword(s)
vortex dynamics
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. Restricting to three vortices with zero net circulation, the symmetries are used to reduce each system to a one-degree-of-freedom Hamiltonian. The phase portrait of the 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 analyze these isotopy classes, and in certain cases strong implications about the chaotic dynamics of the advection can be drawn. This points to an important mechanism by which the topological kinematics of large-scale, two-dimensional fluid motions generate chaotic advection.
Publisher
Department of Theoretical and Applied Mechanics (UIUC)
Series/Report Name or Number
TAM Reports 1012
ISSN
0073-5264
Type of Resource
text
Language
en
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http://hdl.handle.net/2142/279

Owning Collections

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.