Topological mixing with ghost rods

Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland, Aref, and Stremler [J. Fluid Mech. 403, 277 (2000)] have studied a specific...

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Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2006-03, Vol.73 (3 Pt 2), p.036311-036311, Article 036311
Main Authors: Gouillart, Emmanuelle, Thiffeault, Jean-Luc, Finn, Matthew D
Format: Article
Language:English
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Summary:Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland, Aref, and Stremler [J. Fluid Mech. 403, 277 (2000)] have studied a specific periodic motion of rods that exhibits topological chaos in a viscous fluid. We show that it is possible to extend their work to cases where the motion of the stirring rods is topologically trivial by considering the dynamics of special periodic points that we call "ghost rods", because they play a similar role to stirring rods. The ghost rods framework provides a new technique for quantifying chaos and gives insight into the mechanisms that produce chaos and mixing. Numerical simulations for Stokes flow support our results.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.73.036311