Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2005-07-12
Physica D 221 (1), 92-100 (2006)
Nonlinear Sciences
Chaotic Dynamics
18 pages, 14 figures. RevTeX4 style with psfrag macros. Final version
Scientific paper
10.1016/j.physd.2006.07.018
Topologically chaotic fluid advection is examined in two-dimensional flows with either or both directions spatially periodic. Topological chaos is created by driving flow with moving stirrers whose trajectories are chosen to form various braids. For spatially periodic flows, in addition to the usual stirrer-exchange braiding motions, there are additional topologically-nontrivial motions corresponding to stirrers traversing the periodic directions. This leads to a study of the braid group on the cylinder and the torus. Methods for finding topological entropy lower bounds for such flows are examined. These bounds are then compared to numerical stirring simulations of Stokes flow to evaluate their sharpness. The sine flow is also examined from a topological perspective.
Finn Matthew D.
Gouillart Emmanuelle
Thiffeault Jean-Luc
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