Topological Chaos in Spatially Periodic Mixers
arXiv:nlin/0507023 · doi:10.1016/j.physd.2006.07.018
Abstract
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.
arXiv comment18 pages, 14 figures. RevTeX4 style with psfrag macros. Final version
References in corpus (3)
Cited by in corpus (12)
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- Topological Entropy of Braids on the Torus
- Measures of mixing quality in open flows with chaotic advection
- Braidlab: A Software Package for Braids and Loops
- Using braids to quantify interface growth and coherence in a rotor-oscillator flow
- Estimating topological entropy from the motion of stirring rods
- Reynolds number effects on mixing due to topological chaos