2007
DOI: 10.1063/1.2772881
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Generating topological chaos in lid-driven cavity flow

Abstract: Periodic motion of three stirrers in a two-dimensional flow can lead to chaotic transport of the surrounding fluid. For certain stirrer motions, the generation of chaos is guaranteed solely by the topology of that motion and continuity of the fluid. Work in this area has focused largely on using physical rods as stirrers, but the theory also applies when the “stirrers” are passive fluid particles. We demonstrate the occurrence of topological chaos for Stokes flow in a two-dimensional lid-driven cavity without … Show more

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Cited by 33 publications
(26 citation statements)
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“…Each strand returns to its initial position every Át ¼ 3 f ¼ b , which gives one period of the braid. The topology of this braid is identical to that in [7,13].…”
mentioning
confidence: 60%
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“…Each strand returns to its initial position every Át ¼ 3 f ¼ b , which gives one period of the braid. The topology of this braid is identical to that in [7,13].…”
mentioning
confidence: 60%
“…The analysis of dynamical systems using the TNCT has been largely dependent on the presence and identification of exactly periodic orbits [11,13]. Recently, the analysis of ghost rod topology in a fluid has been extended to aperiodic orbits [14,15], relaxing a substantial restriction in the application of the TNCT.…”
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confidence: 99%
“…However, as we will see in this section, their presence can still be inferred by examining the topological properties of the rod motion, including if necessary the motion of ghost rods. This section also helps to clarify the type of topological information that can be gleaned from the motion of rods: 7,15,29 • If the motion of the rods themselves forms a pseudoAnosov braid, then the rod motion yields interesting topological information even with no knowledge of ghost rods. This is the case with all the protocols in the paper thus far ͑except the figure-eight, which involves two obvious ghost rods͒.…”
Section: Hyperbolic Injection Cuspsmentioning
confidence: 99%
“…If we assume the axial flow in the present system is uniform, the results in Ref. 18 can be applied directly to steady channel flow by identifying time with axial position. However, the appropriate assumption is to satisfy the no-slip condition on the channel walls.…”
mentioning
confidence: 99%
“…1͑c͒ and Ref. 18. We take the flow to be spatially periodic in the axial direction with period ᐉ f =2ᐉ.…”
mentioning
confidence: 99%