Topology of Chaotic Mixing Patterns
arXiv:0804.2520 · doi:10.1063/1.2973815
Abstract
A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at least a minimum amount of stretching of material lines, which is important for chaotic mixing. We use topological considerations to describe the nature of the injection of unmixed material into a central mixing region, which takes place at injection cusps. A topological index formula allow us to predict the possible types of unstable foliations that can arise for a fixed number of rods.
15 pages, 13 figures, RevTeX4 macros. Final version
References in corpus (8)
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Cited by in corpus (9)
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- Braidlab: A Software Package for Braids and Loops
- Intermittent flow in yield-stress fluids slows down chaotic mixing
- Optimal initial condition of passive tracers for their maximal mixing in finite time
- Estimating topological entropy from the motion of stirring rods
- Reynolds number effects on mixing due to topological chaos