Beigle, Darin and Leonard, Anthony and Wiggins, Stephen (1991) A global study of enhanced stretching and diffusion in chaotic tangles. Physics of Fluids A, 3 (5). pp. 1039-1050. ISSN 0899-8213. http://resolver.caltech.edu/CaltechAUTHORS:BEIpofa91
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A global, finite-time study is made of stretching and diffusion in a class of chaotic tangles associated with fluids described by periodically forced two-dimensional dynamical systems. Invariant lobe structures formed by intersecting global stable and unstable manifolds of persisting invariant hyperbolic sets provide the geometrical framework for studying stretching of interfaces and diffusion of passive scalars across these interfaces. In particular, the present study focuses on the material curve that initially lies on the unstable manifold segment of the boundary of the entraining turnstile lobe.A knowledge of the stretch profile of a corresponding curve that evolves according to the unperturbed flow, coupled with an appreciation of a symbolic dynamics that applies to the entire original material curve in the perturbed flow, provides the framework for understanding the mechanism for, and topology of, enhanced stretching in chaotic tangles. Secondary intersection points (SIP's) of the stable and unstable manifolds are particularly relevant to the topology, and the perturbed stretch profile is understood in terms of the unperturbed stretch profile approximately repeating itself on smaller and smaller scales. For sufficiently thin diffusion zones, diffusion of passive scalars across interfaces can be treated as a one-dimensional process, and diffusion rates across interfaces are directly related to the stretch history of the interface.An understanding of interface stretching thus directly translates to an understanding of diffusion across interfaces. However, a notable exception to the thin diffusion zone approximation occurs when an interface folds on top of itself so that neighboring diffusion zones overlap. An analysis which takes into account the overlap of nearest neighbor diffusion zones is presented, which is sufficient to capture new phenomena relevant to efficiency of mixing. The analysis adds to the concentration profile a saturation term that depends on the distance between neighboring segments of the interface. Efficiency of diffusion thus depends not only on efficiency of stretching along the interface, but on how this stretching is distributed relative to the distance between neighboring segments of the interface.
|Additional Information:||Copyright © 1991 American Institute of Physics. Received 28 August 1990; accepted 7 December 1990. This material is based upon work supported by a National Science Foundation Graduate Fellowship, the National Science Foundation Presidential Young Investigator Program, the Office of Naval Research Young Investigator Program, and Caltech’s Program in Advanced Technologies, sponsored by Aerojet General, General Motors, and TRW.|
|Subject Keywords:||DIFFUSION, CHAOTIC SYSTEMS, FLUIDS, FORCES, TWO−DIMENSIONAL CALCULATIONS, INVARIANCE PRINCIPLES, MATHEMATICAL MANIFOLDS, MIXING, INTERFACES, ADVECTION, LYAPUNOV METHOD, TIMING PROPERTIES, CHEMICAL REACTIONS|
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|Deposited On:||17 Jan 2009 05:51|
|Last Modified:||26 Dec 2012 10:44|
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