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Chaotic advection in a Rayleigh-Bénard flow

Camassa, R. and Wiggins, S. (1991) Chaotic advection in a Rayleigh-Bénard flow. Physical Review A, 43 (2). pp. 774-797. ISSN 1050-2947. doi:10.1103/PhysRevA.43.774.

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We consider the problem of transport of a passive tracer in the time-dependent flow corresponding to a Rayleigh number scrR slightly above the scrRt at the onset of the even oscillatory instability for Rayleigh-Bénard convection rolls. By modeling the flow with a stream function, we show how to construct and identify invariant structures in the flow that act as a ‘‘template’’ for the motion of fluid particles, in the absence of molecular diffusivity. This approach and symmetry considerations allow us to write explicit formulas that describe the tracer transport for finite times. In the limit of small amplitude of the oscillation, i.e., when (scrR-scrRt)1/2 is small, we show that the amount of fluid transported across a roll boundary grows linearly with the amplitude, in agreement with the experimental and numerical findings of Solomon and Gollub [Phys. Rev. A 38, 6280 (1988)]. The presence of molecular diffusivity introduces a (long) time scale into the problem. We discuss the applicability of the theory in this situation, by introducing a simple rule for determining when the effects of diffusivity are negligible, and perform numerical simulations of the flow in this case to provide an example.

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Additional Information:©1991 The American Physical Society. Received 3 August 1990. This research was partially supported by the National Science Foundation and The Office of Naval Research.
Issue or Number:2
Record Number:CaltechAUTHORS:CAMpra91
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6127
Deposited By: Tony Diaz
Deposited On:25 Nov 2006
Last Modified:08 Nov 2021 20:31

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