Chaotic advection in a Rayleigh-Benard flow
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (US) California Institute of Technology, Pasadena, California 91125
We consider the problem of transport of a passive tracer in the time-dependent flow corresponding to a Rayleigh number {ital scrR} slightly above the {ital scrR}{sub {ital t}} at the onset of the even oscillatory instability for Rayleigh-Benard 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 ({ital scrR}{minus}{ital scrR}{sub {ital t}}){sup 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.
- OSTI ID:
- 6203207
- Journal Information:
- Physical Review, A; (USA), Vol. 43:2; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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