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The relaxation of two-dimensional rolls in Rayleigh–Bénard convection

Paul, M. R. and Catton, I. (2004) The relaxation of two-dimensional rolls in Rayleigh–Bénard convection. Physics of Fluids, 16 (5). pp. 1262-1266. ISSN 1070-6631. doi:10.1063/1.1669335.

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Large aspect ratio, two-dimensional, periodic convection layers containing a Boussinesq fluid of finite Prandtl number bounded by rigid or free horizontal surfaces are investigated numerically. The fluid equations are solved using both a standard pseudospectral and a Fourier integral method for the time evolution of finite initial perturbations, both random thermal perturbations and localized roll disturbances, into a final equilibrium state. The suggestion that a Fourier integral solution method is required to yield roll relaxation, the two-dimensional process increasing the convection wavelength to values larger than critical, is investigated. Roll relaxation is found for both free-slip and no-slip surfaces using either solution method as long as the initial state is chosen to be of the form of a localized roll disturbance. A wide variety of simulations are performed and roll relaxation is found to be independent of the periodic domain length, weakly dependent on the Rayleigh number and dependent upon the magnitude of the initial localized roll disturbances.

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Additional Information:©2004 American Institute of Physics. Received 19 October 2003; accepted 21 January 2004; published online 2 April 2004. We are grateful to R. E. Kelly, P. H. Roberts, and W. Meechum for helpful discussions.
Subject Keywords:flow simulation; slip flow; Benard convection; integral equations; Fourier analysis; relaxation; numerical analysis
Issue or Number:5
Record Number:CaltechAUTHORS:PAUpof04
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4169
Deposited By: Tony Diaz
Deposited On:07 Aug 2006
Last Modified:08 Nov 2021 20:15

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