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Nonlinear Rayleigh–Bénard convection with square planform

Published online by Cambridge University Press:  20 April 2006

Wayne Arter
Wayne Arter
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, CB3 9EW Present address: Culham Laboratory, Abingdon, Oxon, OX14 3DB (UKAEA/Euratom Fusion Association).
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Abstract

Fully three-dimensional numerical solutions are presented for Rayleigh-Bénard convection subject to stress-free boundary conditions. A motion with square planform is studied for varying Rayleigh number R and Prandtl number σ. It may be understood partly in terms of a truncated modal representation (after Lorenz 1963). Thermal layers of unusual structure are found at high R. For small σ, steady solutions exist, but are not of ‘flywheel’ type, and the heat transport depends strongly on σ. The study also verifies that laminar convective flows may be ergodic.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 152 , March 1985 , pp. 391 - 418
Copyright
© 1985 Cambridge University Press

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