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Boundary conditions and linear analysis of finite-cell Rayleigh–Bénard convection

Published online by Cambridge University Press:  26 April 2006

Yih-Yuh Chen
Yih-Yuh Chen
Affiliation:
Condensed Matter Physics 114-36, California Institute of Technology. Pasadena. CA 91125, USA Present address: Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan, ROC.
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Abstract

The linear stability of finite-cell pure-fluid Rayleigh–Bénard convection subject to any homogeneous viscous and/or thermal boundary conditions is investigated via a variational formalism and a perturbative approach. Some general properties of the critical Rayleigh number with respect to change of boundary conditions or system size are derived. It is shown that the chemical reaction–diffusion model of spatial-pattern-forming systems in developmental biology can be thought of as a special case of the convection problem. We also prove that, as a result of the imposed realistic boundary conditions, the nodal surfaces of the temperature of a nonlinear stationary state have a tendency to be parallel or orthogonal to the sidewalls, because the full fluid equations become linear close to the boundary, thus suggesting similar trend for the experimentally observed convective rolls.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 241 , August 1992 , pp. 549 - 585
Copyright
© 1992 Cambridge University Press

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