Effects of boundaries on Rayleigh-Benard convection

Citation

Chen, Yih-Yuh (1991) Effects of boundaries on Rayleigh-Benard convection. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/akka-0t17. https://resolver.caltech.edu/CaltechETD:etd-06142007-085426

Abstract

The effects of boundary conditions on the linear stability of finite cell pure fluid Rayleigh-Benard convection are investigated via a variational formalism and a perturbative approach. Some general properties of the critical Rayleigh number, Rc, with respect to change of boundary conditions or system size are derived. I argue that Rc differs from its infinite cell limit by an amount that is inversely proportional to the square of the system size, and that the fluid variables must become vanishingly small near the sidewall when compared to their bulk values, thus generalizing the known results derivable from the amplitude equation approach for a two-dimensional problem. It is also shown that the reaction-diffusion models of spatial pattern forming systems in developmental biology can be thought of as a special case of the convection problem. The similarity and major difference between the two systems are discussed. I also show that, as far as the onset stability is concerned, one can replace the sidewall of a convection cell by a mathematically simpler homogeneous boundary condition while still retaining the basic physics involved.

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