Journal of Fluid Mechanics

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

Yih-Yuh  Chen a1p1
a1 Condensed Matter Physics 114-36, California Institute of Technology. Pasadena. CA 91125, USA

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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.

(Published Online April 26 2006)
(Received January 18 1991)
(Revised January 24 1992)

p1 Present address: Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan, ROC.