All Physics Faculty Publications

Document Type

Article

Journal/Book Title/Conference

Physics of Fluids

Volume

27

Issue

12

Publisher

American Institute of Physics

Publication Date

7-1984

First Page

2795

Last Page

2802

DOI

10.1063/1.864594

Abstract

Rayleigh–Bénard convection in a laterally unbounded classical fluid layer with low Prandtl number P (ratio of kinematic viscosity to thermal diffusivity) is reexamined. An amplitude expansion with only a few normal modes yields lateral oscillations of the convective rolls, which are therefore only weakly nonlinear. For free boundary conditions, additional modes (absent for rigid boundaries) lead to long wavelength (‘‘hydrodynamic’’) oscillations, with explicit nonlinear distortions in the velocity and temperature fields. For oscillations with rigid boundaries, the finite critical wavenumbers are approximately independent of P for small P, and the calculated Rayleigh number, frequency, and wavenumber at onset agree well with observations in air. Discrepancies with experiments in dilute superfluid 3He–4He systems with small aspect ratios (ratio of horizontal to vertical dimensions) suggest that lateral boundaries or two‐fluid effects play an important role in these systems.

Comments

Published by the American Institute of Physics in Physics of Fluids.

http://link.aip.org/link/doi/10.1063/1.864594

Publisher PDF is available for download through the link above.

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