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Finite bandwidth, finite amplitude convection

Published online by Cambridge University Press:  29 March 2006

Alan C. Newell  and
J. A. Whitehead
Alan C. Newell
Affiliation:
Department of Planetary and Space Science, Department of Mathematics
J. A. Whitehead
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles
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Abstract

The main purpose of this work is to show how a continuous finite bandwidth of modes can be readily incorporated into the description of post-critical Rayleigh-Bénard convection by the use of slowly varying (in space and time) amplitudes. Previous attempts have used a multimodal discrete analysis. We show that in addition to obtaining results consistent with the discrete mode approach, there is a larger class of stable and realizable solutions. The main feature of these solutions is that the amplitude and wave-number of the motion is that of the most unstable mode almost everywhere, but, depending on external and initial conditions, the roll couplets in different parts of space may be 180° out of phase. The resulting discontinuities are smoothed by hyperbolic tangent functions. In addition, it is clear that the mechanism for propagating spatial nonuniformities is diffusive in character.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 2 , 3 September 1969 , pp. 279 - 303
Copyright
© 1969 Cambridge University Press

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