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The spectral dynamics of laminar convection

Published online by Cambridge University Press:  28 March 2006

George W. Platzman
George W. Platzman
Affiliation:
Department of the Geophysical Sciences, The University of Chicago
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Abstract

The non-linear equations of the Bénard convection problem are transformed to the spectral domain. The spectral basis consists of the supercritical normal modes of the characteristic-value problem in which the exponential growth rates are characteristic values. The norm of the spectrum is the variance of an arbitrary finite-amplitude state of convection. The equations that govern the spectrum are solvable by linear methods when the spectrum is truncated by exclusion of all convective modes except those of lowest-order symmetric vertical structure. Numerical computations of heat flux for a spectrum that contains only one convective mode are in good agreement with experimental data for water in the laminar régime.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 3 , November 1965 , pp. 481 - 510
Copyright
© 1965 Cambridge University Press

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