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Some predictions from the mean-field thermosolutal equations

Published online by Cambridge University Press:  12 April 2006

N. Riahi
N. Riahi
Affiliation:
Department of Mathematics, Winthrop College, Rock Hill, South Carolina 29733
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Abstract

Nonlinear thermosolutal convection is investigated using the mean-field approximation (Herring 1963; Busse 1970). The boundary-layer method for rigid boundaries is used by assuming a large Rayleigh number R for different ranges of the diffusivity ratio τ and the solute Rayleigh number RS. The heat and solute fluxes F and FS are determined for the values of the wavenumbers αn which optimize F. The αN mode (where N denotes the total number of modes) is shown to have a solute-layer thickness of order $\tau^{\frac{1}{3}}\delta _{tN}$ (δtN denoting the temperature-layer thickness in the αN mode), and it is also proved that it is only for this mode that the solute concentration affects the boundary-layer structure. Solutions are possible if K = FSRS/FR < 1. For K ≥ 1, the stabilizing effect of solute is unimportant and there can be infinitely many modes. However, as K → 1 −, N, αn, F and FS decrease rapidly and the maximizing convection is suppressed entirely by the solute concentration. A simple interpretation of the model for the diffusive system leads also to the results for the salt-finger system.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 4 , 29 August 1978 , pp. 737 - 748
Copyright
© 1978 Cambridge University Press

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