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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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References

Busse, F. H. 1969 J. Fluid Mech. 37, 457.
Busse, F. H. 1970 Max-Planck-Inst. Phys. Astrophys. Rep. MPI-PAE/Astro 31.
Busse, F. H. & Joseph, D. D. 1972 J. Fluid Mech. 54, 521.
Chan, S. K. 1971 Stud. Appl. Math. 50, 13.
Chan, S. K. 1974 J. Fluid Mech. 64, 477.
Degens, E. T. & Ross, D. A. (eds.) 1969 Hot Brines and Recent Heavy Metal Deposits in the Red Sea. Springer.
Gupta, V. P. & Joseph, D. D. 1973 J. Fluid Mech. 57, 491.
Herring, J. R. 1963 J. Atmos. Sci. 20, 325.
Howard, L. N. 1963 J. Fluid Mech. 17, 405.
Lindberg, W. R. 1971 J. Phys. Ocean. 1, 187.
Malkus, W. V. R. 1954 Proc. Roy. Soc. A 225, 196.
Neal, V. T., Neshyba, S. & Denner, W. 1969 Science 166, 373.
Neshyba, S., Neal, V. T. & Denner, W. 1971 J. Geophys. Res. 76, 8117.
Riahi, N. 1977 J. Fluid Mech. 81, 523.
Straus, J. 1972 J. Fluid Mech. 56, 353.
Straus, J. 1974 Phys. Fluids 17, 520.
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Turner, J. S. 1974 Ann. Rev. Fluid Mech. 6, 37.
Veronis, G. 1965 J. Mar. Res. 23, 1.
Veronis, G. 1968 J. Fluid Mech. 34, 315.