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The effect of viscous dissipation on non-linear convection at high Rayleigh number

Published online by Cambridge University Press:  17 February 2009

R. Van der Borght
R. Van der Borght
Affiliation:
Department of Mathematics, Monash University, Clayton, Vic., 3168, Australia.
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Abstract

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When studying deep convection in a compressible medium the effects of viscous dissipation can become important and must be taken into account in any realistic model. But even in shallow convection, for which the Boussinesq approximation is valid, the viscous dissipation effects will become important at high Rayleigh numbers. These effects are estimated with the help of asymptotic methods and the results are compared with those obtained by numerical integration.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 2 , December 1975 , pp. 165 - 172
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Hewitt, J. M., McKenzie, D. P. and Weiss, N. O., ‘Dissipative heating in convective flows’, J. Fluid Mech. 68 (1975), 721.CrossRefGoogle Scholar
[2]Howard, L. N., ‘Notes from summer program in geophysical fluid dynamics’, Woodshole Oceanographic Inst., 65–51, Vol. 1 (1965), 125.Google Scholar
[3]Ledoux, P., Schwarzchild, M. and Spiegel, E. A., ‘On the spectrum of turbulent convection’, Ap. J. 133 (1961), 184.CrossRefGoogle Scholar
[4]Turcotte, D. L., Hsui, A. T., Torrance, K. E. and Schubert, G., ‘Influence of viscous dissipation on Bénard convection’, J. Fluid Mech. 64 (1974), 369.CrossRefGoogle Scholar
[5]Van der Borght, R., ‘Finite amplitude convection in a compressible medium’, Publ. Astr. Soc. Japan 23 (1971), 539.Google Scholar
[6]Van der Borght, R. and Murphy, J. O., ‘The combined effect of rotation and magnetic field on finite amplitude thermal convection’, Austr. J. Phys. 26 (1973), 617.CrossRefGoogle Scholar
[7]Van der Borght, R., ‘Finite amplitude Convection in a compressible layer with polytropic structure’, Austr. J. Phys. 28 (1975), 437.CrossRefGoogle Scholar
[8]Waters, B. E., Ph.D. Thesis, Monash University (1971).Google Scholar