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An asymptotic model of two-dimensional convection in the limit of low Prandtl number

Published online by Cambridge University Press:  20 April 2006

F. H. Busse  and
R. M. Clever
F. H. Busse
Affiliation:
Institute of Geophysics and Planetary Physics and Department of Earth and Space Sciences, University of California, Los Angeles, California 90024
R. M. Clever
Affiliation:
Institute of Geophysics and Planetary Physics and Department of Earth and Space Sciences, University of California, Los Angeles, California 90024
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Abstract

An approximate solution of two-dimensional convection in the limit of low Prandtl number is presented in which the buoyancy force is balanced by the inertial terms. The results indicate that inertial convection becomes possible when the Rayleigh number exceeds a critical value of about 7 × 103. Beyond this value the velocity and temperature fields become independent of the Prandtl number except in thin boundary layers. The convective heat transport approaches the law Nu = 0·175 R¼ for the Nusselt number Nu. These results are in reasonably close agreement with the numerical results described in the preceding paper by Clever & Busse (1980).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 102 , January 1981 , pp. 75 - 83
Copyright
© 1981 Cambridge University Press

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