Journal of Fluid Mechanics



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


F. H.  Busse a1 and R. M.  Clever a1
a1 Institute of Geophysics and Planetary Physics and Department of Earth and Space Sciences, University of California, Los Angeles, California 90024

Article author query
busse fh   [Google Scholar] 
clever rm   [Google Scholar] 
 

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).

(Published Online April 20 2006)
(Received November 5 1979)
(Revised March 5 1980)



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