Journal of Fluid Mechanics

Transition to time-dependent convection

R. M.  Clever a1 and F. H.  Busse a2
a1 Science Applications, Inc., El Segundo, California 90245
a2 Department of Planetary and Space Sciences, University of California, Los Angeles

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


Steady solutions in the form of two-dimensional rolls are obtained for convection in a horizontal layer of fluid heated from below as a function of the Rayleigh and Prandtl numbers. Rigid boundaries of infinite heat conductivity are assumed. The stability of the two-dimensional rolls with respect to three-dimensional disturbances is analysed. It is found that convection rolls are unstable for Prandtl numbers less than about 5 with respect to an oscillatory instability investigated earlier by Busse (1972) for the case of free boundaries. Since the instability is caused by the momentum advection terms in the equations of motion the Rayleigh number for the onset of instability increases strongly with Prandtl number. Good agreement with various experimental observations is found.

(Published Online March 29 2006)
(Received December 20 1973)