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The oscillatory instability of convection rolls in a low Prandtl number fluid

Published online by Cambridge University Press:  29 March 2006

F. H. Busse
Affiliation:
Department of Planetary and Space Science, University of California, Los Angeles

Abstract

The instability of convection rolls in a fluid layer heated from below is investigated for stress-free boundaries in the limit of small Prandtl number. It is shown that the two-dimensional rolls become unstable to oscillatory three-dimensional disturbances when the amplitude of the convective motion exceeds a finite critical value. The instability corresponds to the generation of vertical vorticity, a mechanism which is likely to operate in the case of a variety of roll-like motions. In all aspects in which the theory can be related to experiments, reasonable agreement with the observations is found.

Type
Research Article
Copyright
© 1972 Cambridge University Press

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References

Busse, F. H. 1967 On the instability of two-dimensional convection in a layer heated from below. J. Math. Phys. 46, 140.Google Scholar
Busse, F. H. & Whitehead, J. A. 1971 Instabilities of convection rolls in a high Prandtl number fluid. J. Fluid Mech. 47, 306.Google Scholar
Davey, A, Diphima, R. C. & Stuart, J. T. 1968 On tho instability of Taylor vort.ices. J. Fluid Mech. 31, 17.Google Scholar
Krishnamurti, R. 1970 On the transition to turbulent convection. Part 2. Transition to time-dopendent flow. J. Fluid Mech. 42, 309.Google Scholar
Meyer, K. 1966 A two-dimensional time-dependent numerical study of rotational Couetto flow. Los Alamos Rep. LA-3497.
Rossby, H. T. 1969 A study of BBnlard convoction with and without rotation. J. Fluid Mech. 36, 309.Google Scholar
Schlüter, A., Lortz, D. & Busse, F. H. 1965 On tho stability of stencly finite aniplitude convection. J. Fluid Mech. 23, 129.Google Scholar
Willis, G. E. & Deardorff, J. W. 1970 The oscillatory motions of Rayleigh convcction. J. Fluid Mech. 44, 661.Google Scholar
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