Hostname: page-component-6587cd75c8-ptrpl Total loading time: 0 Render date: 2025-04-23T17:37:37.373Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  29 March 2006

F. H. Busse
F. H. Busse
Affiliation:
Department of Planetary and Space Science, University of California, Los Angeles
Get access Rights & Permissions [Opens in a new window]

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
Information
Journal of Fluid Mechanics , Volume 52 , Issue 1 , 14 March 1972 , pp. 97 - 112
Copyright
© 1972 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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