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Instabilities of convection rolls with stress-free boundaries near threshold

Published online by Cambridge University Press:  20 April 2006

F. H. Busse  and
E. W. Bolton
F. H. Busse
Affiliation:
Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles
E. W. Bolton
Affiliation:
Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles
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Abstract

The stability properties of steady two-dimensional solutions describing convection in a horizontal fluid layer heated from below with stress-free boundaries are investigated in the neighbourhood of the critical Rayleigh number. The region of stable convection rolls as a function of the wavenumber α and the Rayleigh number R is bounded towards higher α by the monotonic skewed varicose instability, while towards low wavenumbers stability is limited by the zigzag instability or by the oscillatory skewed varicose instability. Only for a limited range of Prandtl numbers, 0·543 < P < ∞, does a finite domain of stability exist. In particular, convection rolls with the critical wavenumber αc are always unstable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 146 , September 1984 , pp. 115 - 125
Copyright
© 1984 Cambridge University Press

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References

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