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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.

Information

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

Bolton, E. W. & Busse, F. H. 1984 Stability of convection rolls in a layer with stress-free boundaries. (Submitted to J. Fluid Mech.)Google Scholar
Busse, F. H. 1971 Stability regions of cellular fluid flow. In Instability of Continuous Systems (ed. H. Leipholz), pp. 41–47. Springer.
Busse, F. H. 1972 The oscillatory instability of convection rolls in a low Prandtl number fluid. J. Fluid Mech. 52, 97–112.Google Scholar
Busse, F. H. & Clever, R. M. 1979 Instabilities of convection rolls in a fluid of moderate Prandtl number. J. Fluid Mech. 91, 319–335.Google Scholar
Clever, R. M. & Busse, F. H. 1974 Transition to time-dependent convection. J. Fluid Mech. 65, 625–645.Google Scholar
Goldstein, R. J. & Graham, D. J. 1969 Stability of a horizontal fluid layer with zero shear boundaries. Phys. Fluids 12, 1133–1137.Google Scholar
Gollub, J. P., McCarriar, A. R. & Steinman, J. F. 1982 Convective pattern evolution and secondary instabilities. J. Fluid Mech. 125, 259–281.Google Scholar
Schlüter, A., Lortz, D. & Busse, F. 1965 On the stability of steady finite amplitude convection. J. Fluid Mech. 23, 129–144.Google Scholar
Siggia, E. D. & Zippelius, A. 1981 Pattern selection in Rayleigh-Bénard convection near threshold. Phys. Rev. Lett. 47, 835–838.Google Scholar
Zippelius, A. & Siggia, E. D. 1982 Disappearance of stable convective between free-slip boundaries. Phys. Rev. A 26, 1788–1790.Google Scholar
Zippelius, A. & Siggia, E. D. 1983 Stability of finite-amplitude convection. Phys. Fluids 26, 2905–2915.Google Scholar