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Stability of convection rolls in a layer with stress-free boundaries

Published online by Cambridge University Press:  20 April 2006

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

Steady finite-amplitude solutions for two-dimensional convection in a layer heated from below with stress-free boundaries are obtained numerically by a Galerkin method. The stability of the steady convection rolls with respect to arbitrary three-dimensional infinitesimal disturbances is investigated. Stability is found only in a small fraction of the Rayleigh-number-wavenumber space where steady solutions exist. The cross-roll instability and the oscillatory and monotonic skewed varicose instabilities are most important in limiting the stability of steady convection rolls. The Prandtlnumbers P = 0.71, 7, 104 areemphasized, but the stability boundaries are sufficiently smoothly dependent on the parameters of the problem to permit qualitative extrapolations to other Prandtl numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 150 , January 1985 , pp. 487 - 498
Copyright
© 1985 Cambridge University Press

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