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Asymptotic theory of wall-attached convection in a rotating fluid layer

Published online by Cambridge University Press:  26 April 2006

J. Herrmann  and
F. H. Busse
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Abstract

Asymptotic expressions for the onset of convection in a horizontal fluid layer of finite extent heated from below and rotating about a vertical axis are derived in the limit of large rotation rates in the case of stress-free upper and lower boundaries. In the presence of vertical sidewalls, the critical Rayleigh number Rc is much lower than the classical value for an infinitely extended layer. In particular, we find that Rc grows in proportion to τ when the sidewall is insulating, where τ is the dimensionless rotation rate. When the sidewall is infinitely conducting, Rc grows in proportion to $\tau^{\frac{4}{3}}$ as in the case of an infinitely extended layer but with a lower coefficient of proportionality. Numerical results obtained at finite values of τ show good agreement with the asymptotic formulae.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 255 , October 1993 , pp. 183 - 194
Copyright
© 1993 Cambridge University Press

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