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Two-dimensional oscillatory convection in a gravitationally modulated fluid layer

Published online by Cambridge University Press:  26 April 2006

R. Clever ,
G. Schubert  and
F. H. Busse
R. Clever
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024, USA
G. Schubert
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024, USA
F. H. Busse
Affiliation:
Physikalisches Institut, Universität Bayreuth, Postfach 101251, D8580 Bayreuth, Germany
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Abstract

A Galerkin method is used to study the two-dimensional modes of oscillatory convection in a gravitationally modulated fluid layer with rigid, isothermal boundaries heated either from below or from above. Nonlinear solutions are obtained for dimensionless frequencies ω (frequency is made non-dimensional with the timescale d2/κ where d is the depth of the fluid layer and κ is the thermal diffusivity) in the range 100–3000, dimensionless accelerations ε (εg is the amplitude of the externally imposed oscillatory vertical acceleration and g is the constant vertical acceleration of gravity) in the range of 1–104, and Prandtl numbers P in the range 0.71 (air) to 7 (water). The problem of convective onset is explored for a broader range of parameters than heretofore considered, including Prandtl numbers between 0.71 and 50. Both synchronous and subharmonic modes of convection are identified and it is found that finite-amplitude synchronous convection can be unstable to subharmonic modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 253 , August 1993 , pp. 663 - 680
Copyright
© 1993 Cambridge University Press

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