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The three-dimensional stability of finite-amplitude convection in a layered porous medium heated from below

Published online by Cambridge University Press:  26 April 2006

D. A. S. Rees  and
D. S. Riley
D. A. S. Rees
Affiliation:
School of Mathematics, University Walk, Bristol BS8 1TW, UK Present address: Mathematics Department, North Park Road, Exeter EX4 4QE, UK.
D. S. Riley
Affiliation:
School of Mathematics, University Walk, Bristol BS8 1TW, UK
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Abstract

Landau–Ginzburg equations are derived and used to study the three-dimensional stability of convection in a layered porous medium of infinite horizontal extent. Criteria for the stability of convection with banded or square planform are determined and results are presented for two-layer and symmetric three-layer systems. In general the neutral curve is uni-modal and parameter space is divided into regions where either rolls or square cells are stable. For certain ranges of parameters, however, the neutral curve is bimodal and there exists a locus of parameters where two modes with different wavenumbers have simultaneous onset.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 211 , February 1990 , pp. 437 - 461
Copyright
© 1990 Cambridge University Press

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