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Square-pattern convection in fluids with strongly temperature-dependent viscosity

Published online by Cambridge University Press:  20 April 2006

F. H. Busse  and
H. Frick
F. H. Busse
Affiliation:
Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90024
H. Frick
Affiliation:
Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90024
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Abstract

Three-dimensional numerical solutions are obtained describing convection with a square lattice in a layer heated from below with no-slip top and bottom boundaries. The limit of infinite Prandtl number and a linear dependence of the viscosity on temperature are assumed. The stability of the three-dimensional solutions with respect to disturbances fitting the square lattice is analysed. It is shown that convection in the form of two-dimensional rolls is stable for low variations of viscosity, while square-pattern convection becomes stable when the viscosity contrast between upper and lower parts of the fluid layer is sufficiently strong. The theoretical results are in qualitative agreement with experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 150 , January 1985 , pp. 451 - 465
Copyright
© 1985 Cambridge University Press

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