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Zero-Prandtl-number convection

Published online by Cambridge University Press:  26 April 2006

Olivier Thual
Olivier Thual
Affiliation:
National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307, USA Present address: CERFACS, 42 Av. Coriolis, 31057 Toulouse Cedex, France.
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Abstract

The zero-Prandtl-number limit of the Oberbeck—Boussinesq equations is compared to small-Prandtl-number Rayleigh—Bénard convection through numerical simulations. Both no-slip and free-slip boundary conditions, imposed at the top and bottom of a small-aspect-ratio, horizontally periodic box are considered. A rich variety of regimes is observed as the Rayleigh number is increased: supercritical oscillatory instabilities for various values of the aspect ratios, competition between two-dimensional rolls, squares and hexagonal patterns, competition between travelling and standing waves, transition to chaos, and scalings laws for the first Rayleigh-number decade. This multiplicity of regimes can be attributed to the close interaction between the stationary and oscillatory instabilities at zero Prandtl number.

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Type
Research Article
Information
Journal of Fluid Mechanics , Volume 240 , July 1992 , pp. 229 - 258
Copyright
© 1992 Cambridge University Press

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