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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.

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

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