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Nonlinear transition in three-dimensional convection

Published online by Cambridge University Press:  21 April 2006

R. Kessler
R. Kessler
Affiliation:
Institute for Theoretical Fluid Mechanics, DFVLR, Bunsenstrasse 10, D-3400 Göttingen, West Germany Present address: Lehrstuhl für Strömungsmechanik, Universität Erlangen, Egerlandstrasse 13, D-8520 Erlangen, West Germany.
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Abstract

Steady and oscillatory convection in a rectangular box heated from below are studied by means of a numerical solution of the three-dimensional, time-dependent Boussinesq equations. The effect of the rigid sidewalls of the box on the spatial structure and the dynamical behaviour of the flow is analysed. Both conducting and adiabatic sidewalls are considered. Calculated streamlines illustrate the three-dimensional structure of the steady flow with Prandtl numbers 0.71 and 7. The onset and the frequency of the oscillatory instability are calculated and compared with available experimental and theoretical data. With increasing Rayleigh number a subharmonic bifurcation and the onset of a quasi-periodic flow can be observed. A comparison of the different time-dependent solutions shows some interesting relations between the spatial structure and the dynamical behaviour of the confined flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 174 , January 1987 , pp. 357 - 379
Copyright
© 1987 Cambridge University Press

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