The limit of the Boussinesq system of Rayleigh-Bénard convection as the Prandtl number approaches infinity

In this paper, the initial layer problem and infinite Prandtl number limit of Rayleigh-B é nard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating solution with expansions u...

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Bibliographic Details
Published in:Applied Mathematics-A Journal of Chinese Universities 2011-12, Vol.26 (4), p.493-502
Main Authors: Shi, Jian-guo, Wu, Zhong-lin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:In this paper, the initial layer problem and infinite Prandtl number limit of Rayleigh-B é nard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating solution with expansions up to any order are given and the convergence rates O ( ɛ m +1/2 ) and the optimal convergence rates O ( ɛ m +1 ) are obtained respectively. This improves the result of J.G. SHI.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-011-2207-7