Critical Rayleigh number in Rayleigh-Bénard convection
Authors:
Yan Guo and Yongqian Han
Journal:
Quart. Appl. Math. 68 (2010), 149-160
MSC (2000):
Primary 35B40, 35B41, 35B45, 35Q35, 35K45, {\bf, Chinese, Library, Classification}:, O175.29
DOI:
https://doi.org/10.1090/S0033-569X-09-01179-4
Published electronically:
October 28, 2009
MathSciNet review:
2598887
Full-text PDF Free Access
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Additional Information
Abstract: The Rayleigh-Bénard convection is a classical problem in fluid dynamics. In the presence of rigid boundary condition, we identify the critical Rayleigh number $R_{a}^{\ast }$ by a reduced variational problem. We prove nonlinear asymptotic stability for motionless steady states for $R_{a}<R_{a}^{\ast },$ and their nonlinear instability for $R_{a}>R_{a}^{\ast }.$ The dynamic of such instability is determined by the leading growing mode(s) for the corresponding linearized system within the time interval of instability.
References
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Additional Information
Yan Guo
Affiliation:
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
Email:
guoy@dam.brown.edu
Yongqian Han
Affiliation:
Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, People’s Republic of China
Keywords:
Nonlinear instability,
Rayleigh-Bénard convection,
Boussinesq approximation.
Received by editor(s):
December 31, 2008
Published electronically:
October 28, 2009
Dedicated:
Dedicated to Prof. W. A. Strauss on the occasion of his 70th birthday
Article copyright:
© Copyright 2009
Brown University
The copyright for this article reverts to public domain 28 years after publication.
