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

2011 ◽  
Vol 26 (4) ◽  
pp. 493-502
Author(s):  
Jian-guo Shi ◽  
Zhong-lin Wu
Keyword(s):  
Prandtl Number ◽  
Boussinesq System ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

scholarly journals Initial layer problem of the Boussinesq system for Rayleigh-Bénard convection with infinite Prandtl number limit

2018 ◽  
Vol 16 (1) ◽  
pp. 1145-1160
Author(s):  
Xiaoting Fan ◽  
Shu Wang ◽  
Wen-Qing Xu ◽  
Mingshuo Liu
Keyword(s):  
Prandtl Number ◽  
Convergence Rates ◽  
Boussinesq System ◽  
Singular Perturbation Theory ◽  
Initial Layer ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Layer Problem

AbstractThe main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Bénard convection with an ill prepared initial data. We use the asymptotic expansion methods of singular perturbation theory and the two-time-scale approach to obtain an exact approximating solution and the convergence rates $O(\varepsilon^{\frac{3}{2}})$ and O(ε2).

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