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

Abstract

The 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(ε32)$O(\varepsilon^{\frac{3}{2}})$ and O(ε2).

Keywords

• boussinesq system
• rayleigh-bénard convection
• infinite prandtl number limit
• initial layers
• asymptotic expansion
• two-time-scale approach
• 35b25
• 35b40
• 35k57