Abstract
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).
Highlights
In atmospheric and oceanographic sciences, uid phenomena with heat transfer has been extensively studied in a large variety of contexts, see, for instance, [1,2,3,4]
The main purpose of this paper is to study the initial layer problem and the in nite Prandtl number limit of Rayleigh-Benard convection with an ill prepared initial data
The thermal convection of a uid powered by the di erence of temperature between two horizontal parallel plates, known as Rayleigh-Benard convection see [2, 4,5,6,7,8,9,10], obeys the rotating Boussinesq system:
Summary
In atmospheric and oceanographic sciences, uid phenomena with heat transfer has been extensively studied in a large variety of contexts, see, for instance, [1,2,3,4]. E ∶= ( , , ), ν is the kinematic viscosity, g is the gravity acceleration constant, α is the thermal expansion coe cient, T is the scalar temperature eld of the uid, and κ is the thermal di usion coe cient. We impose the periodic boundary conditions in the horizontal directions for simplicity. This work is licensed under the Creative Commons Attribution-. This system with rotation is a dynamic model having 3D incompressible Navier-Stokes equations via a buoyancy force proportional to temperature coupled with the heat advection-di usion of the temperature [5, 10,11,12,13].
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