Internal heating driven convection at infinite Prandtl number

Internal heating driven convection at infinite Prandtl number

Bifurcation of Infinite Prandtl Number Rotating Convection

We consider infinite Prandtl number convection with rotation which is the basic model in geophysical fluid dynamics. For the rotation free case, the rigorous analysis has been provided by Park [15, 16, 17] under various boundary conditions. By thoroughly investigating We prove in this paper that the solutions bifurcate from the trivial solution u = 0 to an attractor ΣR which consists of only on...

Effects of vertical boundaries on infinite Prandtl number thermal convection

The physics of thermomechanical coupling of the continental lithosphere and its surrounding mantle is studied using a simple hydrodynamic model in which a fluid is heated from below and is bounded by rigid side walls. Rayleigh numbers up to 10 are considered. A series of finite-element stability analyses is employed to characterize systematically the nature of convective instability in such a s...

Infinite Prandtl Number Limit of Rayleigh-Bénard Convection

We rigorously justify the infinite Prandtl number model of convection as the limit of the Boussinesq approximation to the Rayleigh-Bénard convection as the Prandtl number approaches infinity. This is a singular limit problem involving an initial layer.

Two-Dimensional Infinite Prandtl Number Convection: Structure of Bifurcated Solutions

This paper examines the bifurcation and structure of the bifurcated solutions of the two-dimensional infinite Prandtl number convection problem. The existence of a bifurcation from the trivial solution to an attractor ΣR was proved by Park [14]. We prove in this paper that the bifurcated attractor ΣR consists of only one cycle of steady state solutions and that it is homeomorphic to S1. By thor...