Nonlinear hydromagnetic convection in a moderate prandtl number fluid

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...

Prandtl number dependence of unsteady natural convection along a vertical plate in a stably stratified fluid

The Prandtl number dependence of unsteady laminar natural convection along an infinite vertical plate in a thermally stratified fluid is investigated. Flows are induced by an impulsive (step) change in plate temperature and by a suddenly imposed plate heat flux. Analytical solutions of the viscous equations of motion and thermodynamic energy are obtained for Prandtl numbers near unity by the me...

Onset of zero Prandtl number convection

The transition to convection in a zero Prandtl number fluid with stress-free and perfectly conducting boundaries differs significantly from finite Prandtl number convection, giving rise to a three-dimensional pattern. Two possible scenarios are described and compared with recent numerical simulations by Thual Ii]. The Prandtl number of a fluid can approach zero in one of two ways either because...

Turbulent Rayleigh–Bénard convection for a Prandtl number of 0.67

For the Rayleigh-number range 10 Ra 10 we report measurements of the Nusselt number Nu and of properties of the large-scale circulation (LSC) for cylindrical samples of helium gas (Prandtl number Pr=0.674) that have aspect ratio Γ ≡D/L=0.50 (D and L are the diameter and the height respectively) and are heated from below. The results for Nu are consistent with recent direct numerical simulations...

Logarithmic Bounds for In nite Prandtl Number Rotating Convection