Similarities between 2D and 3D convection for large Prandtl number

Thermal convection for large Prandtl numbers.

The Rayleigh-Bénard theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)] is extended towards very large Prandtl numbers Pr. The Nusselt number Nu is found here to be independent of Pr. However, for fixed Rayleigh numbers Ra a maximum in the Nu(Pr) dependence is predicted. We moreover offer the full functional dependences of Nu(Ra,Pr) and Re(Ra,Pr) within this extended theory, rather th...

Reynolds-number measurements for low-Prandtl-number turbulent convection of large-aspect-ratio samples

We present experimental results for the Reynolds number ReU based on the horizontal mean-flow velocity U and for ReV based on the root-mean-square horizontal fluctuation velocity V for turbulent Rayleigh–Bénard convection in a cylindrical sample of aspect ratio Γ = 10.9 over the Prandtl number range 0.18 6 Pr 6 0.88. The results were derived from space–time cross-correlation functions of shadow...

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...

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...

Logarithmic Bounds for In nite Prandtl Number Rotating Convection