Comparison between two and three dimensional Rayleigh-B\'enard convection

TL;DR

This paper compares 2D and 3D Rayleigh-Bénard convection using simulations and experiments, revealing similarities in Nu(Ra) at high Prandtl numbers and notable differences at lower Pr, especially around Pr=1.

Contribution

It provides a comprehensive comparison of 2D and 3D Rayleigh-Bénard convection, highlighting where their behaviors align and diverge across different parameters.

Findings

Nu(Ra) scaling is similar in 2D and 3D at high Pr, differing only by a constant factor.

Large differences in Nu(Ra) occur at low Pr due to roll state dependence.

Reynolds numbers are higher in 2D and converge at large Pr.

Abstract

Two dimensional (2D) and three dimensional (3D) Rayleigh-B\'enard convection is compared using results from direct numerical simulations and prior experiments. The explored phase diagrams for both cases are reviewed. The differences and similarities between 2D and 3D are studied using Nu(Ra) for Pr = 4.38 and Pr = 0.7 and Nu(Pr) for Ra up to $10^8$. In the Nu(Ra) scaling at higher Pr, 2D and 3D are very similar; differing only by a constant factor up to $\text{Ra} = 10^{10}$. In contrast, the difference is large at lower Pr, due to the strong roll state dependence of Nu in 2D. The behaviour of Nu(Pr) is similar in 2D and 3D at large Pr. However, it differs significantly around Pr = 1. The Reynolds number values are consistently higher in 2D and additionally converge at large Pr. Finally, the thermal boundary layer profiles are compared in 2D and 3D.