Comparison between two- and three-dimensional Rayleigh-Bénard convection

Two-dimensional and three-dimensional Rayleigh–Bénard convection is compared using results from direct numerical simulations and previous experiments. The phase diagrams for both cases are reviewed. The differences and similarities between two- and three-dimensional convection are studied using Nu(Ra) for Pr=4.38 and Pr=0.7 and Nu(Pr) for Ra up to 108. In the Nu(Ra) scaling at higher Pr, two- and three-dimensional convection is very similar, differing only by a constant factor up to Ra=1010. In contrast, the difference is large at lower Pr, due to the strong roll state dependence of Nu in two dimensions. The behaviour of Nu(Pr) is similar in two and three dimensions at large Pr. However, it differs significantly around Pr=1. The Reynolds number values are consistently higher in two dimensions and additionally converge at large Pr. Finally, the thermal boundary layer profiles are compared in two and three dimensions