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.