Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection

Results from direct numerical simulation for three-dimensional Rayleigh-B\'enard convection in samples of aspect ratio $\Gamma=0.23$ and $\Gamma=0.5$ up to Rayleigh number $Ra=2\times10^{12}$ are presented. This includes the largest spatially resolved turbulent flow simulation ever performed in a closed system, setting a benchmark also for experiments. In addition, the broad range of Prandtl numbers $0.5<Pr<10$ is considered. We do not see any increase in $Nu/Ra^{1/3}$, neither due to $Pr$ number effects, nor due to a constant heat flux boundary condition at the bottom plate instead of constant temperature boundary conditions.