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

Results from direct numerical simulation for three-dimensional Rayleigh Benard convection in samples of aspect ratio Gamma = 0.23 and Gamma = 1/2 up to Rayleigh number Ra = 2 x 10(12) are presented. The broad range of Prandtl numbers 0.5 < Pr < 10 is considered. In contrast to some experiments, we do not see any increase in Nu/Ra-1/3 with increasing Ra, neither due to an increasing Pr, nor due to constant heat flux boundary conditions at the bottom plate instead of constant temperature boundary conditions. Even at these very high Ra, both the thermal and kinetic boundary layer thicknesses obey Prandtl Blasius scaling.