Ultimate-state transition of turbulent Rayleigh-Benard convection

Recently Schumacher et al. [Phys. Rev. Fluids 1, 084402 (2016)] used direct numerical simulation to calculate the shear stress exerted on the top and bottom viscous boundary layers (BLs) of Rayleigh-Benard convection with a Prandtl number Pr = 0.021 and aspect ration Gamma = 1 for Rayleigh numbers Ra up to 4 x 10(8). By extrapolating their results to larger Ra, they concluded that the sample would undergo a transition to turbulent BLs and enter the ultimate state at Ra* similar or equal to 10(11) for Pr = 0.021. Here we show that their result is consistent with the experimentally determined Ra* = 2 x 10(13) for Pr = 0.82 by He et al. [ Phys. Rev. Lett. 108, 024502 (2012); New J. Phys. 17, 063028 (2015)] and the Pr dependence of Ra* predicted by Grossmann and Lohse [ Phys. Rev. E 66, 016305 (2002)]. Thus the numerical results of Schumacher et al. support the interpretation of the experimentally observed transition at Ra* = 2 x 10(13) for Pr = 0.82 as the ultimate-state transition.