In this talk, Dr. Zhu will present "the newest results" on fully developed Rayleigh-Bénard turbulence. For the first time in numerical simulations we find the transition to the ultimate regime, namely at Ra*= 10^13. We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling. Beyond the transition, the temperature profiles are only locally logarithmic, namely within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling exponent of 0.38 with respect to Ra, corresponding to the effective scaling in the ultimate regime.

Furthermore, we analyse the local scaling properties of the lateral temperature structure functions in the boundary layers (BL), employing extended self-similarity (ESS) (i.e., plotting the structure functions against each other, rather than only against the scale) in the spirit of the attached eddy hypothesis. We find no ESS scaling below the transition and in the near wall region. However, beyond the transition and for large enough wall distance, we find clear ESS behaviour, as expected for a scalar in a turbulent boundary layer. In striking correspondence to the Nu scaling, the ESS scaling region is negligible at Ra = 10^11 and well developed at Ra = 10^14 , thus providing strong evidence that the observed transition in the global Nusselt number at Ra*= 10^13 indeed is the transition from a laminar type BL to a turbulent type BL.