Ultimate Regime of Rayleigh-Bénard Turbulence: Subregimes and Their Scaling Relations for the Nusselt vs Rayleigh and Prandtl Numbers.

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We offer a new model for the heat transfer and the turbulence intensity in strongly driven Rayleigh-Bénard turbulence (the so-called ultimate regime), which in contrast to hitherto models is consistent with the new mathematically exact heat transfer upper bound of Choffrut etal. [Upper bounds on Nusselt number at finite Prandtl number, J. Differ. Equations 260, 3860 (2016).JDEQAK0022-039610.1016/j.jde.2015.10.051] and thus enables extrapolations of the heat transfer to geo- and astrophysical flows. The model distinguishes between four subregimes of the ultimate regime and well describes the measured heat transfer in various large-Rayleigh experiments. In this new representation, which properly accounts for the Prandtl number dependence, the onset to the ultimate regime is seen in all available large-Rayleigh datasets, though at different Rayleigh numbers, as to be expected for a non-normal-nonlinear instability.