Transition to the ultimate regime in a radiatively driven convection experiment

We report on the transition between two regimes of heat transport in a radiatively driven convection experiment, where a fluid gets heated up within a tunable heating length in the vicinity of the bottom of the tank. The first regime is similar to that observed in standard Rayleigh–Bénard experiments, the Nusselt number $Nu$ being related to the Rayleigh number $Ra$ through the power law Nu~ Ra1/3 . The second regime corresponds to the ‘ultimate’ or mixing-length scaling regime of thermal convection, where $Nu$ varies as the square root of $Ra$ . Evidence for these two scaling regimes has been reported in Lepot et al. ( Proc. Natl Acad. Sci. USA , vol. 115, 2018, pp. 8937–8941), and we now study in detail how the system transitions from one to the other. We propose a simple model describing radiatively driven convection in the mixing-length regime. It leads to the scaling relation Nu~ ( /H)Pr1/2Ra1/2 , where H is the height of the cell and $Pr$ is the Prandtl number, thereby allowing us to deduce the values of $Ra$ and $Nu$ at which the system transitions from one regime to the other. These predictions are confirmed by the experimental data gathered at various $Ra$ and . We conclude by showing that boundary layer corrections can persistently modify the Prandtl number dependence of $Nu$ at large $Ra$ , for Pr 1 .