Transition to the ultimate regime in a radiatively driven convection experiment

TL;DR

This study investigates the transition between standard and ultimate regimes of heat transport in radiatively driven convection, proposing a model that predicts the conditions for regime change and confirming it with experimental data.

Contribution

The paper introduces a simple model for radiatively driven convection in the mixing-length regime and validates it with experimental data, elucidating the transition between two heat transport regimes.

Findings

Identification of two distinct heat transport regimes with different scaling laws.

Validation of the model predicting the transition point between regimes.

Observation that boundary layer effects influence Prandtl number dependence at high Rayleigh numbers.

Abstract

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 $\ell$ in the vicinity of the bottom of the tank. The first regime is similar to the one observed in standard Rayleigh-B\'enard experiments, the Nusselt number $Nu$ being related to the Rayleigh number $Ra$ through the power-law $Nu \sim Ra^{1/3}$. 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 have been reported in Lepot et al. (Proc. Nat. Acad. Sci. U S A, {\bf 115}, 36, 2018), 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. \corr{It leads to the scaling relation $Nu \sim \frac{\ell}{H} Pr^{1/2} Ra^{1/2}$,} where $H$ is the height of the cell, 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 $\ell$. \corr{We conclude by showing that boundary layer corrections can persistently modify the Prandtl number dependence of $Nu$ at large $Ra$, for $Pr \gtrsim 1$.