Ultimate regime of Rayleigh-Benard turbulence: Sub-regimes and their scaling relations for Nu vs. Ra and Pr

TL;DR

This paper introduces a new model for heat transfer in the ultimate regime of Rayleigh-Benard turbulence, aligning with recent mathematical bounds and explaining experimental data across different regimes and Prandtl numbers.

Contribution

The paper presents a novel model that accurately describes heat transfer and turbulence in the ultimate regime, consistent with exact mathematical bounds and applicable to geo- and astrophysical flows.

Findings

Model distinguishes four subregimes of the ultimate regime.

Accurately describes heat transfer in large-Ra experiments.

Onset of the ultimate regime observed at different Ra in various datasets.

Abstract

We offer a new model for the heat transfer and the turbulence intensity in strongly driven Rayleigh-Benard 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 et al. [J. Differential Equations 260, 3860 (2016)] 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-Ra 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-Ra data sets, though at different Rayleigh numbers, as to be expected for a non-normal-nonlinear instability.