Distributed chaos and Rayleigh-Benard turbulence at very high Ra

TL;DR

This paper investigates the transition in Rayleigh-Bénard turbulence at extremely high Rayleigh numbers, revealing a symmetry-breaking process that alters the temperature spectrum, with implications similar to polymer additive effects.

Contribution

It introduces a novel analysis of turbulence transition at very high Ra using distributed chaos, highlighting spontaneous symmetry breaking and spectral changes.

Findings

Transition occurs at Ra > 10^{14} with symmetry breaking.

Temperature spectrum exhibits a stretched exponential form with β=2/5.

Helicity and Lagrangian relabeling symmetry are central to the transition.

Abstract

It is shown, by the means of distributed chaos approach and using the experimental data, that at very large Rayleigh number $Ra > 10^{14}$ and Prandtl number $Pr \sim 1$ the Rayleigh-B\'{e}nard turbulence can undergo a transition related to spontaneous breaking of the fundamental Lagrangian relabeling symmetry. Due to the Noether's theorem helicity plays central role in this process. After the transition the temperature spectrum has a stretched exponential form $E (k) \propto \exp(-k/k_{\beta})^{\beta}$ with $\beta =2/5$ both at the cell midplain and at the near-wall (low boundary) regions. There is a similarity between this phenomenon and the effects of polymer additives.