Chaos from turbulence: stochastic-chaotic equilibrium in turbulent convection at high Rayleigh numbers

TL;DR

The paper demonstrates that in high Rayleigh number turbulent convection, the mean wind exhibits chaotic behavior with long correlation times, indicating a stochastic-chaotic equilibrium in the system.

Contribution

It introduces an analysis of the chaotic and stochastic components in turbulent convection at high Rayleigh numbers, revealing their equilibrium state.

Findings

Exponential decay of correlation function with long correlation time.

Positive Lyapunov exponent indicating chaos.

Identification of stochastic-chaotic equilibrium in mean wind fluctuations.

Abstract

It is shown that correlation function of the mean wind velocity generated by a turbulent thermal convection (Rayleigh number $Ra \sim 10^{11}$) exhibits exponential decay with a very long correlation time, while corresponding largest Lyapunov exponent is certainly positive. These results together with the reconstructed phase portrait indicate presence of chaotic component in the examined mean wind. Telegraph approximation is also used to study relative contribution of the chaotic and stochastic components to the mean wind fluctuations and an equilibrium between these components has been studied in detail.