Strong turbulent convection: distributed chaos and large-scale circulation

TL;DR

This paper investigates two types of spontaneous symmetry breaking in turbulent thermal convection at high Rayleigh numbers, linking boundary effects and inertial range development to specific spectral behaviors and large-scale circulation dynamics.

Contribution

It identifies distinct spectral signatures associated with boundary effects and inertial range emergence in turbulent convection, connecting them to large-scale circulation phenomena.

Findings

Spectral forms characterized by stretched exponentials with specific beta values.

Good agreement with experimental data at high Rayleigh numbers.

Large-scale circulation frequency related to spectral parameters.

Abstract

Two types of spontaneous breaking of the space translational symmetry in distributed chaos have been considered for turbulent thermal convection at large values of Rayleigh number. First type is related to boundaries and second type is related to appearance of inertial range of scales. The first type is dominated by vorticity correlation integral: $\int_{V} \langle {\boldsymbol \omega} ({\bf x},t) \cdot {\boldsymbol \omega} ({\bf x} + {\bf r},t) \rangle_{V} d{\bf r}$ and is characterized by stretched exponential spectrum $\exp-(k/k_{\beta})^{\beta }$ with $\beta =1/2$. The second type is dominated by energy correlation integral: $\int_{V} \langle {\bf u}^2 ({\bf x},t) ~ {\bf u}^2({\bf x} + {\bf r},t) \rangle_{V} d{\bf r}$ and is characterized by $\beta =3/5$. Good agreement has been established with laboratory experimental data obtained at large values of Rayleigh number $Ra \sim 10^{11}-10^{14}$ (the range relevant to solar photosphere) in upright cylinder cells. Taylor hypothesis transforms the wavenumber spectrum into frequency spectrum $\exp-(f/f_{\beta})^{1/2}$. It is shown that turnover frequency of large-scale circulation (wind): $f_w = f_{\beta}/2$. Results of an experiment in horizontal cylinder are also briefly discussed. The analysis suggests that in this case the large-scale circulation can be considered as a natural (harmonic) part of the distributed chaos.