Turbulence and distributed chaos with spontaneously broken symmetry

TL;DR

This paper demonstrates that turbulent flows with spontaneously broken translational symmetry exhibit a specific stretched exponential energy spectrum, supported by simulations, experiments, and astrophysical data analysis.

Contribution

It introduces a theoretical model predicting a stretched exponential spectrum with 2 exponent in broken-symmetry turbulence, validated by diverse data sets.

Findings

Spectrum follows 2 stretched exponential form

Good agreement between theory and simulation/experimental data

Application to galaxy distribution aligns with SDSS-III observations

Abstract

It is shown that in turbulent flows the distributed chaos with spontaneously broken translational space symmetry (homogeneity) has a stretched exponential spectrum $\exp-(k/k_{\beta})^{\beta }$ with $\beta =1/2$. Good agreement has been established between the theory and the data of direct numerical simulations of isotropic homogeneous turbulence (energy dissipation rate field), of a channel flow (velocity field), of a fully developed boundary layer flow (velocity field), and the experimental data at the plasma edges of different fusion devices (stellarators and tokamaks). An astrophysical application to the large-scale galaxies distribution has been briefly discussed and good agreement with the data of recent Sloan Digital Sky Survey SDSS-III has been established.