Distributed chaos and isotropic turbulence

TL;DR

This paper develops an asymptotic theory to estimate the stretched exponential decay exponent in the power spectrum of isotropic turbulence, finding $eta=3/4$, and confirms this with numerical simulation data.

Contribution

The paper introduces a theoretical estimate for the spectral decay exponent in isotropic turbulence and validates it against numerical simulation data.

Findings

The spectral decay exponent $eta$ is estimated to be 3/4.

Numerical data confirms the theory for velocity, scalar, dissipation, and magnetic fields.

Isotropic turbulence emerges from distributed chaos according to the study.

Abstract

Power spectrum of the distributed chaos can be represented by a weighted superposition of the exponential functions which is converged to a stretched exponential $\propto \exp-(k/k_{\beta})^{\beta }$. An asymptotic theory has been developed in order to estimate the value of $\beta$ for the isotropic turbulence. This value has been found to be $\beta =3/4$. Excellent agreement has been established between this theory and the data of direct numerical simulations not only for the velocity field but also for the passive scalar, energy dissipation rate, and magnetic fields. One can conclude that the isotropic turbulence emerges from the distributed chaos.