Information-theoretic characterization of turbulence intermittency

TL;DR

This paper uses information theory to analyze turbulence intermittency, revealing new scaling laws and symmetry properties that distinguish turbulence effects from purely kinematic phenomena.

Contribution

It introduces an information-theoretic framework using KL divergence and Shannon entropy to characterize turbulence intermittency and identifies critical Reynolds numbers affecting uncertainty.

Findings

Intermittency grows logarithmically with Reynolds number.

Two critical Reynolds numbers mark changes in uncertainty behavior.

Turbulence produces equal intermittency in dissipation and enstrophy.

Abstract

We present an information-theoretic characterization of small-scale intermittency in turbulent flows, that distinguishes turbulence-induced intermittency from purely kinematic effects. Kullback-Leibler (KL) divergence is used to quantify the deviation of pseudodissipation, dissipation or enstrophy of a turbulent flow field from that of a Gaussian random velocity field, serving as a comprehensive measure of the small-scale intermittency arising from turbulence dynamics. Shannon entropy is employed to evaluate the uncertainty of these small-scale quantities. Analysis of direct numerical simulation data of forced homogeneous isotropic turbulent flow across a wide range of Taylor Reynolds numbers demonstrates the existence of two critical Reynolds numbers where the variation of uncertainty changes. The study reveals a new scaling behavior and presence of a symmetry: (i) turbulence-induced intermittency grows logarithmically with Reynolds number unlike the commonly reported power-law scaling and (ii) turbulence dynamics produce equal intermittency in both dissipation rate and enstrophy, in contrast to the prevailing assumptions of asymmetry in strain-rate and vorticity dynamics.