A Kullback-Leibler divergence measure of intermittency: application to turbulence

TL;DR

This paper introduces a new information-theoretic measure based on Kullback-Leibler divergence to analyze intermittency and multifractality in complex systems like turbulence, providing a model-independent tool for scale-dependent analysis.

Contribution

The paper proposes a novel, simple measure using Shannon entropy and Kullback-Leibler divergence to quantify intermittency and multifractality in systems with power law behaviors.

Findings

Effective in analyzing turbulence data

Applicable to synthetic and experimental data

Provides insights into scale-dependent probability density deformation

Abstract

For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a new, and yet simple, tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the deformation of a probability density function from Gaussian at large scales to non-Gaussian at smaller scales. Our framework is based on information theory, and uses Shannon entropy and Kullback-Leibler divergence. We propose an extensive application to three-dimensional fully developed turbulence, seen here as a paradigmatic complex system where intermittency was historically defined. Moreover, the concepts of scale invariance and multifractality were extensively studied in this field and, most importantly, benchmarked. We compute our measure on experimental Eulerian velocity measurements, as well as on synthetic processes and a phenomenological model of fluid turbulence.Our approach is very general and does not require any underlying model of the system, although it can probe the relevance of such a model.