Scaling of Information in Turbulence

TL;DR

This paper introduces an information-theoretic approach to analyze turbulence by computing the entropy rate of velocity signals across scales, revealing insights into energy transfer and cascade mechanisms.

Contribution

It presents a novel application of entropy rate analysis to turbulence, enabling the identification of different flow regimes and asymmetries in energy transfer.

Findings

Entropy rate describes information distribution across scales.

Method aligns with Batchelor and fractional Brownian motion models.

Conditioning procedure reveals asymmetries in energy cascade.

Abstract

We propose a new perspective on Turbulence using Information Theory. We compute the entropy rate of a turbulent velocity signal and we particularly focus on its dependence on the scale. We first report how the entropy rate is able to describe the distribution of information amongst scales, and how one can use it to isolate the injection, inertial and dissipative ranges, in perfect agreement with the Batchelor model and with a fBM model. In a second stage, we design a conditioning procedure in order to finely probe the asymmetries in the statistics that are responsible for the energy cascade. Our approach is very generic and can be applied to any multiscale complex system.