Scaling of information in turbulence
Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS UMR 5672, Laboratoire de Physique F-69342 Lyon, France
Received: 19 July 2016
Accepted: 20 September 2016
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 fractional Brownian motion (fBM) model. We provide analytical derivations of the entropy rate scalings in these two models. 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.
PACS: 89.70.Cf – Entropy and other measures of information / 47.27.Jv – High-Reynolds-number turbulence / 89.75.Da – Systems obeying scaling laws
© EPLA, 2016