Predicting two-dimensional turbulence

Abstract

Prediction is a fundamental objective of science. It is more difficult for chaotic and complex systems like turbulence. Here we use information theory to quantify spatial prediction using experimental data from a turbulent soap film. At high Reynolds number, Re, where a cascade exists, turbulence becomes easier to predict as the inertial range broadens. The development of a cascade at low Re is also detected.

The first-digit frequencies in data of turbulent flows

“…Moreover, this information entropy can also be seen as a numerical measure which describes how informative a particular probability distribution is, ranging from zero (completely uninformative) to H max = log 10 9 ≈ 0.9542 (completely informative). With this point of view, the conclusion above is consistent with results presented by Cerbus and Goldburg [20,21]. Cerbus and Goldburg observed, from experiments in a turbulent soap film, that turbulence is easier to predict where a cascade exists, or equivalently, for flows with a significant inertial range.…”

Multiscale Sample Entropy of Two-Dimensional Decaying Turbulence

“…Inspired by the advancement of information theory, there have been efforts to shed new light on turbulence by considering it as a flow of information. There was a paucity of studies under this paradigm, with a notable exception by Aubry et al [5] Later additions include investigations by Kim [6] and Cerbus and Goldburg [7,8] addressing the properties of turbulence as a set of information. In recent years, "data science" is considered as an independent discipline, and there is an increasing number of studies that treat fluid motion as data flow [9,10].…”