Rory Cerbus | Searcharxiv

arXiv2014

Predicting 2D Turbulence

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 is becoming easier to predict as the inertial range broadens. A transition corresponding to the emergence of a cascade at low $Re$ is detected by looking at turbulence through prediction.

physics.flu-dyn↗

arXiv2013

Information Content of Turbulence

We treat a turbulent velocity field as a message in the same way as a book or a picture. All messages can be described by their entropy per symbol $h$, defined as in Shannon's theory of communication. In a turbulent flow, as the Reynolds number $Re$ increases, more correlated degrees of freedom are excited and participate in the turbulent cascade. Experiments in a turbulent soap film suggest that the spatial entropy density $h$ is a decreasing function of $Re$, namely $h \propto -\log Re$ + const. In the logistic map, also analyzed here, increasing the control parameter $r$ increases $h$. A modified logistic map with additional coupling to past iterations suggests the significance of correlations.

nlin.CD↗