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arXiv · 1210.3411

Information Content of Turbulence

Rory Cerbus·Walter Goldburg
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Abstract

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.

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Rory Cerbus, Walter Goldburg. 2013-07-03. Information Content of Turbulence. https://doi.org/10.1103/physreve.88.053012

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