Information Content of Turbulence

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.

arXiv comment8 pages, 9 figures

References in corpus (7)

• Particles and fields in fluid turbulence
• Entropy estimation of symbol sequences
• Time's Barbed Arrow: Irreversibility, Crypticity, and Stored Information
• Statistical Complexity of Simple 1D Spin Systems
• Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy
• Experimental study of Taylor's hypothesis in a turbulent soap film
• Measuring complexity with zippers

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• Using Kernel-Based Statistical Distance to Study the Dynamics of Charged Particle Beams in Particle-Based Simulation Codes
• Turbulence as Information