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Updated: May 4, 2026
10:53
Simultaneous Measurement of Turbulence and Particle Kinematics Using Flow Imaging Techniques
Published on: March 12, 2019
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Information content of turbulence.
1Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15221, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2013
Summary
Turbulent velocity fields are analyzed as messages using Shannon
Area of Science:
- Fluid dynamics
- Information theory
- Statistical mechanics
Background:
- Turbulent flows involve complex dynamics across multiple scales.
- Shannon's information theory provides a framework for quantifying message complexity.
- The relationship between turbulence and information entropy is not fully understood.
Purpose of the Study:
- To investigate turbulent velocity fields as information-theoretic messages.
- To explore the relationship between spatial entropy density and Reynolds number in turbulent flows.
- To analyze the behavior of entropy in dynamical systems like the logistic map.
Main Methods:
- Treating turbulent velocity fields as messages.
- Applying Shannon's entropy per symbol (h) for quantification.
- Analyzing experimental data from turbulent soap films.
- Investigating the logistic map and a modified, coupled version.
Main Results:
- Spatial entropy density (h) in turbulent soap films decreases with increasing Reynolds number (Re).
- The relationship observed is h proportional to -logRe + const.
- In the logistic map, entropy (h) increases with the control parameter (r).
- Correlations significantly impact entropy in the modified logistic map.
Conclusions:
- Turbulent velocity fields can be effectively characterized using information entropy.
- Entropy density is a decreasing function of Reynolds number in turbulent flows.
- Correlations play a crucial role in the information content of dynamical systems.
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