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Multimode correlations and the entropy of turbulence in shell models
Gregory Falkovich1,2, Yotam Kadish1, Natalia Vladimirova2,3
1Weizmann Institute of Science, Rehovot 76100, Israel.
Physical Review. E
|August 16, 2023
Summary
Multimode correlations offer a new lens for turbulence studies, revealing hidden states. This approach, applied to shell models, shows higher-order correlations grow with mode number, akin to entanglement entropy.
Area of Science:
- * Fluid dynamics
- * Statistical physics
Background:
- * Traditional turbulence studies often focus on single-mode statistics.
- * Understanding complex turbulent states requires analyzing interactions between multiple modes.
Purpose of the Study:
- * Introduce multimode correlations as a novel approach to characterize turbulence.
- * Investigate the behavior of these correlations in shell models near thermal equilibrium.
Main Methods:
- * Application of multimode correlation analysis to shell models of turbulence.
- * Analytical derivation and numerical confirmation of scaling laws for cumulant growth.
- * Comparison of multimode distributions to Gaussian approximations using relative entropy.
Main Results:
- * One-mode statistics approach Gaussian as mode number increases.
- * Energy flux (three-mode cumulant) remains constant.
- * Higher-order multimode cumulants exhibit growth with order, following a derived scaling law.
- * Relative entropy between full and Gaussian distributions grows logarithmically with the number of modes.
Conclusions:
- * Multimode correlations provide a new, powerful method for characterizing turbulence.
- * This approach may enable the classification of turbulent states into universality classes.
- * The findings suggest a potential link between turbulence and concepts like entanglement entropy in critical phenomena.
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