Turbulence as a problem in non-equilibrium statistical mechanics

The transitional and well-developed regimes of turbulent shear flows exhibit a variety of remarkable scaling laws that are only now beginning to be systematically studied and understood. In the first part of this article, we summarize recent progress in understanding the friction factor of turbulent...

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Bibliographic Details
Published inarXiv.org
Main Authors Goldenfeld, Nigel, Hong-Yan, Shih
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.11.2016
Subjects
Equilibrium
Extreme values
Fluid dynamics
Fluid flow
Friction factor
Percolation
Physics - Fluid Dynamics
Physics - Statistical Mechanics
Pipes
Quantitative Biology - Populations and Evolution
Reynolds number
Scaling laws
Soap films
Statistical mechanics
Turbulence
Variation
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Summary:The transitional and well-developed regimes of turbulent shear flows exhibit a variety of remarkable scaling laws that are only now beginning to be systematically studied and understood. In the first part of this article, we summarize recent progress in understanding the friction factor of turbulent flows in rough pipes and quasi-two-dimensional soap films, showing how the data obey a two-parameter scaling law known as roughness-induced criticality, and exhibit power-law scaling of friction factor with Reynolds number that depends on the precise form of the nature of the turbulent cascade. These results hint at a non-equilibrium fluctuation-dissipation relation that applies to turbulent flows. The second part of this article concerns the lifetime statistics in smooth pipes around the transition, showing how the remarkable super-exponential scaling with Reynolds number reflects deep connections between large deviation theory, extreme value statistics, directed percolation and the onset of coexistence in predator-prey ecosystems. Both these phenomena reflect the way in which turbulence can be fruitfully approached as a problem in non-equilibrium statistical mechanics.
ISSN:2331-8422
DOI:10.48550/arxiv.1611.02778