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Energy flux and high-order statistics of hydrodynamic turbulence

Published online by Cambridge University Press:  15 November 2023

Yuri V. Lvov Open the ORCID record for Yuri V. Lvov [Opens in a new window]  and
Victor S. L'vov
Yuri V. Lvov*
Affiliation:
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Victor S. L'vov
Affiliation:
Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel
*
†Email address for correspondence: lvovy@rpi.edu
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Abstract

We use the Dyson–Wyld diagrammatic technique to analyse the infinite series for the correlation functions of the velocity in hydrodynamic turbulence. We demonstrate the fundamental role played by the triple correlator of the velocity in determining the entire statistics of the hydrodynamic turbulence. All higher-order correlation functions are expressed through the triple correlator. This is shown through the suggested triangular re-summation of the infinite diagrammatic series for multi-point correlation functions. The triangular re-summation is the next logical step after the Dyson–Wyld line re-summation for the Green's function and the double correlator. In particular, it allows us to explain why the inverse cascade of the two-dimensional hydrodynamic turbulence is close to Gaussian. Since the triple correlator dictates the flux of energy $\varepsilon$ through the scales, we support the Kolmogorov-1941 idea that $\varepsilon$ is one of the main characteristics of hydrodynamic turbulence.

JFM classification

Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 975 , 25 November 2023 , A17
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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