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Statistical mechanics of the Euler equations without vortex stretching

Published online by Cambridge University Press:  19 October 2021

Tong Wu Open the ORCID record for Tong Wu [Opens in a new window]  and
Wouter J.T. Bos Open the ORCID record for Wouter J.T. Bos [Opens in a new window]
Tong Wu
Affiliation:
Univ. Lyon, CNRS, Ecole Centrale de Lyon, INSA Lyon, Univ. Claude Bernard Lyon 1, LMFA, UMR5509, 69340 Ecully, France
Wouter J.T. Bos*
Affiliation:
Univ. Lyon, CNRS, Ecole Centrale de Lyon, INSA Lyon, Univ. Claude Bernard Lyon 1, LMFA, UMR5509, 69340 Ecully, France
*
†Email address for correspondence: wouter.bos@ec-lyon.fr
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Abstract

We consider the relaxation to thermal equilibrium of the Galerkin-truncated Euler equations in three dimensions, from which vortex stretching is removed. We prove that helicity and enstrophy are conserved by the system. Using statistical mechanics, we derive analytical predictions for the equilibrium energy and helicity spectra. Results are verified using pseudo-spectral direct numerical simulations. Results show that if the initial condition contains helicity, the system relaxes to a force-free large-scale structure akin to an Arnold–Beltrami–Childress (ABC) flow.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Isotropic turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 929 , 25 December 2021 , A11
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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