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Fully developed isotropic turbulence: Symmetries and exact identities

Léonie Canet1,2, Bertrand Delamotte3,4, and Nicolás Wschebor3,4,5

  • 1Université Grenoble Alpes, UMR 5493, LPMMC, F-38000 Grenoble, France
  • 2CNRS, UMR 5493, LPMMC, F-38000 Grenoble, France
  • 3Sorbonne Universités, UPMC Université Paris 06, UMR 7600, LPTMC, F-75005 Paris, France
  • 4CNRS, UMR 7600, LPTMC, F-75005 Paris, France
  • 5Instituto de Física, Facultad de Ingeniería, Universidad de la República, J.H.y Reissig 565, 11000 Montevideo, Uruguay

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Phys. Rev. E 91, 053004 – Published 11 May, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.053004

Abstract

We consider the regime of fully developed isotropic and homogeneous turbulence of the Navier-Stokes equation with a stochastic forcing. We present two gauge symmetries of the corresponding Navier-Stokes field theory and derive the associated general Ward identities. Furthermore, by introducing a local source bilinear in the velocity field, we show that these symmetries entail an infinite set of exact and local relations between correlation functions. They include in particular the Kármán-Howarth relation and another exact relation for a pressure-velocity correlation function recently derived in G. Falkovich, I. Fouxon, and Y. Oz [J. Fluid Mech. 644, 465 (2010)] that we further generalize.

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Phys. Rev. E 91, 053004– Published 11 May, 2015
  • Received 28 November 2014

©2015 American Physical Society

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