title: Fully developed isotropic turbulence: Symmetries and exact identities.
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.
authors.affiliation: Université Grenoble Alpes, UMR 5493, LPMMC, F-38000 Grenoble, France.|CNRS, UMR 5493, LPMMC, F-38000 Grenoble, France.
authors.forename: Léonie
authors.initials: L
authors.lastname: Canet
authors.affiliation: Sorbonne Universités, UPMC Université Paris 06, UMR 7600, LPTMC, F-75005 Paris, France.|CNRS, UMR 7600, LPTMC, F-75005 Paris, France.
authors.forename: Bertrand
authors.initials: B
authors.lastname: Delamotte
authors.affiliation: Sorbonne Universités, UPMC Université Paris 06, UMR 7600, LPTMC, F-75005 Paris, France.|CNRS, UMR 7600, LPTMC, F-75005 Paris, France.|Instituto de Física, Facultad de Ingeniería, Universidad de la República, J.H.y Reissig 565, 11000 Montevideo, Uruguay.
authors.forename: Nicolás
authors.initials: N
authors.lastname: Wschebor