title: Spatiotemporal velocity-velocity correlation function in fully developed turbulence.
abstract: Turbulence is a ubiquitous phenomenon in natural and industrial flows. Since the celebrated work of Kolmogorov in 1941, understanding the statistical properties of fully developed turbulence has remained a major quest. In particular, deriving the properties of turbulent flows from a mesoscopic description, that is, from the Navier-Stokes equation, has eluded most theoretical attempts. Here, we provide a theoretical prediction for the functional space and time dependence of the velocity-velocity correlation function of homogeneous and isotropic turbulence from the field theory associated to the Navier-Stokes equation with stochastic forcing. This prediction, which goes beyond Kolmogorov theory, is the analytical fixed point solution of nonperturbative renormalization group flow equations, which are exact in the limit of large wave numbers. This solution is compared to two-point two-times correlation functions computed in direct numerical simulations. We obtain a remarkable agreement both in the inertial and in the dissipative ranges.
authors.affiliation: Université Grenoble Alpes and Centre National de la Recherche Scientifique, LPMMC, UMR 5493, 38042 Grenoble, France.
authors.forename: Léonie
authors.initials: L
authors.lastname: Canet
authors.affiliation: Université Grenoble Alpes and Centre National de la Recherche Scientifique, LPMMC, UMR 5493, 38042 Grenoble, France.
authors.forename: Vincent
authors.initials: V
authors.lastname: Rossetto
authors.affiliation: 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
authors.affiliation: Université Grenoble Alpes and Centre National de la Recherche Scientifique, LEGI, UMR 5519, 38042 Grenoble, France.
authors.forename: Guillaume
authors.initials: G
authors.lastname: Balarac