Spatiotemporal velocity-velocity correlation function in fully developed turbulence
arXiv:1607.03098 · doi:10.1103/PhysRevE.95.023107
Abstract
Turbulence is an 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 Navier-Stokes equation, has eluded most theoretical attempts. Here, we provide a theoretical prediction for the {\it space and time} dependent velocity-velocity correlation function of homogeneous and isotropic turbulence from the field theory associated to Navier-Stokes equation with stochastic forcing. This prediction is the analytical fixed-point solution of Non-Perturbative Renormalisation Group flow equations, which are exact in a certain large wave-number limit. 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.
8 pages, 4 figures, improved version