Canet Léonie, Rossetto Vincent, Wschebor Nicolás, Balarac Guillaume
Université Grenoble Alpes and Centre National de la Recherche Scientifique, LPMMC, UMR 5493, 38042 Grenoble, France.
Instituto de Física, Facultad de Ingeniería, Universidad de la República, J.H.y Reissig 565, 11000 Montevideo, Uruguay.
Phys Rev E. 2017 Feb;95(2-1):023107. doi: 10.1103/PhysRevE.95.023107. Epub 2017 Feb 16.
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.
湍流是自然流动和工业流动中普遍存在的现象。自1941年柯尔莫哥洛夫的著名工作以来，理解充分发展湍流的统计特性一直是一个主要的研究目标。特别是，从介观描述（即从纳维-斯托克斯方程）推导湍流流动的特性，一直是大多数理论尝试难以实现的。在这里，我们从与具有随机强迫的纳维-斯托克斯方程相关的场论出发，对均匀各向同性湍流的速度-速度关联函数的泛函空间和时间依赖性给出了理论预测。这一超越柯尔莫哥洛夫理论的预测，是非微扰重整化群流方程的解析不动点解，在大波数极限下是精确的。该解与直接数值模拟中计算的两点两时间关联函数进行了比较。我们在惯性范围和耗散范围内都得到了显著的一致性。
