QUASI-CLOSURE AND SCALING OF TURBULENCE

Abstract

A statistically stationary isotropic turbulence is of quasi-closure, i.e. its high-order statistical moments can be derived from its low-order moments. A workable quasi-closure scheme is developed for the structure functions of incompressible homogeneous isotropic turbulence based upon a non-Gaussian statistical model. The second order structure function is obtained by solving the spectral dynamic equation or by using an empirical formula such as the Batchelor fit, and then the high-order structure functions is calculated by the quasi-closure scheme. We study the absolute and relative scaling of the structure functions of isotropic turbulence in connection with Kolmogorovs' 1941 theory (K41) and his 1962 theory (K62). In contrast to K62 and various intermittency models, our results suggest a different picture of scaling of isotropic turbulence: the anomalous scaling of structure functions observed in experiments and numerical simulations is a finite Reynolds number effect, and the K41 normal scaling is valid in the real Kolmogorov inertial range corresponding to an infinite Reynolds number.