Probability density and scaling exponents of the moments of longitudinal velocity difference in strong turbulence

作     者：Victor Yakhot 

作者机构：Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 

出 版 物：《Physical Review E》 (物理学评论E辑：统计、非线性和软体物理学)

年 卷 期：1998年第57卷第2期

页      面：1737-1737页

核心收录：

学科分类：07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

摘      要：We consider a few cases of homogeneous and isotropic turbulence differing by the mechanisms of turbulence generation. The advective terms in the Navier-Stokes and Burgers equations are similar. It is proposed that the longitudinal structure functions Sn(r) in homogeneous and isotropic three-dimensional turbulence are governed by a one-dimensional (1D) equation of motion, resembling the 1D Burgers equation, with the strongly nonlocal pressure contributions accounted for by Galilean invariance-breaking terms. The resulting equations, not involving parameters taken from experimental data, give both scaling exponents and amplitudes of the structure functions in an excellent agreement with experimental data. The derived probability density function P(Δu,r)≠P(−Δu,r), but P(Δu,r)=P(−Δu,−r), in accord with the symmetry properties of the Navier-Stokes equations. With decrease of the displacement r, the probability density, which cannot be represented in a scale-invariant form, shows smooth variation from the Gaussian at the large scales to close-to-exponential function, thus demonstrating onset of small-scale intermittency. It is shown that accounting for the subdominant contributions to the structure functions Sn(r)∝rξn is crucial for a derivation of the amplitudes of the moments of the velocity difference.