The non-dimensional prefactor of the Kolmogorov 2/3 law in the inertial range of homogeneous isotropic turbulence (HIT) has been believed to be a universal constant for many years, and then people have continued intensive search for evaluation of the constant by theory, experiment, and direct numerical simulation (DNS). Here a simple consideration is presented on this problem. First, a piecewise analytical form of longitudinal velocity autocorrelation ρ₁ is contrived such as to satisfy various physical conditions, so far known from theory and experiment. On this basis, it turns out that the constant must vary depending on Reynolds number. Next, by exactly solving the Karman–Howarth equation (for the ρ₁ given), the longitudinal third-order velocity correlation σ₁ is formulated for a decaying HIT. There it is verified that the Kolmogorov −4/5 law for third-order velocity structure function approximately holds near the origin for high Reynolds numbers inside the inertial range. Furthermore, the characteristic function of two-point velocity probability density function (PDF) in the Monin–Lundgren hierarchy, related to the already known one-point velocity PDF, is sketched towards the search for the fourth-order cumulants which must completely govern the intermittency in HIT.

中文翻译：

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衰减均匀各向同性湍流的新方法：柯尔莫哥洛夫常数 (1941) 的雷诺数相关性、速度差的偏度和两点速度概率密度的特征函数

多年来，Kolmogorov 2/3 定律在均质各向同性湍流 (HIT) 的惯性范围内的无量纲前因子一直被认为是一个普遍常数，随后人们继续深入探索理论对该常数的评价，实验和直接数值模拟 (DNS)。这里就这个问题做一个简单的考虑。首先，设计了纵向速度自相关ρ ₁的分段分析形式以满足迄今为止从理论和实验已知的各种物理条件。在此基础上，事实证明常数必须根据雷诺数而变化。接下来，通过精确求解 Karman-Howarth 方程（对于ρ ₁给定），纵向三阶速度相关性σ ₁是为衰减的HIT制定的。在那里验证了三阶速度结构函数的 Kolmogorov -4/5 定律在惯性范围内的高雷诺数的原点附近近似成立。此外，与已知的单点速度 PDF 相关的 Monin-Lundgren 层次结构中的两点速度概率密度函数 (PDF) 的特征函数被描绘成寻找四阶累积量，该四阶累积量必须完全控制HIT 的间歇性。