Multifractal Analysis of Various PDF in Turbulence based on Generalized Statistics: A Way to Tangle in Superfluid He
Multifractal Analysis of Various PDF in Turbulence based on Generalized Statistics: A Way to Tangle in Superfluid He
复制标题
基于广义统计的湍流中各种PDF的多重分形分析：超流体He中缠结的一种方法
DOI：
10.1063/1.1639584
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
N. Arimitsu
中科院分区：
文献类型：
--
作者：
T. Arimitsu;N. Arimitsu
利用多重分形分析（MFA），将概率密度函数（PDF）的表达式统一为一个简洁的解析公式，该公式适用于湍流中的各种量。结果表明，该公式可以准确地解释实验观察到的PDF在对数和线性尺度。PDF由两部分组成，即，尾部和中部。PDF尾部的结构主要由不透明度指数决定，代表了间歇性的大偏差，这是物理空间中奇异性的多重分形分布的表现，这是由于大雷诺数下Navier-Stokes方程的尺度不变性。另一方面，中心部分的结构表示由于热波动和/或观测误差而违反尺度不变性的小偏差。
By means of the multifractal analysis (MFA), the expressions of the probability density functions (PDFs) are unified in a compact analytical formula which is valid for various quantities in turbulence. It is shown that the formula can explain precisely the experimentally observed PDFs both on log and linear scales. The PDF consists of two parts, i.e., the tail part and the center part. The structure of the tail part of the PDFs, determined mostly by the intermittency exponent, represents the intermittent large deviations that is a manifestation of the multifractal distribution of singularities in physical space due to the scale invariance of the Navier‐Stokes equation for large Reynolds number. On the other hand, the structure of the center part represents small deviations violating the scale invariance due to thermal fluctuations and/or observation error.