Experimental indications for Markov properties of small-scale turbulence
Experimental indications for Markov properties of small-scale turbulence
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DOI：
10.1017/s0022112001003597
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发表时间：
2001-04
影响因子：
3.7
通讯作者：
C. Renner;J. Peinke;R. Friedrich
中科院分区：
文献类型：
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作者：
C. Renner;J. Peinke;R. Friedrich
本文对一个由1.25 × 107个在圆形自由射流湍流区测得的局部速度样本组成的数据集进行了随机分析。我们发现的证据表明，纵向速度增量v（r）的统计可以被描述为一个马尔可夫过程。这种表征小尺度湍流的新方法导致了概率密度函数（p.d.f.）v（r）。p（v，r）的该方程完全由两个系数D1（v，r）和D2（v，r）（分别为漂移系数和扩散系数）确定。它示出了这些系数可以直接从实验数据估计，而不使用任何假设或模型的基本随机过程。所得到的福克-普朗克方程的解决方案进行了比较实验确定的概率密度函数。结果表明，Fokker-Planck方程描述了测量的p.d.f. (s)正确的，包括间接影响。此外，Fokker-Planck方程的知识还允许确定N个不同尺度p（v1，r1，...，vN，rN）上的N个增量的联合概率密度。
We present a stochastic analysis of a data set consisting of 1.25 × 107 samples of the local velocity measured in the turbulent region of a round free jet. We find evidence that the statistics of the longitudinal velocity increment v(r) can be described as a Markov process. This new approach to characterize small-scale turbulence leads to a Fokker–Planck equation for the r-evolution of the probability density function (p.d.f.) of v(r). This equation for p(v, r) is completely determined by two coefficients D1(v, r) and D2(v, r) (drift and diffusion coefficient, respectively). It is shown how these coefficients can be estimated directly from the experimental data without using any assumptions or models for the underlying stochastic process. The solutions of the resulting Fokker–Planck equation are compared with experimentally determined probability density functions. It is shown that the Fokker–Planck equation describes the measured p.d.f.(s) correctly, including intermittency effects. Furthermore, knowledge of the Fokker–Planck equation also allows the joint probability density of N increments on N different scales p(v1, r1, …, vN, rN) to be determined.