On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics
On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics
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从非平衡热力学角度论湍流级联的普遍特征
DOI：
10.1017/jfm.2018.360
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发表时间：
2017
影响因子：
3.7
通讯作者：
J. Peinke
中科院分区：
文献类型：
--
作者：
N. Reinke;A. Fuchs;D. Nickelsen;J. Peinke
湍流叶栅的特征进行了研究的各种数据集从三个不同的湍流流动，即自由射流以及尾流的规则的网格和圆柱。分析的重点是充分发展的湍流是否表现出普遍的小尺度特征的问题。有两种方法可以回答这个问题。首先，两点统计，即纵向速度增量的结构函数，和，第二，这些速度增量的联合多尺度统计进行了分析。联合多尺度表征包括在一个联合概率密度函数的整个级联。的数据集的基础上，证据的马尔可夫性质的湍流级联，这对应于一个三点封闭，减少了联合多尺度统计简单的条件概率密度函数（cPDF）。cPDF在尺度上由Fokker-Planck方程及其Kramers-Moyal系数（KMCs）描述。KMC是通过自洽优化程序从测量数据中获得的，并导致每个数据集的福克-普朗克方程。这些随机级联方程的知识使人们能够利用非平衡态热力学的概念，从而确定沿沿着个别级联轨迹的熵产生。除了这个新的概念，它表明，局部熵产生几乎完美平衡的所有数据集的积分波动定理（IFT）。因此，IFT的有效性可以作为湍流级联的一个新的定律，同时独立地证实了湍流级联的物理是一个无记忆的马尔可夫过程的尺度。IFT作为一种新的工具，以证明最佳的Fokker-Planck方程的功能形式，并随后调查的问题，小尺度湍流的数据集的普遍性。分析结果表明，湍流叶栅具有普适性和非普适性特征。我们确定小规模的不稳定性作为一个普遍性的突破功能。我们的结论是，特定的湍流有自己的特定的多尺度级联，换句话说，他们自己的随机指纹。
Features of the turbulent cascade are investigated for various datasets from three different turbulent flows, namely free jets as well as wake flows of a regular grid and a cylinder. The analysis is focused on the question as to whether fully developed turbulent flows show universal small-scale features. Two approaches are used to answer this question. First, two-point statistics, namely structure functions of longitudinal velocity increments, and, second, joint multiscale statistics of these velocity increments are analysed. The joint multiscale characterisation encompasses the whole cascade in one joint probability density function. On the basis of the datasets, evidence of the Markov property for the turbulent cascade is shown, which corresponds to a three-point closure that reduces the joint multiscale statistics to simple conditional probability density functions (cPDFs). The cPDFs are described by the Fokker–Planck equation in scale and its Kramers–Moyal coefficients (KMCs). The KMCs are obtained by a self-consistent optimisation procedure from the measured data and result in a Fokker–Planck equation for each dataset. Knowledge of these stochastic cascade equations enables one to make use of the concepts of non-equilibrium thermodynamics and thus to determine the entropy production along individual cascade trajectories. In addition to this new concept, it is shown that the local entropy production is nearly perfectly balanced for all datasets by the integral fluctuation theorem (IFT). Thus, the validity of the IFT can be taken as a new law of the turbulent cascade and at the same time independently confirms that the physics of the turbulent cascade is a memoryless Markov process in scale. The IFT is taken as a new tool to prove the optimal functional form of the Fokker–Planck equations and subsequently to investigate the question of universality of small-scale turbulence in the datasets. The results of our analysis show that the turbulent cascade contains universal and non-universal features. We identify small-scale intermittency as a universality breaking feature. We conclude that specific turbulent flows have their own particular multiscale cascades, in other words, their own stochastic fingerprints.