An identification of Energy Cascade in Turbulence by Orthonormal Wavelet Analysis
An identification of Energy Cascade in Turbulence by Orthonormal Wavelet Analysis
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DOI：
10.1143/ptp/86.4.799
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发表时间：
1991-10
影响因子：
--
通讯作者：
M. Yamada;K. Ohkitani
中科院分区：
文献类型：
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作者：
M. Yamada;K. Ohkitani
正交小波展开法应用于大气湍流数据的分析，该数据显示了二十多年的惯性子范围谱。讨论了湍流数据的正交小波分析结果与人工随机噪声的结果。湍流的局部小波谱显示出特征结构。它在人工随机噪声中不存在，并且可以通过能量级联过程的痕迹来识别。速度的高阶结构函数。通过小波分析得到。展示了流场的间歇·帐篷结构。 1941年，柯尔莫哥洛夫提出了流体湍流的普遍理论，其中假设与流场惯性子范围有关的每个统计量仅由能量耗散率决定。根据这一理论，相隔空间距离 r 的两点之间的 n 阶速度差的平均值与 r"13 成正比。这一预测已在高雷诺数流的精确实验中得到反复检验，现在人们普遍认为，就低阶速度差而言，r 依赖性与柯尔莫哥洛夫理论非常吻合。特别是，对应于 n=2 的速度场能谱的实验形式与以下形式的柯尔莫哥洛夫形式一致： k- 5/3 然而，经过反复证实，高阶速度差具有与柯尔莫哥洛夫预测不同的统计特性，使得速度场的n阶结构函数在经过二阶速度差归一化后，表现出明显的r依赖性，这一事实意味着惯性子范围内的能量级联过程与柯尔莫哥洛夫图有不可忽略的偏差，该偏差反映在速度差的概率分布函数的形状上。这种偏差通常被称为间歇性，其特征被认为是流体湍流的核心问题之一。间歇性在较小尺度上变得更加突出，这表明间歇性是能量级联过程的重要组成部分。然而，这种级联过程本身（有时称为理查森级联）仅是一个理论考虑问题，其特征结构尚未在实验或数值模拟中得到清晰的体现。
Orthonormal wavelet expansion method is applied to an analysis of atmospheric turbulence data which shows more than two decades of the inertial subrange spectrum. The result of the orthonor mal wavelet analysis of the turbulence data is discussed in comparison with those of an artificial random noise. The local wavelet spectra of turbulence show a characteristic structure. which is absent in the artificial random noise and is identified with the trace of the energy cascade process. The higher· order structure function of velocity. obtained by the wavelet analysis. shows the intermit· tent structure of the flow field. In 1941 Kolmogorov proposed a universal theory of fluid turbulence/) in which every statistical quantity concerning the inertial subrange of flow field is assumed to be determined only by the energy dissiation rate. According to this theory, the average of the n-th order of velocity difference between two points separated by spatial distance r is proportional to r"13. This prediction has been repeatedly examined in accurate experiments in high Reynolds number flows, and it is now widely accepted that as far as lower order of velocity difference is concerned, the r-dependence agrees well with the Kolmogorov theory. In particular, experimental forms of the energy spectrum of the velocity field, which corresponds to n=2, coincide with the Kolmogorov form of k- 5/3 • However, it has been repeatedly confirmed that higher order of the velocity difference has a statistical property different from Kolmogorov's prediction, so that the n-th order structure function of the velocity field, when normalized by the second order of the velocity difference, shows a clear r-dependence. This fact implies that the energy cascade process in the inertial subrange has an unnegligible deviation from the Kolmogorov picture. The deviation is reflected in the shape of the probability distribution function of the velocity difference, which has longer tail for smaller distance r. This deviation is often called intermittency, and its characterization is regarded as one of the central problems of fluid turbulence. The fact that intermittency becomes more prominent at smaller scales indicates that the intermittency is an essential part of the energy cascade process. However, this cascade process itself, sometimes called Richardson cascade, has been only a matter of theoretical consideration, and its characteristic structure has not yet been clearly captured in experiments or in numerical simula tions.