The statistical relationships among the turbulence structures of the streamwise velocity fluctuations along the streamwise and azimuthal directions in a turbulent pipe flow were examined using direct numerical simulation data at Reτ = 3008. Two-point correlations of the streamwise velocity fluctuations showed a linear relationship between the streamwise and azimuthal length scales (lx and lθ), where lθ/lx = 0.07 along the wall-normal distance, indicating the long coherent structures called very-large-scale motions (VLSMs). The one-dimensional pre-multiplied energy spectra of the streamwise velocity fluctuations showed that the streamwise and the azimuthal wavelengths (λx and λθ) grew linearly along the wall-normal distance, λx/y = 20 and λθ/y = 7, respectively. The ratio between the two linear relationships was determined to be λθ/λx = 0.35, indicative of large-scale motions (LSMs). The energetic modes obtained from a proper orthogonal decomposition (POD) analysis using the translational invariance method...

中文翻译：

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湍流管道流中的流向和方位角长度尺度之间的关系

利用 Reτ = 3008 处的直接数值模拟数据，研究了湍流管流中沿流向和方位向的流向速度波动的湍流结构之间的统计关系。流向速度波动的两点相关性表明流向和方位角长度尺度（lx 和 lθ），其中沿壁法向距离的 lθ/lx = 0.07，表示称为超大规模运动 (VLSM) 的长相干结构。流向速度波动的一维预乘能谱表明，流向和方位角波长（λx 和 λθ）沿壁法向距离线性增长，分别为 λx/y = 20 和 λθ/y = 7。两个线性关系之间的比率确定为λθ/λx = 0.35，指示大规模运动（LSM）。使用平移不变性方法从适当的正交分解 (POD) 分析中获得的能量模式...