Self-similar geometries within the inertial subrange of scales in boundary layer turbulence
Self-similar geometries within the inertial subrange of scales in boundary layer turbulence
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DOI：
10.1017/jfm.2022.409
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发表时间：
2021-08
影响因子：
3.7
通讯作者：
M. Heisel;C. D. de Silva;G. Katul;M. Chamecki
中科院分区：
文献类型：
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作者：
M. Heisel;C. D. de Silva;G. Katul;M. Chamecki
摘要 湍流尺度的惯性子范围通常通过系综统计中的幂律特征来反映，例如能谱和结构函数——无论是在理论上还是在观测中。尽管在湍流中的分形几何主题上取得了有希望的发现，但对于与惯性子范围中的这种统计特征相对应的物理流特征，还没有公认的图像。本研究使用边界层湍流测量来评估速度等值面的自相似几何特性，并研究它们对速度信号统计的影响。流向速度等值面的分形维数表明沿每个等值面“皱纹”大小的统计自相似性，仅在尺度的惯性子范围内是恒定的。对于惯性子范围和生产范围之间的过渡，推断最大的皱纹越来越受到大尺度相干速度区域（例如均匀动量区域）的总体尺寸的限制。等值面的自相似性在随后的一维统计中产生幂律趋势。例如，结构函数的理论 2/3 幂律指数可以通过考虑众多等值面水平集的集体行为来恢复。结果表明，惯性子范围涡旋的物理存在体现在等值面的自相似皱纹中。
Abstract The inertial subrange of turbulent scales is commonly reflected by a power law signature in ensemble statistics such as the energy spectrum and structure functions – both in theory and from observations. Despite promising findings on the topic of fractal geometries in turbulence, there is no accepted image for the physical flow features corresponding to this statistical signature in the inertial subrange. The present study uses boundary layer turbulence measurements to evaluate the self-similar geometric properties of velocity isosurfaces and investigate their influence on statistics for the velocity signal. The fractal dimension of streamwise velocity isosurfaces, indicating statistical self-similarity in the size of ‘wrinkles’ along each isosurface, is shown to be constant only within the inertial subrange of scales. For the transition between the inertial subrange and production range, it is inferred that the largest wrinkles become increasingly confined by the overall size of large-scale coherent velocity regions such as uniform momentum zones. The self-similarity of isosurfaces yields power-law trends in subsequent one-dimensional statistics. For instance, the theoretical 2/3 power-law exponent for the structure function can be recovered by considering the collective behaviour of numerous isosurface level sets. The results suggest that the physical presence of inertial subrange eddies is manifested in the self-similar wrinkles of isosurfaces.