Abstract We have conducted direct numerical simulations of a turbulent boundary layer for the momentum-thickness-based Reynolds number Re θ = 180–4600. To extract the largest-scale vortices, we coarse-grain the fluctuating velocity fields by using a Gaussian filter with the filter width comparable to the boundary layer thickness. Most of the largest-scale vortices identified by isosurfaces of the second invariant of the coarse-grained velocity gradient tensor are similar to coherent vortices observed in low-Reynolds-number regions, that is, hairpin vortices or quasi-streamwise vortices inclined to the wall. We also develop a percolation analysis to investigate the threshold-dependence of the isosurfaces and objectively identify the largest-scale hairpin vortices in terms of the coarse-grained vorticity, which leads to the quantitative evidence that they never disappear even in fully developed turbulent regions. Hence, we conclude that hairpin vortices exist in the largest-scale structures irrespective of the Reynolds number.

中文翻译：

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湍流边界层最大尺度中的发夹涡

摘要 我们对基于动量厚度的雷诺数 Re θ = 180–4600 的湍流边界层进行了直接数值模拟。为了提取最大尺度的涡流，我们通过使用高斯滤波器粗粒化波动速度场，其滤波器宽度与边界层厚度相当。粗粒度速度梯度张量的第二不变量的等值面识别出的大部分最大尺度涡类似于在低雷诺数区域观察到的相干涡，即向壁倾斜的发夹涡或准流向涡. 我们还开发了渗流分析来研究等值面的阈值依赖性，并根据粗粒度涡度客观地识别最大尺度的发夹涡流，这导致定量证据表明即使在完全发展的湍流区域它们也永远不会消失。因此，我们得出结论，无论雷诺数如何，在最大尺度结构中都存在发夹涡旋。