The multi-scale geometry of the near field in an axisymmetric jet
The multi-scale geometry of the near field in an axisymmetric jet
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DOI：
10.1017/jfm.2017.899
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发表时间：
2018-01
影响因子：
3.7
通讯作者：
Dhiren Mistry;J. Dawson;A. Kerstein
中科院分区：
文献类型：
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作者：
Dhiren Mistry;J. Dawson;A. Kerstein
轴对称射流和一般湍流剪切流的一个特征是穿过湍流/非湍流界面（TNTI）的质量夹带。TNTI表面积的多尺度性质最近被观察到表现出幂律标度与分形维数，$D_{f}$之间，$D_{f}=2.3{-}2.4$，从二维数据推断，在高雷诺数边界层和轴对称射流的远场。在本文中，我们表明，分形标度以前观察到的轴对称射流的远场建立在年底的潜在核心。同时测量的速度和标量场和粗粒度过滤应用超过二十年的尺度分离，显示$D_{f}$演变到${\approx}2.35$在$x/d=4.6$，这是类似的$D_{f}$发现在远场之间的$x/d=40{-}60$。这是证据表明，尺度分离变得足够发达，以实现规模不变性的TNTI表面积在近场的射流以及自相似性之前建立。我们还观察到，这种几何尺度不变性的发病与两点速度相关性所示的径向均匀性的发病相吻合。最后，我们提出了一个简单的理论基础，这些结果使用精确的分形结构的基础上的科赫曲线和应用粗粒度过滤分析。
A characteristic feature of axisymmetric jets, and turbulent shear flows in general, is the entrainment of mass across the turbulent/non-turbulent interface (TNTI). The multi-scale nature of the TNTI surface area was recently observed to exhibit power-law scaling with a fractal dimension, $D_{f}$ , between $D_{f}=2.3{-}2.4$ , inferred from two-dimensional data, in both high Reynolds number boundary layers and the far field of axisymmetric jets. In this paper, we show that the fractal scaling previously observed in the far field of an axisymmetric jet is established at the end of the potential core. Simultaneous measurements of the velocity and scalar fields were obtained and coarse grain filtering was applied over two decades of scale separation, showing that $D_{f}$ evolves to ${\approx}2.35$ at $x/d=4.6$ , which is similar to $D_{f}$ found in the far field between $x/d=40{-}60$ . This is evidence that scale separation becomes sufficiently developed to achieve scale invariance of the TNTI surface area in the near field of the jet well before self-similarity is established. We also observe that the onset of this geometric scale invariance coincides with the onset of radial homogeneity shown by two-point velocity correlations. Finally, we present a simple theoretical basis for these results using an exact fractal construction based on the Koch curve and applying a coarse-grain filtering analysis.