Inertial particles, i.e., small heavy particles, can inhomogeneously distribute and form clusters even in statistically homogeneous turbulence. When the Reynolds number of turbulence is sufficiently high so that coherent structures with various length and time scales coexist, particles form clusters by the action of the coherent structures when the particle velocity relaxation time is in the inertial-range time scales. In general, thus formed clusters are larger for larger Stokes numbers (the nondimensional relaxation time). We propose a method to objectively describe the particle cluster created by the action of coherent structures in the inertial range. For this purpose, we generalize the sweep-stick mechanism [S. Goto and J. C. Vassilicos, Phys. Rev. Lett. 100, 054503 (2008)] to express two-dimensional sheetlike clusters in terms of the coarse-grained acceleration field of turbulence. The generalized mechanism also predicts the thickness of the clusters, which depends on the particle relaxation time, the magnitude of acceleration gradients, and the lifetime of coherent flow structures. The direct numerical simulations of fully developed turbulence in a periodic cube with the Taylor-length Reynolds number being about 740 support the proposed mechanism.

中文翻译：

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湍流中惯性粒子聚类的广义扫杆机制

惯性粒子，即小的重粒子，即使在统计上均一的湍流中也可能不均匀地分布并形成团簇。当湍流的雷诺数足够高，以至于各种长度和时间尺度的相干结构共存时，当粒子速度弛豫时间在惯性范围内时，粒子会通过相干结构的作用而形成簇。通常，对于较大的斯托克斯数（无量纲弛豫时间），这样形成的簇较大。我们提出一种方法来客观地描述由惯性范围内的相干结构的作用创建的粒子簇。为了这个目的，我们概括了扫杆机制[S。Goto和JC Vassilicos，物理学。莱特牧师 100，054503（2008）]来表示二维片状簇，这是湍流的粗粒度加速场。通用机制还可以预测团簇的厚度，这取决于粒子的弛豫时间，加速度梯度的大小以及相干流结构的寿命。泰勒长度雷诺数约为740的周期立方体中完全发展的湍流的直接数值模拟支持了所提出的机制。