Spatial distributions of heavy particles suspended in an incompressibleisotropic and homogeneous turbulent flow are investigated by means of highresolution direct numerical simulations. In the dissipative range, it is shownthat particles form fractal clusters with properties independent of theReynolds number. Clustering is there optimal when the particle response time isof the order of the Kolmogorov time scale $\tau_\eta$. In the inertial range,the particle distribution is no longer scale-invariant. It is however shownthat deviations from uniformity depend on a rescaled contraction rate, which isdifferent from the local Stokes number given by dimensional analysis. Particledistribution is characterized by voids spanning all scales of the turbulentflow; their signature in the coarse-grained mass probability distribution is analgebraic behavior at small densities.
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机译：通过高分辨率直接数值模拟研究了悬浮在不可压缩的各向同性和均匀湍流中的重粒子的空间分布。在耗散范围内，表明粒子形成分形簇，其性质与雷诺数无关。当粒子响应时间约为Kolmogorov时间标度$ \ tau_ \ eta $时，聚类是最佳的。在惯性范围内，粒子分布不再是尺度不变的。然而，表明均匀性的偏差取决于重新缩放的收缩率，该收缩率与尺寸分析给出的局部斯托克斯数不同。颗粒分布的特征是空隙遍布湍流的所有尺度。它们在粗粒度质量概率分布中的特征是小密度下的代数行为。
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