When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy particles, with mass densities larger than that of the carrying fluid, can detach from the flow. This results in preferential sampling, small-scale fractal clustering, and large relative velocities. To describe these effects of particle inertia, one must consider both particle positions and velocities in phase space. In recent years, statistical phase-space models have significantly contributed to our understanding of inertial-particle dynamics in turbulence. These models help to identify the key mechanisms and nondimensional parameters governing the particle dynamics and have made qualitative and, in some cases, quantitative predictions. This article reviews statistical phase-space models for the dynamics of small, yet heavy, spherical particles in turbulence. We evaluate their effectiveness by comparing their predictions with results from numerical simulations and laboratory experiments, and we summarize their successes and failures.

中文翻译：

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湍流中重粒子动力学的统计模型

当非常小的颗粒悬浮在运动的流体中时，它们往往会跟随流动。统计模型已成功描述了此类示踪粒子如何通过湍流混合、传输和分散。质量密度大于携带流体的重颗粒可能会从流体中分离。这导致优先采样、小规模分形聚类和大的相对速度。为了描述粒子惯性的这些影响，必须考虑相空间中的粒子位置和速度。近年来，统计相空间模型极大地促进了我们对湍流中惯性粒子动力学的理解。这些模型有助于识别控制粒子动力学的关键机制和无量纲参数，并做出定性预测，在某些情况下还做出定量预测。本文回顾了湍流中小而重的球形粒子动力学的统计相空间模型。我们通过将他们的预测与数值模拟和实验室实验的结果进行比较来评估他们的有效性，并总结他们的成功和失败。