The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations have demonstrated that heavy particles respond in intricate ways to turbulent fluctuations of the carrying fluid: non-interacting particles may cluster together and form spatial patterns even though the fluid is incompressible, and the relative speeds of nearby particles can fluctuate strongly. Both phenomena depend sensitively on the parameters of the system. This parameter dependence is difficult to model from first principles since turbulence plays an essential role. Laboratory experiments are also very difficult, precisely since they must refer to a turbulent environment. But in recent years it has become clear that important aspects of the dynamics of heavy particles in turbulence can be understood in terms of statistical models where the turbulent fluctuations are approximated by Gaussian random functions with appropriate correlation functions. In this review, we summarise how such statistical-model calculations have led to a detailed understanding of the factors that determine heavy-particle dynamics in turbulence. We concentrate on spatial clustering of heavy particles in turbulence. This is an important question because spatial clustering affects the collision rate between the particles and thus the long-term fate of the system.

中文翻译：

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湍流中重粒子空间模式的统计模型

悬浮在湍流中的重粒子的动力学对于天体物理学、大气物理学、海洋学和技术领域的广泛问题至关重要。实验室实验和数值模拟表明，重粒子以复杂的方式响应携带流体的湍流波动：即使流体是不可压缩的，非相互作用的粒子也可能聚集在一起并形成空间模式，并且附近粒子的相对速度可以剧烈波动. 这两种现象都敏感地取决于系统的参数。由于湍流起着至关重要的作用，因此很难根据第一原理对这种参数依赖性进行建模。实验室实验也非常困难，正是因为它们必须涉及湍流环境。但近年来，很明显，湍流中重粒子动力学的重要方面可以根据统计模型来理解，其中湍流波动由具有适当相关函数的高斯随机函数近似。在这篇综述中，我们总结了这种统计模型计算如何导致对决定湍流中重粒子动力学的因素的详细理解。我们专注于湍流中重粒子的空间聚类。这是一个重要的问题，因为空间聚类会影响粒子之间的碰撞率，从而影响系统的长期命运。