Abstract: Heavy particles suspended in an incompressible turbulent flow form a turbulent aerosol. Understanding the dynamics of particles in turbulent aerosols is important for a wide range of systems, such as droplet growth in turbulent rain clouds and planet formation in accretion disks. Laboratory experiments and numerical simulations show that if the inertia of the aerosol particles is significant, then the 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 these phenomena depend sensitively on the particle inertia, and they both affect collision rates and collision outcomes in the turbulent aerosol. Understanding the collision mechanisms in a turbulent aerosol is important to determine the long-term stability of the turbulent aerosol. But due to the complicated nature of turbulence, it is hard to model from first principles the dependence of collision statistics on the particle inertia and other parameters of the system.
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 talk I describe in what limits we may expect simulations of inertial particles in the statistical-model to give a qualitative agreement with direct numerical simulations or experiments of particles in turbulence. An advantage in strudying statistical models is that they are tractable for analytical calculations. I describe some of the analytical results we have obtained in the statistical model, and what these results can tell us about particles in turbulence.
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