Bernhard Mehlig: Statistical models for turbulent aerosols
Turbulent aerosols are suspensions of small particles in a turbulent gas. The analysis of such highly non-linear and multi-scale dynamical systems poses formidable challenges. Laboratory experiments resolving the particle dynamics have only recently become possible, and direct numerical simulations of such systems are still immensely difficult. In this talk I describe recent progress in understanding the dynamics of turbulent aerosols using highly idealised statistical models that capture the relevant physics, and that allow systematic mathematical analysis using dynamical-systems theory. I summarise how this helps to understand fundamental mechanisms determining the particle dynamics: small-scale fractal clustering, caustic singularities, and anomalously large relative particle velocities. I highlight successes and failures of this approach, as well as the most important open questions.
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