Clustering and caustics in one-dimensional models of turbulent aerosols

Heavy particles suspended in turbulent fluid flows, so-called turbulent aerosols, are common in Nature and in technological applications. A prominent example is rain droplets in turbulent clouds. Due to their inertia, ensembles of aerosol particles distribute inhomogeneously over space and can develop large relative velocities at small separations. We use statistical models that mimic turbulent flow by means of Gaussian random velocity fields to describe these systems. Compared to models that involve actual turbulence, our statistical models are simpler to study and allow for an analytical treatment in certain limits. Despite their simplic- ity, statistical models qualitatively explain the results of direct numerical simulations and experiments. In this Licentiate thesis, we focus primarily on studying one-dimensional versions of the statistical model. The results of these systems create intuition for, and give important insights into the behaviour of higher dimensional models of particles in turbulence