Fluid mechanics is rich in mean field results like those of point vortex approximation in 2D. Deviation from the mean field is also a next step of great interest. We illustrate these facts with the example of particle aggregation in a turbulent fluid, a problem of interest for initial rain formation or planet formation in stellar dust disks. The particles have inertia, measured by the so-called Stokes number. When Stokes is large, the mean field theory describes reality well and produces physical laws coherent with experiments. But when Stokes is small, the mean field is not sufficient and a complete solution is still debated. Rigorous elements of the theory and heuristics about the Physics will be given.[-]

Fluid mechanics is rich in mean field results like those of point vortex approximation in 2D. Deviation from the mean field is also a next step of great interest. We illustrate these facts with the example of particle aggregation in a turbulent fluid, a problem of interest for initial rain formation or planet formation in stellar dust disks. The particles have inertia, measured by the so-called Stokes number. When Stokes is large, the mean field theory describes reality well and produces physical laws coherent with experiments. But when Stokes is small, the mean field is not sufficient and a complete solution is still debated. Rigorous elements of the theory and heuristics about the Physics will be given.[-]

Fluid mechanics is rich in mean field results like those of point vortex approximation in 2D. Deviation from the mean field is also a next step of great interest. We illustrate these facts with the example of particle aggregation in a turbulent fluid, a problem of interest for initial rain formation or planet formation in stellar dust disks. The particles have inertia, measured by the so-called Stokes number. When Stokes is large, the mean field theory describes reality well and produces physical laws coherent with experiments. But when Stokes is small, the mean field is not sufficient and a complete solution is still debated. Rigorous elements of the theory and heuristics about the Physics will be given.[-]