The physics of particle clustering in turbulent flows is not fully understood, but the general principle is simple: Every time a region of the gas flow is subject to an acceleration, inertial particles in that region relax to the new flow velocity with a delay, of order the particle friction time. During this process, the particles can sometimes accumulate into very dense clusters, even if the turbulent gas flow were incompressible. The complex network of flow accelerations in a turbulent flow results therefore in an equally complex network of particle clusters and voids (see the sample images from my simulations). Numerical simulations have quantified this process to some extent. For example, we know that the amplitude of particle clustering grows toward smaller scales, below the Kolmogorov dissipation scales. However, the dependence of the clustering amplitude on the Reynolds number of the flow is not well established and its spatial properties well below the Kolmogorov scale are unknown. This is due to the limited range of scales in the turbulent flows simulated so far, and to the limited number of particles in those flows.
Turbulence is ubiquitous in molecular clouds (MCs), but its origin is still unclear because MCs are usually assumed to live longer than the turbulence dissipation time. It has been shown that interstellar medium (ISM) turbulence is likely driven by SN explosions, but it has never been demonstrated that SN explosions can establish and maintain a turbulent cascade inside MCs consistent with the observations. In my work, I carry out simulations of SN-driven turbulence in a volume of (250 pc)3, specifically designed to test if SN driving alone can be responsible for the observed turbulence inside MCs. We find that SN driving establishes a velocity scaling consistent with the usual scaling laws of supersonic turbulence. I also find the same scaling laws extend to the interior of MCs, and their normalization is consistent with the observations, as shown by the velocity-size relation of MCs selected from my simulations. MCs from my simulations have properties very similar to those of observed MCs, such as velocity-size and mass-size relations, mass and size probability distributions, and magnetic field-density relation, besides the velocity scaling.