Diffusion and clustering of sedimenting tracers in random hydrodynamic flows

The analysis presented in 1, 2] is extended to sedimenting low-inertia tracers advected by random divergence-free hydrodynamic flows. The key feature of the process is the clustering of the tracers due to the divergence of tracer-velocity field. This phenomenon has probability one; i.e., it takes place in almost every realization of the process. Both spatial diffusivity and diffusivity in the density space (responsible for clustering) are calculated. The low inertia of the tracers does not affect the spatial diffusivity. The indispensable use of a finite velocity correlation time leads to an anisotropic spatial diffusivity. The calculations performed in the study are based on a diffusion approximation.