  Spatial clustering of identical particles falling through a turbulent flow
enhances the collision rate between the falling particles, an important problem
in aerosol science. We analyse this problem using perturbation theory in a
dimensionless parameter, the so-called Kubo number. This allows us to derive an
analytical theory quantifying the spatial clustering. We find that clustering
of small particles in incompressible random velocity fields may be reduced or
enhanced by the effect of gravity (depending on the Stokes number of the
particles) and may be strongly anisotropic.
