  We show quantitatively how the collision rate of droplets of visible moisture
in turbulent air increases very abruptly as the intensity of the turbulence
passes a threshold, due to the formation of fold caustics in their velocity
field. The formation of caustics is an activated process, in which a measure of
the intensity of the turbulence, termed the Stokes number St, is analogous to
temperature in a chemical reaction: the rate of collision contains a factor
exp(-C/St). Our results are relevant to the long-standing problem of explaining
the rapid onset of rainfall from convecting clouds. Our theory does not involve
spatial clustering of particles.
