  We compute the distribution of relative velocities for a one-dimensional
model of heavy particles suspended in a turbulent flow, quantifying the caustic
contribution to the moments of relative velocities. The same principles
determine the corresponding caustic contribution in $d$ spatial dimensions. The
distribution of relative velocities \Delta v at small separations R acquires
the universal form \rho(\Delta v,R) ~ R^{d-1}|\Delta v|^{D_2-2d} for large (but
not too large) values of |\Delta v|. Here D_2 is the phase-space correlation
dimension. Our conclusions are in excellent agreement with numerical
simulations of particles suspended in a randomly mixing flow in two dimensions,
and in quantitative agreement with published data on direct numerical
simulations of particles in turbulent flows.
