  We show that the growth rate of dust grains in cold molecular clouds is
enhanced by the high degree of compressibility of a turbulent, dilute gas. By
means of high resolution (10243) numerical simulations, we confirm the theory
that the spatial mean growth rate is proportional to the gas-density variance.
This also results in broadening of the grain-size distribution (GSD) due to
turbulence-induced variation of the grain-growth rate. We show, for the first
time in a detailed numerical simulation of hydrodynamic turbulence, that the
GSD evolves towards a shape which is a reflection of the gas-density
distribution, regardless of the initial distribution. That is, in case of
isothermal, rotationally forced turbulence, the GSD tends to be a lognormal
distribution. We also show that in hypersonic turbulence, decoupling of gas and
dust becomes important and that this leads to an even further accelerated grain
growth.
