  A Cahn-Hilliard-type theory for hydrodynamic fluctuations is proposed that
gives a quantitative description of the slowly evolving spatial correlations
and structures in density and flow fields in the early stages of evolution of
freely cooling granular fluids. Two mechanisms for pattern selection and
structure formation are identified: unstable modes leading to density
clustering (compare spinodal decomposition), and selective noise reduction
(compare peneplanation in structural geology) leading to vortex structures. As
time increases, the structure factor for the density field develops a maximum,
which shifts to smaller wave numbers. This corresponds to an approximately
diffusively growing length scale for density clusters. The spatial velocity
correlations exhibit algebraic decay $\sim r^{-d}$ on intermediate length
scales. The theoretical predictions for spatial correlation functions and
structure factors agree well with molecular dynamics simulations of a system of
inelastic hard disks.
