  For a freely evolving granular fluid, the buildup of spatial correlations in
density and flow field is described using fluctuating hydrodynamics. The theory
for incompressible flows is extended to the general, compressible case,
including longitudinal velocity and density fluctuations, and yields
qualitatively different results for long range correlations. The structure
factor of density fluctuations shows a maximum at finite wavenumber, shifting
in time to smaller wavenumbers and corresponding to a growing correlation
length. It agrees well with two-dimensional molecular dynamics simulations.
