Spatial Correlations in Compressible Granular Flows

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.