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Static and dynamical structure factors for shear and longitudinal modes ofthe velocity and density fields are computed for a granular system fluidized bya stochastic bath with friction. Analytical expressions are obtained throughfluctuating hydrodynamics and are successfully compared with numericalsimulations up to a volume fraction $\sim 50%$. Hydrodynamic noise is the sumof external noise due to the bath and internal one due to collisions. Only thelatter is assumed to satisfy the fluctuation-dissipation relation with theaverage granular temperature. Static velocity structure factors $S_\perp(k)$and $S_\parallel(k)$ display a general non-constant behavior with two plateauxat large and small $k$, representing the granular temperature $T_g$ and thebath temperature $T_b>T_g$ respectively. From this behavior, two differentvelocity correlation lengths are measured, both increasing as the packingfraction is raised. This growth of spatial order is in agreement with thebehaviour of dynamical structure factors, the decay of which becomes slower andslower at increasing density.

Fluctuating hydrodynamics and correlation lengths in a driven granular fluid