Long-time, large-scale properties of a randomly stirred compressible fluid

The large-scale, long-time properties of a compressible fluid stirred by a Gaussian random force with correlation 〈${\mathit{f}}_{\mathit{i}}$ ${\mathit{f}}_{\mathit{j}}$〉∝${\mathit{k}}^{\mathrm{-}\mathit{y}}$ are investigated. It is shown that when ε=4+y-d>3 (d=space dimension) the effective sound velocity becomes scale dependent in the limit k→0 and the fluid obeys a universal equation of state. The effective Mach number is also scale dependent, reaching a fixed-point value ${\mathit{Ma}}^{\mathrm{*}}$(k)<1 when k→0. The predictions of the theory are compared with the results of direct numerical simulations.