Density power spectrum of compressible hydrodynamic turbulent flows

Turbulent flows are ubiquitous in astrophysical environments, and understanding density structures and their statistics in turbulent media is of great importance in astrophysics. In this Letter, we study the density power spectra P-rho of transonic and supersonic turbulent flows through one- and three- dimensional simulations of driven, isothermal hydrodynamic turbulence with rms Mach numbers in the range. From one- dimensional 1 less than or similar to M-rms less than or similar to 10 rms experiments we find that the slope of the density power spectra becomes gradually shallower as the rms Mach number increases. This is because the density distribution is transformed from the profile with discontinuities having P-rho proportional to k(-2) for M-rms similar to 1 to the profile with peaks having P-rho proportional to K-0 for M-rms >> 1. We also find that the same trend is carried to three dimensions; that is, the density power spectrum flattens as the Mach number increases. But the density power spectrum of the flow with M-rms similar to 1 has a Kolmogorov slope. The flattening is a consequence of the dominant density structures of filaments and sheets. Observations have claimed different slopes of density power spectra for electron density and cold H I gas in the interstellar medium. We argue that while the Kolmogorov spectrum for electron density reflects the transonic turbulence of M-rms similar to 1 in the warm ionized medium, the shallower spectrum of cold H I gas reflects the supersonic turbulence of M (rms) similar to a few in the cold neutral medium.