  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 paper, 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 root-mean-square Mach number in the range of $1 \la M_{\rm rms} \la 10$.
  From one-dimensional experiments we find that the slope of the density power
spectra becomes gradually shallower as the rms Mach number increases. It is
because the density distribution transforms from the profile with {\it
discontinuities} having $P_{\rho} \propto k^{-2}$ for $M_{\rm rms} \sim 1$ to
the profile with {\it peaks} having $P_{\rho} \propto k^0$ for $M_{\rm rms} \gg
1$. We also find that the same trend is carried to three-dimension; that is,
the density power spectrum flattens as the Mach number increases. But the
density power spectrum of the flow with $M_{\rm rms} \sim 1$ has the Kolmogorov
slope. The flattening is the consequence of the dominant density structures of
{\it filaments} and {\it 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 {\it transonic} turbulence of $M_{\rm rms} \sim 1$ in the warm
ionized medium, the shallower spectrum of cold H I gas reflects the {\it
supersonic} turbulence of $M_{\rm rms} \sim$ a few in the cold neutral medium.
