Supernova-regulated ISM -- V. Space- and time-correlations
  We apply correlation analysis to random fields in numerical simulations of
the supernova-driven interstellar medium (ISM) with the magnetic field produced
by dynamo action. We solve the thermo-magnetohydrodynamic (MHD) equations in a
shearing, Cartesian box representing a local region of the ISM, subject to
thermal and kinetic energy injection by supernova explosions, and parameterized
optically-thin radiative cooling. We consider the cold, warm\, and hot phases
of the ISM separately; the analysis mostly considers the warm gas, which
occupies the bulk of the domain. Various physical variables have different
correlation lengths in the warm phase: $40 pc$, $50 pc$, and $60 pc$ for random
magnetic field, density, and velocity, respectively, in the midplane. The
correlation time of the random velocity is comparable to the eddy turnover
time, about $10^7 yr$, although it may be shorter in regions with higher star
formation rate. The random magnetic field is anisotropic, with the standard
deviations of its components $b_x/b_y/b_z$ having approximate ratios
$0.5/0.6/0.6$ in the midplane. The anisotropy is attributed to the global
velocity shear from galactic differential rotation, and locally inhomogeneous
outflow to the galactic halo. The correlation length of Faraday depth along the
$z$-axis, $120 pc$, is greater than for electron density, $60 - 90 pc$, and
vertical magnetic field, $60 pc$. Such comparisons may be sensitive to the
orientation of the line of sight. Uncertainties of the structure functions of
synchrotron intensity rapidly increase with the scale. This feature is hidden
in power spectrum analysis, which can undermine the usefulness of power spectra
for detailed studies of interstellar turbulence.
