  We carry out direct numerical simulations of turbulent astrophysical media
exposed to the redshift zero metagalactic background. The simulations assume
solar composition and explicitly track ionizations, recombinations, and
ion-by-ion radiative cooling for hydrogen, helium, carbon, nitrogen, oxygen,
neon, sodium, magnesium, silicon, sulfur, calcium, and iron. Each run reaches a
global steady state that not only depends on the ionization parameter, $U,$ and
mass-weighted average temperature, $T_{\rm MW},$ but also on the the
one-dimensional turbulent velocity dispersion, \soned. We carry out runs that
span a grid of models with $U$ ranging from 0 to 10$^{-1}$ and \soned\ ranging
from 3.5 to 58 km s$^{-1}$, and we vary the product of the mean density and the
driving scale of the turbulence, $nL,$ which determines the average temperature
of the medium, from $nL =10^{16}$ to $nL =10^{20}$ cm$^{-2}$. The turbulent
Mach numbers of our simulations vary from $M \approx 0.5$ for the lowest
velocity dispersions cases to $M \approx 20$ for the largest velocity
dispersion cases. When $M \lesssim1,$ turbulent effects are minimal, and the
species abundances are reasonably described as those of a uniform photoionized
medium at a fixed temperature. On the other hand, when $M \gtrsim 1,$ dynamical
simulations such as the ones carried out here are required to accurately
predict the species abundances. We gather our results into a set of tables, to
allow future redshift zero studies of the intergalactic medium to account for
turbulent effects.
