  We carry out direct numerical simulations of turbulent astrophysical media
that explicitly track ionizations, recombinations, and species-by-species
radiative cooling. The simulations assume solar composition and follows the
evolution of hydrogen, helium, carbon, oxygen, sodium, and magnesium, but they
do not include the presence of an ionizing background. In this case, the medium
reaches a global steady state that is purely a function of the one-dimensional
turbulent velocity dispersion, $\sigma_{\rm 1D},$ and the product of the mean
density and the driving scale of turbulence, $n L.$ Our simulations span a grid
of models with $\sigma_{\rm 1D}$ ranging from 6 to 58 km s$^{-1}$ and $n L$
ranging from 10$^{16}$ to 10$^{20}$ cm$^{-2},$ which correspond to turbulent
Mach numbers from $M=0.2$ to 10.6. The species abundances are well described by
single-temperature estimates whenever $M$ is small, but local equilibrium
models can not accurately predict the global equilibrium abundances when $M
\gtrsim 1.$ To allow future studies to account for nonequilibrium effects in
turbulent media, we gather our results into a series of tables, which we will
extend in the future to encompass a wider range of elements, compositions, and
ionizing processes.
