  Motivated by the observed differences in the nebular emission of nearby and
high-redshift galaxies, we carry out a set of direct numerical simulations of
turbulent astrophysical media exposed to a UV background. The simulations
assume a metallicity of $Z/Z_{\odot}$=0.5 and explicitly track ionization,
recombination, charge transfer, and ion-by-ion radiative cooling for several
astrophysically important elements. Each model is run to a global steady state
that depends on the ionization parameter $U$, and the one-dimensional turbulent
velocity dispersion, $\sigma_{\rm 1D}$, and the turbulent driving scale. We
carry out a suite of models with a T=42,000K blackbody spectrum, $n_e$ = 100
cm$^{-3}$ and $\sigma_{\rm 1D}$ ranging between 0.7 to 42 km s$^{-1},$
corresponding to turbulent Mach numbers varying between 0.05 and 2.6. We report
our results as several nebular diagnostic diagrams and compare them to
observations of star-forming galaxies at a redshift of $z\approx$2.5, whose
higher surface densities may also lead to more turbulent interstellar media. We
find that subsonic, transsonic turbulence, and turbulence driven on scales of 1
parsec or greater, have little or no effect on the line ratios. Supersonic,
small-scale turbulence, on the other hand, generally increases the computed
line emission. In fact with a driving scale $\approx 0.1$ pc, a moderate amount
of turbulence, $\sigma_{\rm 1D}$=21-28 km s$^{-1},$ can reproduce many of the
differences between high and low redshift observations without resorting to
harder spectral shapes.
