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 $zapprox$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.
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