In recent years, numerical simulations of magneto-hydrodynamic (MHD) interstellar turbulence in a variety of regimes have been presented by several groups. Some of them have modeled the atomic and ionized ISM at large scales including self-gravity, parameterized heating and cooling and stellar-like forcing from ionization heating (Passot et al. 1995), while others have modeled isothermal flows with random forcing or else in decaying regimes (Gammie & Ostriker 1996; Padoan & Nordlund 1998; Ostriker et al. 1998; Mac Low et al. 1998). The latter group of simulations differ also in the scale at which the forcing is applied and the characteristic scales of the random initial conditions of the turbulence. Given the large available parameter space, it becomes necessary to constrain the parameters by comparing the simulation results with suitable observational data.
The best suited observations for characterizing the turbulent parameters of the ISM are densely sampled, high-resolution spectral maps of molecular and atomic gas. These provide information on the two-dimensional (in the plane of the sky) distribution of the gas, and on the radial component of the velocity.
In this work we present 3-D numerical simulations of compressible turbulence suitable for comparison with such spectral-line map observational data, allowing the projection of the simulated data onto one axis, and the separation in velocity channels. We consider full simulations of the atomic and ionized ISM, analogous to the two-dimensional simulations of Passot et al. (1995), including self-gravity, parameterized heating and cooling, star formation and rotation. Next we discuss the effects of representing the data in position-velocity space, noting that important differences arise compared to the physical-space representation. Finally, we present results from a Principal Component Analysis (PCA) and calculate the velocity dispersion-size relationship of the simulated data, comparing with an analogous study of molecular clouds by Heyer & Schloerb (1997) and pseudo-simulations by Heyer & Brunt (1999).