Characterizing the structure of interstellar turbulence

Modeling the structure of molecular clouds depends on good methods to statistically compare simulations with observations in order to constrain the models. Here we characterize a suite of hydrodynamical and magnetohydrodynamical (MHD) simulations of supersonic turbulence using an averaged wavelet transform, the Delta-variance, that has been successfully used to characterize observations. We find that, independent of numerical resolution and dissipation, the only models that produce scale-free, power-law Delta-variance spectra are those with hypersonic Mach numbers above M ~ 4, while slower supersonic turbulence tends to show characteristic scales and produce non-power-law spectra. Magnetic fields have only a minor influence on this tendency, though they tend to reduce the scale-free nature of the turbulence, and increase the transfer of energy from large to small scales. The evolution of the characteristic length scale seen in supersonic turbulence follows exactly the t^{1/2} power-law predicted from recent studies of the kinetic energy decay rate.