Characterizing the structure of interstellar turbulence

Modeling the structure of molecular clouds depends upon good methods to sta tistically compare simulations with observations in order to constrain the models. Here we characterize a suite of hydrodynamical and magnetohydrodyna mical (MHD) simulations of supersonic turbulence using an averaged wavelet transform, the Delta-variance, that has been successfully used to character ize observations. We find that, independent of numerical resolution and dis sipation, the only models that produce scale-free, power-law Delta-variance spectra are those with hypersonic rms Mach numbers, above M similar to 4, while slower supersonic turbulence tend to show characteristis scales and p roduce non-power-law spectra. Magnetic fields have only a minor influence o n this tendency, though they tend to reduce the scale-free nature of the tu rbulence, and increase the transfer of energy from large to small scales. T he evolution of the characteristic length scale seen in supersonic turbulen ce follows exactly the t(1/2) power-law predicted from recent studies of th e kinetic energy decay rate.