Kolmogorov-Burgers model for star-forming turbulence

The process of star formation in interstellar molecular clouds is believed to be controlled by driven supersonic magnetohydrodynamic turbulence. We suggest that in the inertial range, such turbulence obeys the Kolmogorov law, while in the dissipative range, it behaves as Burgers turbulence developing shock singularities. On the base of the She-Leveque analytical model, we then predict the velocity power spectrum in the inertial range to be E-k similar to k(-174.) This result agrees well with recent numerical findings by Padoan & Nordlund and reproduces the observational Larson law [u(l)(2)] similar to l(0.74...0.76). The application of the model to more general dissipative structures with higher fractal dimensionality is discussed.