Workshop on Turbulence and Hydrodynamical Instabilities

Turbulence within molecular clouds generates shock waves that tear the 
cloud material into a hierarchy of smaller and smaller clumps. It also provides 
the necessary kick to overcome the outward pressure and cause the densest 
cloud cores to collapse leading to the birth of stars. This "turbulent 
fragmentation" is believed to shape the initial mass function of newly born 
stars. However, scaling properties of highly compressible, magnetized 
isotropic turbulence that constitute the basis for this new statistical theory of 
star formation are still poorly understood. In my talk I shall review results from 
large-scale numerical simulations that investigate the properties of 
supersonic hydrodynamic and MHD turbulence. Our nonmagnetic 
simulations are large enough to isolate the inertial range in density and 
velocity statistics. We find strong departure from the incompressible 
Kolmogorov velocity scaling at high turbulent Mach numbers. We propose an 
extension of Kolmogorov's phenomenology to compressible regimes and 
discuss how magnetic fields modify these results. I will also discuss the 
effects of large-scale driving force used in the simulations on the derived 
turbulent statistics, intermittency and fractal dimension of dissipative 
structures in supersonic turbulence.