The Density Probability Distribution in Compressible Isothermal   Turbulence: Solenoidal versus Compressive Forcing
  The probability density function (PDF) of the gas density in turbulent supersonic flows is investigated with high-resolution numerical simulations. In a systematic study, we compare the density statistics of compressible turbulence driven by the usually adopted solenoidal forcing (divergence-free) and by compressive forcing (curl-free). Our results are in agreement with studies using solenoidal forcing. However, compressive forcing yields a significantly broader density distribution with standard deviation ~3 times larger at the same rms Mach number. The standard deviation-Mach number relation used in analytical models of star formation is reviewed and a modification of the existing expression is proposed, which takes into account the ratio of solenoidal and compressive modes of the turbulence forcing. 
Christoph Federrath, Ralf S. Klessen, Wolfram Schmidt