Turbulent Density Statistics

Abstract

The statistics of density fluctuations play a central role for the phenomenology of compressible turbulence, particularly in the supersonic regime. The most important property is the probability density function of the mass density, which is often approximated by a log-normal function. Data from the high-resolution simulations discussed in the previous chapter, however, indicate an influence of the large-scale forcing on the shape and the width of the distribution. To analyze the impact of self-gravity on the density structure of turbulent gas, several methods can be applied. Clump finders search for extended gravitationally unstable regions. The resulting mass distribution, the so-called clump mass function, can be compared to analytical predictions. The employed stability criteria, however, are based on the Jeans or Bonnor-Ebert masses, which follow from linear perturbation analysis or the virial theorem for isolated objects. The dynamical equation for the rate of compression, on the other hand, applies to the fully non-linear regime of supersonic turbulence. By means of a statistical analysis of the relative contributions of gravitational, thermal, and turbulent source terms, the local support of the gas against gravity can be analyzed, without limitations imposed by analytical assumptions.