The Density PDFs of Supersonic Random Flows

Abstract

The question of the shape of the density PDF for supersonic turbulence is adressed, using both analytical and numerical methods. For isothermal supersonic turbulence, the PDF is Log-Normal, with a width that scales approximately linearly with the Mach number. For a polytropic equation of state, with an effective gamma smaller than one, the PDF becomes skewed and becomes reminiscent of (but not equal to) a power law on the high density side.