The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing

TL;DR

This study compares the density PDFs in supersonic turbulence driven by solenoidal and compressive forcing, revealing that compressive forcing produces significantly broader density distributions and proposing a modified relation for the standard deviation-Mach number.

Contribution

It provides a systematic comparison of density PDFs under different forcing types and introduces a modified standard deviation-Mach number relation accounting for forcing mode ratios.

Findings

Compressive forcing results in a density distribution ~3 times broader than solenoidal at the same Mach number.

The standard deviation-Mach number relation is modified to include the ratio of forcing modes.

Results align with previous studies using solenoidal forcing.

Abstract

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.