Density and Velocity Correlations in Isothermal Supersonic Turbulence

TL;DR

This paper develops an analytic model for the joint distribution of density and velocity in isothermal supersonic turbulence, validated against simulations, revealing significant correlations that weaken with increasing Mach number.

Contribution

The authors introduce a new analytic formula for the joint PDF of density and velocity, improving understanding of their correlation in supersonic turbulence.

Findings

Density and velocity are significantly correlated in transsonic turbulence.

Correlations weaken as Mach number increases in supersonic turbulence.

The new model outperforms uncorrelated assumptions by a factor of 3.

Abstract

In star-forming clouds, high velocity flow gives rise to large fluctuations of density. In this work we explore the correlation between velocity magnitude (speed) and density. We develop an analytic formula for the joint probability distribution (PDF) of density and speed, and discuss its properties. In order to develop an accurate model for the joint PDF, we first develop improved models of the marginalized distributions of density and speed. We confront our results with a suite of 12 supersonic isothermal simulations with resolution of $1024^3$ cells in which the turbulence is driven by 3 different forcing modes (solenoidal, mixed and compressive) and 4 r.m.s. Mach numbers (1, 2, 4, 8). We show, that for transsonic turbulence, density and speed are correlated to a considerable degree and the simple assumption of independence fails to accurately describe their statistics. In the supersonic regime, the correlations tend to weaken with growing Mach number. Our new model of the joint and marginalized PDFs are a factor of 3 better than uncorrelated, and provides insight into this important process.