Finite shock model of density in supersonic turbulence

TL;DR

This paper introduces a finite shock model for density distribution in supersonic turbulence, showing it better fits numerical data than the traditional lognormal model, and extends to subsonic flows.

Contribution

The paper proposes a finite shock model for density in turbulent gas, improving upon the lognormal approximation and applicable across subsonic and supersonic regimes.

Findings

Finite shock model fits simulation data better than lognormal.

Model applies to both subsonic and supersonic turbulence.

Deviations from lognormal are significant at finite shock counts.

Abstract

The probability distribution of density in isothermal, supersonic, turbulent gas is approximately lognormal. This behaviour can be traced back to the shock waves travelling through the medium, which randomly adjust the density by a random factor of the local sonic Mach number squared. Provided a certain parcel of gas experiences a large number of shocks, due to the central limit theorem, the resulting distribution for density is lognormal. We explore a model in which parcels of gas undergo finite number of shocks before relaxing to the ambient density, causing the distribution for density to deviate from a lognormal. We confront this model with numerical simulations with various r.m.s. Mach numbers ranging from subsonic as low as 0.1 to supersonic at 25. We find that the fits to the finite formula are an order of magnitude better than a lognormal. The model naturally extends even to subsonic flows, where no shocks exist.