Density-PDFs and Lagrangian Statistics of highly compressible Turbulence

TL;DR

This paper investigates the statistical properties of highly compressible turbulence through numerical simulations, analyzing the probability density functions of mass density and Lagrangian particle dynamics, and proposes a link to log-normal density distributions.

Contribution

It presents high-resolution simulations of compressible turbulence and establishes a novel connection between Lagrangian particle statistics and density fluctuation models.

Findings

Density PDFs follow a log-normal distribution.

Lagrangian particle statistics align with density fluctuation predictions.

Simulations involve $512^3$ grid points and 2 million particles.

Abstract

We report on probability-density-functions (PDF) of the mass density in numerical simulations of highly compressible hydrodynamic flows and the corresponding structure formation of Lagrangian particles advected by the flows. Numerical simulations were performed with $512^3$ collocation points and 2 million tracer particles integrated over several dynamical times. We propose a connection between the PDF of the Lagrangian tracer particles and the predicted log-normal distribution of the density fluctuations in isothermal systems.