Understanding density fluctuations in supersonic, isothermal turbulence

Supersonic turbulence occurs in many environments, particularly in astrophysics. In the crucial case of isothermal turbulence, the probability density function (PDF) of the logarithmic density, s, is well-measured, but a theoretical understanding of the processes leading to this distribution remains elusive. We investigate these processes using Lagrangian tracer particles to track s and ds/dt in direct numerical simulations, and we show that their evolution can be modeled as a stochastic differential process with time-correlated noise. The temporal correlation functions of s and ds/dt decay exponentially, as predicted by the model, and the decay timescale is $\approx$ 1/6 the eddy turnover time. The behavior of the conditional averages of ds/dt and d2s/dt2  is also well explained by the model, which shows that the density PDF arises from a balance between stochastic compressions/expansions, which tend to broaden the PDF, and the acceleration/deceleration of shocks by density gradients, ..., Generated with the FLASH code and reduced as described in the paper., , # Data for Understanding Density Fluctuations in Supersonic, Isothermal Turbulence

[https://doi.org/10.5061/dryad.zgmsbccn0](https://doi.org/10.5061/dryad.zgmsbccn0)

## Description of the data and file structure

A repository of the reduced data and macros used to generate the main results of this paper.

### Files and variables

#### File: Data.zip

**Description:**  A zipped repository of the reduced simulation data used to generate the results in this paper. This includes temporal correlation function data from each of the runs, along with value of ds/dt and d^2s/dt^2 as a function of s.  The data also computes particle values interpolated by CIC, which is shown to be the best method in the paper, as well as a quadratic method, which is shown to be less reliable.  Finally, the repository includes macros for reproducing the main results in the paper.

## Files and Directory Structure

Each directory is named according to its name in the corresponding paper. The naming scheme is det...