Statistical properties of supersonic turbulence in the Lagrangian and Eulerian frameworks

TL;DR

This study investigates how different forcing types affect the statistical properties of supersonic turbulence in both Lagrangian and Eulerian frameworks through high-resolution simulations, revealing key differences in density contrast and intermittency.

Contribution

It provides a systematic analysis of the impact of solenoidal and compressive forcing on turbulence statistics, introducing a model linking structure functions to Mach number.

Findings

Compressively driven turbulence exhibits larger density contrasts.

Structure functions depend only on Mach number, not forcing type.

A Gaussian-based model describes the structure function behavior.

Abstract

We present a systematic study of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We analyse a series of high-resolution, hydrodynamical grid simulations with Lagrangian tracer particles and examine the effects of solenoidal (divergence-free) and compressive (curl-free) forcing on structure functions, their scaling exponents, and the probability density functions of the gas density and velocity increments. Compressively driven simulations show a significantly larger density contrast, a more intermittent behaviour, and larger fractal dimension of the most dissipative structures at the same root mean square Mach number. We show that the absolute values of Lagrangian and Eulerian structure functions of all orders in the integral range are only a function of the root mean square Mach number, but independent of the forcing. With the assumption of a Gaussian distribution for the probability density function of the velocity increments on large scales, we derive a model that describes this behaviour.