Aspects of Density Fluctuations in Compressible MHD Turbulence

TL;DR

This study uses high-resolution simulations to analyze density fluctuations and scaling laws in compressible MHD turbulence, confirming theoretical models and revealing hierarchical density structures relevant to interstellar medium observations.

Contribution

It demonstrates that the density-weighted velocity follows Kolmogorov scaling and that higher order correlations align with She-Léveque scalings across various Mach numbers in compressible MHD turbulence.

Findings

Density-weighted velocity obeys Kolmogorov scaling.

Third order structure functions remain unity across Mach numbers.

Density peaks form a hierarchical structure decreasing with scale.

Abstract

We study scaling relations of compressible isothermal strongly magnetized turbulence using numerical simulations with resolution 512$^3$. We find a good correspondence of our results with the Fleck (1996) model of compressible hydrodynamic turbulence. In particular, we find that the density-weighted velocity, i.e. $\boldsymbol{u} \equiv \rho^{1/3} \boldsymbol{v}$, proposed in Kritsuk et al. (2007) obeys the Kolmogorov scaling, i.e. ${\cal E}_{u}(k)\sim k^{-5/3}$ for the high Mach number turbulence. Similarly, we find that the exponents of the third order structure functions for $\boldsymbol{u}$ stay equal to unity for all Mach numbers studied. The scaling of higher order correlations obeys the She-L\'{e}v\^{e}que (1994) scalings corresponding to the two-dimensional dissipative structures, and this result does not change with the Mach number either. In contrast to velocity $\boldsymbol{v}$ which exhibits different scaling parallel and perpendicular to the local magnetic field, the scaling of $\boldsymbol{u}$ is similar in both directions. In addition, we find that the peaks of density create a hierarchy in which both physical and column densities decrease with the scale in accordance to the Fleck (1996) predictions. This hierarchy can be related ubiquitous small ionized and neutral structures (SINS) in the interstellar gas. We believe that studies of statistics of the column density peaks can provide both consistency check for the turbulence velocity studies and insight into supersonic turbulence, when the velocity information is not available.