The Relationship Between the Turbulence-Driving-Length and the Length-Scale of Density Structures in Magnetohydrodynamic Turbulence

Density fluctuations produced by supersonic turbulence are of great importance to astrophysical chemical models. A property of these density fluctuations is that the two-point correlation function decreases with increasing scale separation. The relation between the density decorrelation length-scale ($L_{\rm dec}$) and the turbulence driving scale ($L_{\rm drive}$) determines how turbulence affects the density and chemical structures in the interstellar medium (ISM), and is a key component for using observations of atomic and molecular tracers to constrain turbulence properties. We run a set of numerical simulations of supersonic magnetohydrodynamic turbulence, driven on varying scales from 1/2.5 to 1/7 the box length, and derive the $L_{\rm dec}-L_{\rm drive}$ relation as a function of driving-scale and the orientation of the line-of-sight (LOS) in respect to the mean magnetic field. We find that $L_{\rm drive}$, $L_{\rm dec}/L_{\rm drive} = 0.231$ when averaging over all LOS. For LOS parallel to the magnetic field the density structures are statistically smaller and the $L_{\rm dec}-L_{\rm drive}$ relation is tighter, with $L_{\rm dec}/L_{\rm drive} = 0.129 \pm 0.011$. We discuss our results in the context of using observations of chemical tracers in the ISM to constrain the dominant turbulence driving scale.