The driving scale -- density decorrelation scale relation in a turbulent
  medium
  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, with
different sonic Mach numbers ($\mathcal{M}_s=4.5, 7$) , and driven on varying
scales (1/2.5, 1/5, 1/7) the box length. We derive the $L_{\rm dec}-L_{\rm
drive}$ relation as a function of Mach number, driving scale, and the
orientation of the line-of-sight (LOS) in respect to the magnetic-field. We
find that the mean ratio $L_{\rm dec}/L_{\rm drive} = 0.19 \pm 0.10$, when
averaged over snapshots, Mach numbers, driving lengths, and the three LOSs. 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 $L_{\rm
dec}/L_{\rm drive} = 0.112 \pm 0.024$. We discuss our results in the context of
using observations of chemical tracers to constrain the dominant turbulence
driving scale in the ISM.
