Scaling laws of passivescalar diffusion in the interstellar medium
Abstract
Passivescalar mixing (metals, molecules, etc.) in the turbulent interstellar medium (ISM) is critical for abundance patterns of stars and clusters, galaxy and star formation, and cooling from the circumgalactic medium. However, the fundamental scaling laws remain poorly understood in the highly supersonic, magnetized, shearing regime relevant for the ISM. We therefore study the full scaling laws governing passivescalar transport in idealized simulations of supersonic turbulence. Using simple phenomenological arguments for the variation of diffusivity with scale based on Richardson diffusion, we propose a simple fractional diffusion equation to describe the turbulent advection of an initial passive scalar distribution. These predictions agree well with the measurements from simulations, and vary with turbulent Mach number in the expected manner, remaining valid even in the presence of a largescale shear flow (e.g. rotation in a galactic disc). The evolution of the scalar distribution is not the same as obtained using simple, constant 'effective diffusivity' as in Smagorinsky models, because the scale dependence of turbulent transport means an initially Gaussian distribution quickly develops highly nonGaussian tails. We also emphasize that these are mean scalings that apply only to ensemble behaviours (assuming many different, random scalar injection sites): individual Lagrangian 'patches' remain coherent (poorly mixed) and simply advect for a large number of turbulent flowcrossing times.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 May 2017
 DOI:
 10.1093/mnras/stx261
 arXiv:
 arXiv:1610.06590
 Bibcode:
 2017MNRAS.467.2421C
 Keywords:

 diffusion;
 methods: analytical;
 methods: numerical;
 stars: formation;
 ISM: evolution;
 galaxies: formation;
 Astrophysics  Astrophysics of Galaxies;
 Mathematics  Numerical Analysis;
 Physics  Computational Physics;
 Physics  Fluid Dynamics;
 85A05;
 85A30;
 85A35
 EPrint:
 accepted by MNRAS, 9 pages, 5 figures, comments welcome