A Caltech Library Service

Scaling laws of passive-scalar diffusion in the interstellar medium

Colbrook, Matthew J. and Ma, Xiangcheng and Hopkins, Philip F. and Squire, Jonathan (2017) Scaling laws of passive-scalar diffusion in the interstellar medium. Monthly Notices of the Royal Astronomical Society, 467 (2). pp. 2421-2429. ISSN 0035-8711. doi:10.1093/mnras/stx261.

[img] PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


Passive-scalar 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 passive-scalar 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 large-scale 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 non-Gaussian 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 flow-crossing times.

Item Type:Article
Related URLs:
URLURL TypeDescription
Ma, Xiangcheng0000-0001-8091-2349
Hopkins, Philip F.0000-0003-3729-1684
Squire, Jonathan0000-0001-8479-962X
Additional Information:© 2017 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. Accepted 2017 January 27. Received 2017 January 24; in original form 2016 October 18. Support for MJC was provided by the Caltech Scholars Program/SURF at Caltech and St John's College, Cambridge. Support for PFH & XM was provided by an Alfred P. Sloan Research Fellowship, NASA ATP Grant NNX14AH35G and NSF Collaborative Research Grant #1411920 and CAREER grant #1455342. Support for JS was provided by the Sherman Fairchild foundation, and by the Gordon and Betty Moore Foundation through Grant GBMF5076 to Lars Bildsten, Eliot Quataert and E. Sterl Phinney. Numerical calculations were run on the Caltech compute cluster ‘Zwicky’ (NSF MRI award #PHY-0960291) and allocation TG-AST130039 granted by the Extreme Science and Engineering Discovery Environment (XSEDE) supported by the NSF.
Group:Astronomy Department
Funding AgencyGrant Number
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Gordon and Betty Moore FoundationGBMF5076
St. John's College, CambridgeUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20170428-101904354
Persistent URL:
Official Citation:Matthew J. Colbrook, Xiangcheng Ma, Philip F. Hopkins, Jonathan Squire; Scaling laws of passive-scalar diffusion in the interstellar medium. Mon Not R Astron Soc 2017; 467 (2): 2421-2429. doi: 10.1093/mnras/stx261
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77053
Deposited By: Ruth Sustaita
Deposited On:28 Apr 2017 17:34
Last Modified:15 Nov 2021 17:05

Repository Staff Only: item control page