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The distribution of density in supersonic turbulence

Squire, Jonathan and Hopkins, Philip F. (2017) The distribution of density in supersonic turbulence. Monthly Notices of the Royal Astronomical Society, 471 (3). pp. 3753-3767. ISSN 0035-8711. doi:10.1093/mnras/stx1817.

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We propose a model for the statistics of the mass density in supersonic turbulence, which plays a crucial role in star formation and the physics of the interstellar medium (ISM). The model is derived by considering the density to be arranged as a collection of strong shocks of width ∼M^(-2), where M is the turbulent Mach number. With two physically motivated parameters, the model predicts all density statistics for M > 1 turbulence: the density probability distribution and its intermittency (deviation from lognormality), the density variance–Mach number relation, power spectra and structure functions. For the proposed model parameters, reasonable agreement is seen between model predictions and numerical simulations, albeit within the large uncertainties associated with current simulation results. More generally, the model could provide a useful framework for more detailed analysis of future simulations and observational data. Due to the simple physical motivations for the model in terms of shocks, it is straightforward to generalize to more complex physical processes, which will be helpful in future more detailed applications to the ISM. We see good qualitative agreement between such extensions and recent simulations of non-isothermal turbulence.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Squire, Jonathan0000-0001-8479-962X
Hopkins, Philip F.0000-0003-3729-1684
Additional Information:© 2017 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. Accepted 2017 July 17. Received 2017 July 14; in original form 2017 February 24. Published: 19 July 2017. It is a pleasure to thank A. Beresnyak, B. Burkhart and A. Schekochihin, as well as the anonymous Referee, for helpful comments and discussion. JS was funded in part by the Gordon and Betty Moore Foundation through Grant GBMF5076 to Lars Bildsten, Eliot Quataert and E. Sterl Phinney. Support for PFH was provided by NASA Astrophysics Theory Grant NNX14AH35G & National Science Foundation Collaborative Research Grant #1411920 and CAREER grant #1455342. Numerical calculations were run on Caltech cluster ‘Zwicky’ (NSF MRI award #PHY-0960291) and XSEDE allocation TG-AST130039 supported by the NSF.
Group:TAPIR, Walter Burke Institute for Theoretical Physics, Astronomy Department
Funding AgencyGrant Number
Gordon and Betty Moore FoundationGBMF5076
Subject Keywords:shock waves – turbulence – ISM: kinematics and dynamics – galaxies: star formation
Issue or Number:3
Record Number:CaltechAUTHORS:20170921-132842035
Persistent URL:
Official Citation:Jonathan Squire, Philip F. Hopkins; The distribution of density in supersonic turbulence, Monthly Notices of the Royal Astronomical Society, Volume 471, Issue 3, 1 November 2017, Pages 3753–3767,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81690
Deposited By: Tony Diaz
Deposited On:21 Sep 2017 21:14
Last Modified:15 Nov 2021 19:45

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