The slope of the power spectrum of the density field in isothermal supersonic compressible turbulence
Abstract
The power spectrum (PS) of the density field in supersonic turbulence is a fundamental quantity that characterizes the statistical properties of the structures formed in compressible flows. It is also widely used to estimate the Mach number in the interstellar medium from simulation-derived relations. In this paper, we provide a first quantitative explanation for the evolution of the slope of the PS of the density field with the Mach number in homogeneous isotropic isothermal turbulence using a time-invariant quantity derived by Chandrasekhar, S. (1951, Proc. R. Soc. Lond. Ser. A, 210, 18). For simulated turbulent flows, the model reproduces the measured slopes for different widths of the inertial range and density variances very well. Our model also provides a comprehensive interpretation of the characteristic slopes of the PS of the density field measured in the interstellar medium. Based on these results, we stress that the Mach number cannot be reliably deduced from the slope of the PS of the density field. In closing, we discuss a resolution criterion that must be fulfilled to correctly simulate a turbulent flow with a given density PS slope.
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BibTeX
@article{dumond2026slope,
title = {{The slope of the power spectrum of the density field in isothermal supersonic compressible turbulence}},
author = {Pierre Dumond and Jérémy Fensch and Gilles Chabrier and Noé Brucy},
journal = {Astronomy \& Astrophysics - A\&A},
year = {2026},
month = may,
doi = {10.1051/0004-6361/202659228},
eprint = {2605.03924},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05736664v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - The slope of the power spectrum of the density field in isothermal supersonic compressible turbulence
AU - Pierre Dumond
AU - Jérémy Fensch
AU - Gilles Chabrier
AU - Noé Brucy
PY - 2026
DA - 2026/05/28
JO - Astronomy & Astrophysics - A&A
DO - 10.1051/0004-6361/202659228
UR - https://hal.science/hal-05736664v1
AB - The power spectrum (PS) of the density field in supersonic turbulence is a fundamental quantity that characterizes the statistical properties of the structures formed in compressible flows. It is also widely used to estimate the Mach number in the interstellar medium from simulation-derived relations. In this paper, we provide a first quantitative explanation for the evolution of the slope of the PS of the density field with the Mach number in homogeneous isotropic isothermal turbulence using a time-invariant quantity derived by Chandrasekhar, S. (1951, Proc. R. Soc. Lond. Ser. A, 210, 18). For simulated turbulent flows, the model reproduces the measured slopes for different widths of the inertial range and density variances very well. Our model also provides a comprehensive interpretation of the characteristic slopes of the PS of the density field measured in the interstellar medium. Based on these results, we stress that the Mach number cannot be reliably deduced from the slope of the PS of the density field. In closing, we discuss a resolution criterion that must be fulfilled to correctly simulate a turbulent flow with a given density PS slope.
SN - 0004-6361
SN - 1432-0746
ER -