Statistical properties of compressible isothermal turbulence from sub- to supersonic conditions

Fuente: arXiv
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Auteurs principaux: Thiesset, F., Federrath, C.
Format: Preprint
Publié: 2025
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author Thiesset, F.
Federrath, C.
author_facet Thiesset, F.
Federrath, C.
contents This paper investigates the statistical properties of isothermal turbulence in both the subsonic and supersonic regimes. The focus is on the influence of the Mach number ($Ma$) and the Reynolds number ($Re$) on both the space-local and scale-dependent fluctuations of relevant gas variables, the density, velocity, their derivatives, and the kinetic energy. We carry out hydrodynamical simulations with explicit viscosity and therefore controlled $Re$. We confirm previous work that the probability density functions (PDFs) of the gas density are approximately log-normal and depend on $Ma$. In contrast, derivatives of the density and velocity field are sensitive to $Re$, with the probability of extreme events growing with $Re$. The PDFs of the density gradient and velocity divergence (dilatation) exhibit increasingly heavy tails with growing $Ma$, signalling enhanced internal intermittency. At sufficiently high $Ma$, the statistics of dilatation are observed to saturate at a level determined solely by $Re$, suggesting that turbulent dilatation becomes limited by viscous effects. We also examine the scale-by-scale distribution of kinetic energy through a compressible form of the Kármán-Howarth-Monin (KHM) equation. In the intermediate range of scales, a marked difference is found between subsonic and supersonic turbulence: while Kolmogorov-like scaling applies in the sub- and transonic regimes, supersonic turbulence aligns more closely with Burgers turbulence predictions. The analysis of individual terms in the KHM equation highlights the role of the pressure-velocity coupling as an additional mechanism for converting kinetic energy from large to small scales. Moreover, the contributions of the KHM terms exhibit non-monotonic behaviour with increasing $Ma$, with dilatational effects becoming more pronounced and acting to oppose the cascade of kinetic energy.
format Preprint
id arxiv_https___arxiv_org_abs_2510_13141
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Statistical properties of compressible isothermal turbulence from sub- to supersonic conditions
Thiesset, F.
Federrath, C.
Fluid Dynamics
Astrophysics of Galaxies
Solar and Stellar Astrophysics
This paper investigates the statistical properties of isothermal turbulence in both the subsonic and supersonic regimes. The focus is on the influence of the Mach number ($Ma$) and the Reynolds number ($Re$) on both the space-local and scale-dependent fluctuations of relevant gas variables, the density, velocity, their derivatives, and the kinetic energy. We carry out hydrodynamical simulations with explicit viscosity and therefore controlled $Re$. We confirm previous work that the probability density functions (PDFs) of the gas density are approximately log-normal and depend on $Ma$. In contrast, derivatives of the density and velocity field are sensitive to $Re$, with the probability of extreme events growing with $Re$. The PDFs of the density gradient and velocity divergence (dilatation) exhibit increasingly heavy tails with growing $Ma$, signalling enhanced internal intermittency. At sufficiently high $Ma$, the statistics of dilatation are observed to saturate at a level determined solely by $Re$, suggesting that turbulent dilatation becomes limited by viscous effects. We also examine the scale-by-scale distribution of kinetic energy through a compressible form of the Kármán-Howarth-Monin (KHM) equation. In the intermediate range of scales, a marked difference is found between subsonic and supersonic turbulence: while Kolmogorov-like scaling applies in the sub- and transonic regimes, supersonic turbulence aligns more closely with Burgers turbulence predictions. The analysis of individual terms in the KHM equation highlights the role of the pressure-velocity coupling as an additional mechanism for converting kinetic energy from large to small scales. Moreover, the contributions of the KHM terms exhibit non-monotonic behaviour with increasing $Ma$, with dilatational effects becoming more pronounced and acting to oppose the cascade of kinetic energy.
title Statistical properties of compressible isothermal turbulence from sub- to supersonic conditions
topic Fluid Dynamics
Astrophysics of Galaxies
Solar and Stellar Astrophysics
url https://arxiv.org/abs/2510.13141