Mach-number-dependent dissipative anomaly in isothermal compressible turbulence
Abstract
Using a comprehensive set of three-dimensional, high-resolution direct numerical simulations, we investigate the existence of a dissipative anomaly in isothermal, homogeneous, isotropic compressible turbulence driven by solenoidal forcing. We find that the total kinetic-energy dissipation rate, as well as its solenoidal and dilatational components, approaches finite asymptotic values with increasing Reynolds number Re. The normalized mean dissipation rates collapse onto two distinct branches: one corresponding to the subsonic and transonic regimes, with root-mean-square Mach numbers (Mrms≲ 1), and another to the highly supersonic regime, with (Mrms≥ 3). This two-branch Mach-number dependence is most pronounced for the total kinetic-energy dissipation. For the solenoidal and dilatational dissipation rate components, the dependence on Re depends in addition on the specific choice of the integral scale and root-mean-square velocity. Despite grid resolutions of up to 20483 points the Reynolds numbers accessible are not sufficiently large to distinguish conclusively between a weak and a strong dissipative anomaly. We substantiate these findings using three complementary approaches: (i) a detailed analysis of the mechanisms responsible for dissipation generation, based on the corresponding dissipation-rate balance equations and their individual production terms; (ii) an investigation of precursors of anomalous dissipation using the Duchon--Robert framework extended to compressible flows; and (iii) a geometrical characterization of regions of intense dissipation. Taken together, these analyses provide consistent evidence for the existence of a dissipative anomaly in isothermal compressible turbulence, while leaving its precise weak or strong character unresolved.
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BibTeX
@misc{alam2026machnumberdependent,
title = {{Mach-number-dependent dissipative anomaly in isothermal compressible turbulence}},
author = {Shadab Alam and Georgy Zinchenko and Christoph Federrath and Jörg Schumacher},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03945},
eprint = {2609.03945},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03945},
}
RIS
TY - UNPB
TI - Mach-number-dependent dissipative anomaly in isothermal compressible turbulence
AU - Shadab Alam
AU - Georgy Zinchenko
AU - Christoph Federrath
AU - Jörg Schumacher
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03945
UR - https://arxiv.org/abs/2609.03945
AB - Using a comprehensive set of three-dimensional, high-resolution direct numerical simulations, we investigate the existence of a dissipative anomaly in isothermal, homogeneous, isotropic compressible turbulence driven by solenoidal forcing. We find that the total kinetic-energy dissipation rate, as well as its solenoidal and dilatational components, approaches finite asymptotic values with increasing Reynolds number Re. The normalized mean dissipation rates collapse onto two distinct branches: one corresponding to the subsonic and transonic regimes, with root-mean-square Mach numbers (M_rms≲ 1), and another to the highly supersonic regime, with (M_rms≥ 3). This two-branch Mach-number dependence is most pronounced for the total kinetic-energy dissipation. For the solenoidal and dilatational dissipation rate components, the dependence on Re depends in addition on the specific choice of the integral scale and root-mean-square velocity. Despite grid resolutions of up to 2048^3 points the Reynolds numbers accessible are not sufficiently large to distinguish conclusively between a weak and a strong dissipative anomaly. We substantiate these findings using three complementary approaches: (i) a detailed analysis of the mechanisms responsible for dissipation generation, based on the corresponding dissipation-rate balance equations and their individual production terms; (ii) an investigation of precursors of anomalous dissipation using the Duchon--Robert framework extended to compressible flows; and (iii) a geometrical characterization of regions of intense dissipation. Taken together, these analyses provide consistent evidence for the existence of a dissipative anomaly in isothermal compressible turbulence, while leaving its precise weak or strong character unresolved.
ER -