{
  "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 ($M_{\\rm rms}\\lesssim 1$), and another to the highly supersonic regime, with ($M_{\\rm rms}\\ge 3$). 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03945",
  "author_total": 4,
  "authors": [
    {
      "name": "Shadab Alam"
    },
    {
      "name": "Georgy Zinchenko"
    },
    {
      "name": "Christoph Federrath"
    },
    {
      "name": "Jörg Schumacher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8kbjdske6q4fy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03945",
  "fulltext_url": null,
  "id": "8kbjdske6q4fy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03945",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Fluid Dynamics and Turbulent Flows"
    ]
  ],
  "openalex": "W7208792389",
  "pdf_url": "https://arxiv.org/pdf/2609.03945",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8kbjdske6q4fy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2609.03945",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03945"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Mach-number-dependent dissipative anomaly in isothermal compressible turbulence",
  "title_text": "Mach-number-dependent dissipative anomaly in isothermal compressible turbulence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:31Z",
  "url": "https://research.draconitic.com/paper/8kbjdske6q4fy",
  "venue": "arXiv",
  "versions": []
}