{
  "abstract": "We present a theoretical model for momentum--scalar coupled turbulence in which both fields undergo anomalous diffusion, described by fractional biharmonic operators of orders $γ/4$ and $α/4$, respectively. Focusing on the long-range external forcing or unforced turbulence, we derive analytical expressions for the kinetic energy spectrum $E_u(k)$, the scalar spectrum $E_s(k)$, and the characteristic wavenumbers $k_K = \\left( \\frac{ε_u^{1/3}}{c_u} \\right)^{1/(γ- 2/3)}$ (reciprocal of Kolmogorov scale) and $k_S = \\left( \\frac{ε_u^{1/3}}{c_s} \\right)^{1/(α- 2/3)}$ (reciprocal of scalar dissipation scale) as functions of $γ$, $α$, turbulent dissipation rate $ε_u$, diffusivities of momentum ($c_u$) and scalar ($c_s$), respectively. An anomalous Schmidt number $Sc_Z = k_0^{γ- α} \\frac{c_u}{c_s}$ is defined to governs the cascade topology. It describes the ratio of diffusion times of scalar and momentum on the minimum wavenumber $k_0$. Superdiffusion ($γ<2$ or $α<2$) is shown to counter-intuitively enlarge $k_K$ and $k_S$, broadening the inertial range. The theory unifies the classical Kolmogorov--Obukhov--Corrsin--Batchelor scalings as special cases when $γ=α=2$, and provides a foundation for understanding non-Fickian transport in complex turbulent systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Transport Phenomena (2026)",
  "arxiv": "2608.23946",
  "author_total": 1,
  "authors": [
    {
      "name": "Wei Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fm5e7tnahhtp9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.23946",
  "fulltext_url": null,
  "id": "fm5e7tnahhtp9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.23946",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2608.23946",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fm5e7tnahhtp9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2608.23946",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.23946"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Momentum-scalar coupled turbulence with anomalous momentum and scalar diffusions. Part 1: Without external force and with long-range external force",
  "title_text": "Momentum-scalar coupled turbulence with anomalous momentum and scalar diffusions. Part 1: Without external force and with long-range external force",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/fm5e7tnahhtp9",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1515/tp-2026-0108",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}