{
  "abstract": "Intermittency, manifested through anomalous scaling, remains one of the central unresolved problems in turbulence theory, with few analytical approaches extending beyond idealized linear transport models. We introduce a perturbative framework for anomalous scaling in turbulent transport based on multiplier statistics, rather than zero-mode calculations. We demonstrate the approach using a shell model combining deterministic and Kraichnan-like stochastic components. We reduce the problem to the analysis of a stationary Fokker-Planck equation for Kolmogorov multipliers, defined as ratios of successive scalar amplitudes. Its solution yields the invariant measure through a perturbative expansion around a Gaussian distribution. Using the resulting multiplier statistics, we compute explicit anomalous scaling exponents for structure functions of arbitrary order, including odd, even, and non-integer moments. Although demonstrated here for a shell model, the framework suggests a systematic perturbative route toward analytical theories of intermittency in turbulence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys. Rev. Lett. 137, 094002 (2026)",
  "arxiv": "2605.26359",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexei A. Mailybaev"
    },
    {
      "name": "Simon Thalabard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cs1wh79458scy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.26359",
  "fulltext_url": null,
  "id": "cs1wh79458scy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.26359",
  "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/2605.26359",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cs1wh79458scy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2605.26359",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.26359"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Perturbative anomalous exponents from Kolmogorov multipliers",
  "title_text": "Perturbative anomalous exponents from Kolmogorov multipliers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:22Z",
  "url": "https://research.draconitic.com/paper/cs1wh79458scy",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/6qrr-3646",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}