{
  "abstract": "We construct a divergence-free velocity field $\\mathbf{u}(\\mathbf{x},t)$ on $\\mathbb{T}^{n}$ that is a genuine function of position and carries both defining properties of turbulent transport: Richardson pair dispersion and a dissipative anomaly. No synthetic field has carried both, because the frame that gives the first destroys the field the second requires. The key is a dichotomy: deforming a spectrally localised pattern smears it across scales, whereas pushing its generating centres forward and re-convolving leaves the spectral envelope exactly invariant --- so transporting the eddy centres preserves both cascade and frame. In the field the finite-size Lyapunov exponent obeys $ζ(R)=h(R)-1$ threshold by threshold within the scaling range, with a sweeping deficit $Δ_{\\rm sw}=+0.038\\pm0.019$, consistent with zero, against $+0.091\\pm0.019$ for the frozen field on the same data, a gap that doubles at Navier--Stokes intermittency. Companion papers prove that this family shows Richardson dispersion and a dissipative anomaly (Fefferman and Mayboroda 2026), and that a scalar advected by this flow obeys Yaglom's relation (De Lellis 2026), at small Kubo number. Trajectories forget their starting point as the smallest eddy is removed: the median separation of pairs released from one point with independent Brownian kicks varies as $κ_{p}^{0.0333\\pm0.0038}$ over 22 decades of particle diffusivity, against $κ_{p}^{1/2}$ for a smooth control. A scalar in the same field closes the exact scale-by-scale variance budget, four independently measured terms balancing the dissipation to 15\\% over 1.2 decades with no adjustable constant, and reaches its inertial--convective asymptote $S_{L}=-χr$ to $0.9995\\pm0.0018$ once the measured diffusive transfer is restored, while under an imposed mean gradient $χ$ changes by 14\\% over a factor 5.8 in $κ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07121",
  "author_total": 5,
  "authors": [
    {
      "name": "Raul Jimenez"
    },
    {
      "name": "Svitlana Mayboroda"
    },
    {
      "name": "Camillo de Lellis"
    },
    {
      "name": "David N. Spergel"
    },
    {
      "name": "Max Engelstein"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/73az2y0ag8wn9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07121",
  "fulltext_url": null,
  "id": "73az2y0ag8wn9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07121",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.GA"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "arxiv",
      "physics.plasm-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07121",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/73az2y0ag8wn9.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2611.07121",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07121"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.GA",
      "subfield": "galaxies"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.plasm-ph",
      "subfield": "plasma"
    }
  ],
  "title": "Eddies that ride the flow: a model of turbulence with Richardson dispersion and anomalous dissipation",
  "title_text": "Eddies that ride the flow: a model of turbulence with Richardson dispersion and anomalous dissipation",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/73az2y0ag8wn9",
  "venue": "arXiv",
  "versions": []
}