{
  "abstract": "The equations of fluid motion are known; retaining their physics after removing most degrees of freedom remains a fundamental problem. Closure must preserve the geometry of the dynamics it replaces. We introduce Symplectic Geometric Closure (SGC), a prognostic stochastic field theory carrying Euler's Hamiltonian, area-preserving transport into two-dimensional and $β$-plane turbulence. SGC couples resolved vorticity to a hidden stochastic reservoir. The coupling conserves augmented enstrophy while permitting bidirectional energy transfer. This yields a compact random attractor in the hyperviscous Navier--Stokes--$β$ realization. Numerically, SGC sustains jets, vortices and filaments in high-Reynolds-number turbulence with high fidelity to filtered DNS at an inertial-range cutoff, preserving geometric identities to machine precision. The induced transport folds, stretches and rearranges vorticity: cross-gradient coupling selects interactions through resolved--reservoir gradient misalignment, retaining geometric selectivity and memory. The same geometry addresses spurious sweeping decorrelation, a longstanding obstacle to Eulerian closure. The interaction vertex excludes uniform translation and is Random Galilean compatible. Eliminating the reservoir generates finite memory, stochastic backscatter and a Dyson--Volterra equation for the dressed propagator. Its one-loop, line-renormalized self-energy reproduces Kraichnan-type Direct-Interaction Approximation architecture with fourth-order infrared suppression of sweeping. Deformation-controlled memory and conservative triad constraints yield the $k^{-5/3}$ inverse-energy and $k^{-3}$ forward-enstrophy cascades under standard assumptions. SGC thus realizes Kraichnan's program through Eulerian field dynamics, opening a route to data-driven closures that learn admissible geometric interactions rather than unconstrained forces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.06606",
  "author_total": 2,
  "authors": [
    {
      "name": "Mickaël D. Chekroun"
    },
    {
      "name": "James C. McWilliams"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e427fgr3sy2c1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.06606",
  "fulltext_url": null,
  "id": "e427fgr3sy2c1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.06606",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Fluid Dynamics and Turbulent Flows"
    ]
  ],
  "openalex": "W7202128404",
  "pdf_url": "https://arxiv.org/pdf/2608.06606",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e427fgr3sy2c1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2608.06606",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.06606"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades",
  "title_text": "A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/e427fgr3sy2c1",
  "venue": "arXiv",
  "versions": []
}