{
  "abstract": "We investigate the fast-advection limit ($\\varepsilon \\to 0$) of the stochastically forced two-dimensional incompressible Navier-Stokes equations on the torus. Numerical simulations are performed at resolution $N = 128$ for four different forcing shells on both the square torus and a thin torus, with the advection parameter $\\varepsilon$ varied over approximately one decade. We find that the stationary distributions become increasingly concentrated on the lowest Fourier modes as $\\varepsilon \\to 0$, with the energy-to-enstrophy ratio $E/Ω$ and the fraction $R$ of enstrophy in the lowest modes both increasing monotonically. At finite $\\varepsilon$ the degree of concentration depends on the forcing shell through the effective spectral value $B_1/B_0$, in agreement with the condensation bound of Sznitman and Widmayer. Linear extrapolation to $\\varepsilon = 0$ suggests that the limiting values may be forcing-independent, with $B_1/B_0$ governing only the rate of convergence. The same qualitative behaviour persists on the thin torus.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27512",
  "author_total": 1,
  "authors": [
    {
      "name": "Tobias Rohner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0622jtkf5e2y4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27512",
  "fulltext_url": null,
  "id": "0622jtkf5e2y4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27512",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214201605",
  "pdf_url": "https://arxiv.org/pdf/2609.27512",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0622jtkf5e2y4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27512",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27512"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Concentration of Stationary Measures onto Large Scales in the Fast-Advection Limit of the Stochastically Forced Two-Dimensional Navier-Stokes Equations",
  "title_text": "Concentration of Stationary Measures onto Large Scales in the Fast-Advection Limit of the Stochastically Forced Two-Dimensional Navier-Stokes Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/0622jtkf5e2y4",
  "venue": "arXiv",
  "versions": []
}