{
  "abstract": "We study the long-time Fourier distribution of driven passive scalars transported by an incompressible alternating shear flow (the Pierrehumbert flow) subjected to IID random phase shifts, in the regime of strong shear-strength. With a novel and self-contained proof, we establish (i) a quantitative version of the cumulative Batchelor's law; (ii) quantitative negative regularity mixing estimates; and (iii) a strong form of `sparsity' -- unevenness in the distribution of Fourier mass in radial sectors in frequency space. Our method uses the strong shear-strength assumption to handle a purely deterministic scalar driving term.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31241",
  "author_total": 2,
  "authors": [
    {
      "name": "Alex Blumenthal"
    },
    {
      "name": "William Cooperman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/chbmy0zg1ypa1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31241",
  "fulltext_url": null,
  "id": "chbmy0zg1ypa1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31241",
  "language": null,
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  "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",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2206|Fluid Dynamics and Turbulent Flows"
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  "openalex": "W7223404753",
  "pdf_url": "https://arxiv.org/pdf/2610.31241",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/chbmy0zg1ypa1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31241",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31241"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Sparse power spectrum for passive scalars under Pierrehumbert flow",
  "title_text": "Sparse power spectrum for passive scalars under Pierrehumbert flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/chbmy0zg1ypa1",
  "venue": "arXiv",
  "versions": []
}