{
  "abstract": "We study the spectral instability of small-amplitude Stokes waves in finite-depth flows with constant vorticity. A center-manifold reduction and the periodic Evans function give two explicit indices, one for long-wave instability near the origin and the other for an order-two resonance away from the origin. We prove instability when the low-frequency index is positive or the high-frequency index is nonzero, and obtain the leading expansions of the unstable spectral points. At low frequency, first- and second-order monodromy coefficients determine the leading figure-eight curve. At high frequency, we prove that the resonance exists uniquely and derive a limiting ellipse. An algebraic identity expresses the high-frequency index as a positive factor times the square of a real coupling coefficient. Thus every parameter pair with nonzero coupling gives high-frequency instability. The explicit formulas also permit a comparison of the two criteria in the parameter plane.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04509",
  "author_total": 3,
  "authors": [
    {
      "name": "Ting-Yang Hsiao"
    },
    {
      "name": "Vera Mikyoung Hur"
    },
    {
      "name": "Zhao Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bzr0a7j8nspdd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04509",
  "fulltext_url": null,
  "id": "bzr0a7j8nspdd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04509",
  "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",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04509",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bzr0a7j8nspdd.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04509",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04509"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Unstable Stokes waves in constant vorticity flows of finite depth",
  "title_text": "Unstable Stokes waves in constant vorticity flows of finite depth",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/bzr0a7j8nspdd",
  "venue": "arXiv",
  "versions": []
}