{
  "abstract": "We study the normal-mode stability of a flat interface between compressible Euler flow in the air and incompressible Euler flow in the water, including gravity and surface tension. The base state is quiescent water beneath a hydrostatic, constant-entropy shear flow $U(z)$ with $U(0)=0$, so the atmosphere is neutrally stratified. For a small ratio $\\varepsilon$ of the air density at the interface to the water density, and for uniformly subsonic wave-relative flow, we establish a compressible analog of the critical-layer instability of Miles, extending the rigorous incompressible theory of Bühler, Shatah, Walsh, and Zeng. For a real phase speed $c_r$, the singular coefficient at a regular critical level $U(z_c)=c_r$ has a residue proportional to $Q=U''+gU'/a^2=\\barρ_0(U'/\\barρ_0)'$, with gravitational acceleration $g$, sound speed $a$, and normalized base-state air density $\\barρ_0$. Thus the gradient of specific vorticity replaces the curvature $U''$ of the incompressible theory. We prove a limiting absorption principle at regular, non-resonant phase speeds and a residue formula for the imaginary part of the boundary value $Z_{\\mathrm a}^+(k,c_r)$ of the air-side pressure response at wavenumber $k>0$. Let $c_k>0$ be the phase speed of the free gravity-capillary wave. If $\\mathrm{Im}\\,Z_{\\mathrm a}^+(k,c_k)>0$, then, for sufficiently small $\\varepsilon$, the dispersion relation has exactly one unstable root $c_\\varepsilon$ in a neighborhood of $c_k$ that does not depend on $\\varepsilon$. A sufficient condition is $Q\\le0$ at every critical level and $Q<0$ at the highest one. As the Mach number $M\\to0$, $Z_{\\mathrm a}^+$ converges to its incompressible counterpart at rate $O(M^2)$. Under the corresponding incompressible sign condition, the unstable root satisfies $|c_\\varepsilon(M)-c_\\varepsilon(0)|\\le C\\varepsilon M^2$ with $C$ independent of $\\varepsilon$ and $M$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02628",
  "author_total": 1,
  "authors": [
    {
      "name": "Tianyi Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/12c8xfarnq4pf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02628",
  "fulltext_url": null,
  "id": "12c8xfarnq4pf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02628",
  "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.AP"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Fluid Dynamics and Turbulent Flows"
    ]
  ],
  "openalex": "W7220404043",
  "pdf_url": "https://arxiv.org/pdf/2610.02628",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/12c8xfarnq4pf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.02628",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02628"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "A Compressible Miles Instability for Wind-Wave Generation in a Neutral Atmosphere",
  "title_text": "A Compressible Miles Instability for Wind-Wave Generation in a Neutral Atmosphere",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/12c8xfarnq4pf",
  "venue": "arXiv",
  "versions": []
}