{
  "abstract": "Godin (\\textit{J. Fluid Mech.}, vol. 767, 2015, pp. 52--64) showed that compressible fluids in a uniform gravity field support finite-amplitude incompressible wave motions, in which every parcel conserves pressure and density, and constructed exact Gerstner-type surface and edge waves, possibly carried by currents. Using the short-wavelength instability method for compressible flows, we show that these waves are linearly unstable above a critical steepness. The stability of each fluid level reduces to a Floquet problem depending on two parameters: the steepness $\\mathfrak{e}=e^{ka_2}$ and $ν^2=(1-\\mathfrak{e}^2)ν_0^2$, where $ν_0^2=\\cos^2α\\,N_0^2/Ω^2$, $N_0$ is the buoyancy frequency of the hydrostatic reference state, $α$ the inclination of the plane of motion and $Ω=(gk\\cosα)^{1/2}$ the intrinsic orbital frequency. In an isentropic fluid, a level is unstable if $\\mathfrak{e}>1/3$, recovering Leblanc's threshold for Gerstner waves (\\textit{J. Fluid Mech.}, vol. 506, 2004, pp. 245--254) and extending it to compressible surface and edge waves; weak stable stratification lowers the threshold to $\\frac13-\\frac{32}{81}ν_0^2+O(ν_0^4)$. In an isothermal atmosphere, $ν_0^2=κ\\cosα/(kH)$, where $H$ is the pressure scale height. For horizontal wavelengths near $5.5\\,H/\\cosα$, principal subharmonic resonance makes the critical steepness vanish. For the fast airglow wave observed by Hecht et al. (\\textit{J. Geophys. Res.}, vol. 107, 2002, D20, 4444), which Godin interpreted with his solution, the lidar temperature places the layer in which this interpretation is consistent on this resonance, where the critical steepness is typically 0.1 instead of $1/3$. Instability is confined to a layer beneath the free surface of surface waves and to a wedge at the shoreline of edge waves.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35210",
  "author_total": 1,
  "authors": [
    {
      "name": "Christian Puntini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/226kcseqvfn2x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35210",
  "fulltext_url": null,
  "id": "226kcseqvfn2x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35210",
  "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.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.CD"
    ],
    [
      "arxiv",
      "physics.ao-ph"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Fluid Dynamics and Turbulent Flows"
    ]
  ],
  "openalex": "W7223880658",
  "pdf_url": "https://arxiv.org/pdf/2610.35210",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/226kcseqvfn2x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2610.35210",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35210"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "arxiv:physics.ao-ph",
      "subfield": "atmospheric"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Instability of exact finite-amplitude acoustic-gravity waves",
  "title_text": "Instability of exact finite-amplitude acoustic-gravity waves",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/226kcseqvfn2x",
  "venue": "arXiv",
  "versions": []
}