{
  "abstract": "Classical gravity--capillary theory locates the restoring-force crossover, but the wave amplitudes and depths for which energy losses remain measurable depend on the constitutive response and on where viscous dissipation occurs. We develop a weak-loss mechanical-energy model for small-steepness progressive surface waves in memoryless power--law liquids. The full invariant of the leading inviscid strain field yields the deep-water bulk law $\\dd A/\\dd t=-C_tA^n$, with $C_t=4Kk^2(2kΩ)^{n-1}/[(n+1)ρ]$, and the corresponding spatial law $\\dd A/\\dd x=-(C_t/v_g)A^n$. For finite depth we calculate bulk dissipation using a phase- and depth-resolved quadrature $J_n(kh)$ and formulate a separate oscillatory power--law bottom layer. We solve the latter numerically in periodic state, obtaining dimensionless integrated wall losses $I_{0.6}\\simeq0.5432$ and $I_{1.4}\\simeq0.4708$ and recovering the exact Newtonian benchmark $I_1=1/2$. These values make it possible to evaluate conditional finite-depth bulk--wall dominance boundaries rather than only their amplitude exponents. The theory is organized into restoring-force, attenuation, local propagation-length, and dissipation-mechanism regime maps; at fixed wave steepness it additionally predicts a capillary-side maximum of normalized temporal damping for $0<n<2/3$. Grid, time-step, domain, and energy-work checks support the reduced wall calculation, while the coupled bulk--wall approximation still requires independent free-surface numerical or experimental validation. The results provide a reproducible single-fluid reference for subsequent two-liquid interfacial-wave modeling.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34351",
  "author_total": 1,
  "authors": [
    {
      "name": "Sabbir Hassan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aewectz9ws90t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34351",
  "fulltext_url": null,
  "id": "aewectz9ws90t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34351",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.app-ph"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7223924618",
  "pdf_url": "https://arxiv.org/pdf/2610.34351",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aewectz9ws90t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.34351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34351"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.app-ph",
      "subfield": "applied-instrumentation"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Amplitude-Dependent Damping of Gravity--Capillary Waves in Power-Law Fluids: An Energy-Dissipation Framework",
  "title_text": "Amplitude-Dependent Damping of Gravity--Capillary Waves in Power-Law Fluids: An Energy-Dissipation Framework",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/aewectz9ws90t",
  "venue": "arXiv",
  "versions": []
}