{
  "annotation_id": "acfa152c-07af-47c5-8175-42c11b6282d1",
  "date_created": "2026-03-02T18:00:57.155000Z",
  "date_modified": "2026-03-02T18:00:57.155000Z",
  "file_hash": "07e98da997e7fd9db7283cab2e018282d961d3fbad5d7246b13219ceeebb4430",
  "private": false,
  "record": {
    "abstract": "The lowest order sigma-transformed momentum equation given by Mellor (J.\nPhys. Oceangr. 2003) takes into account a phase-averaged wave forcing based on\nAiry wave theory. This equation is shown to be generally inconsistent due to\ninadequate approximations of the wave motion. Indeed the evaluation of the\nvertical flux of momentum requires an estimation of the pressure $p$ and\ncoordinate transformation function $s$ to first order in parameters that define\nthe large scale evolution of the wave field, such as the bottom slope.\nUnfortunately there is no analytical expression for $p$ and $s$ at that order.\nA numerical correction method is thus proposed and verified. Alternative\ncoordinate transforms that allow a separation of wave and mean flow momenta do\nnot suffer from this inconsistency nor require a numerical estimation of the\nwave forcing. Indeed, the problematic vertical flux is part of the wave\nmomentum flux, thus distinct from the mean flow momentum flux, and not directly\nrelevant to the mean flow evolution.",
    "arxiv_id": "physics/0504097",
    "authors": [
      "Fabrice Ardhuin",
      "Alastair D. Jenkins",
      "Kostas Belibassakis"
    ],
    "categories": [
      "physics.class-ph"
    ],
    "title": "Commentary on `The Three-Dimensional Current and Surface Wave Equations\u0027   by George Mellor",
    "url": "https://arxiv.org/abs/physics/0504097"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cde184b7-3eb6-4872-993c-cb93fdafbe70",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}