{
  "id": "2012.12808",
  "version": "v1",
  "published": "2020-12-23T17:12:31.000Z",
  "updated": "2020-12-23T17:12:31.000Z",
  "title": "Wave-current interaction on a free surface",
  "authors": [
    "Dan Crisan",
    "Darryl D. Holm",
    "Oliver D. Street"
  ],
  "comment": "1st version, comments welcome (please email)",
  "categories": [
    "physics.flu-dyn",
    "math-ph",
    "math.DS",
    "math.MP",
    "nlin.CD"
  ],
  "abstract": "The classic evolution equations for potential flow on the free surface of a fluid flow are not closed and the wave dynamics do not cause circulation of the fluid velocity on the free surface. The equations for free-surface motion we derive here are closed and they are not restricted to potential flow. Hence, true wave-current interaction occurs. In particular, the Kelvin-Noether theorem demonstrates that wave activity can induce fluid circulation and vorticity dynamics on the free surface. The wave-current interaction equations introduced here open new vistas for both the deterministic and stochastic analysis of nonlinear waves on free surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-23T17:12:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free surface",
      "true wave-current interaction occurs",
      "potential flow",
      "classic evolution equations",
      "kelvin-noether theorem demonstrates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}