{
  "id": "1209.3738",
  "version": "v1",
  "published": "2012-09-17T18:06:43.000Z",
  "updated": "2012-09-17T18:06:43.000Z",
  "title": "No steady water waves of small amplitude are supported by a shear flow with still free surface",
  "authors": [
    "Vladimir Kozlov",
    "Nikolay Kuznetsov"
  ],
  "comment": "12 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. It is proved that no small-amplitude waves are supported by a horizontal shear flow whose free surface is still in a coordinate frame such that the flow is time-independent in it. The class of vorticity distributions for which such flows exist includes all positive constant distributions, as well as linear and quadric ones with arbitrary positive coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-17T18:06:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76B15",
      "35Q35"
    ],
    "keywords": [
      "steady water waves",
      "free surface",
      "shear flow",
      "small amplitude",
      "describing steady gravity waves"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1017/jfm.2012.593",
      "journal": "Journal of Fluid Mechanics",
      "year": 2013,
      "month": "Feb",
      "volume": 717,
      "pages": 523
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JFM...717..523K"
    }
  }
}