{
  "id": "1603.09563",
  "version": "v1",
  "published": "2016-03-31T12:51:36.000Z",
  "updated": "2016-03-31T12:51:36.000Z",
  "title": "A generalization of vortex lines",
  "authors": [
    "Marian Fecko"
  ],
  "comment": "8 pages, 3 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "physics.flu-dyn"
  ],
  "abstract": "Helmholtz theorem states that, in ideal fluid, vortex lines move with the fluid. Another Helmholtz theorem adds that strength of a vortex tube is constant along the tube. The lines may be regarded as integral surfaces of an 1-dimensional integrable distribution (given by the vorticity 2-form). In general setting of theory of integral invariants, due to Poincare and Cartan, one can find $d$-dimensional integrable distribution whose integral surfaces show both properties of vortex lines: they move with (abstract) fluid and, for appropriate generalization of vortex tube, strength of the latter is constant along the tube.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-31T12:51:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalization",
      "integral surfaces",
      "vortex tube",
      "vortex lines move",
      "helmholtz theorem adds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160309563F"
    }
  }
}