{
  "id": "1607.06437",
  "version": "v1",
  "published": "2016-07-21T19:20:00.000Z",
  "updated": "2016-07-21T19:20:00.000Z",
  "title": "Fluid dynamics in the spirit of Cartan: a coordinate-free formulation of fluid dynamics. Part I: Inviscid equations in inertial and non-inertial frames",
  "authors": [
    "Alberto Scotti"
  ],
  "comment": "Contains an appendix with S.M. Mendes-Da Silva",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "Using Cartan's exterior calculus, we derive a coordinate-free formulation of the Euler equations. These equations are invariant under Galileian transformations, which constitute a global symmetry. With the introduction of an appropriate generalized Coriolis force, these equations become symmetric under general coordinate transformations. We show how exterior calculus simplifies dramatically the derivation of conservation laws. We also discuss the advantage of an exterior calculus formulation with respect to symmetry-preserving discretizations of the equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-21T19:20:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76A02",
      "76U05"
    ],
    "keywords": [
      "fluid dynamics",
      "coordinate-free formulation",
      "inviscid equations",
      "non-inertial frames",
      "exterior calculus formulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}