{
  "annotation_id": "3d88d85f-41b4-427e-b22b-33263b873c5b",
  "date_created": "2026-03-02T18:01:11.502000Z",
  "date_modified": "2026-03-02T18:01:11.502000Z",
  "file_hash": "c1f3df898474ad94479909fa942d01110f913ada3b2ae2265d64ce618d30dcf5",
  "private": false,
  "record": {
    "abstract": "A simplified form of the vorticity equation is derived for arbitrary\ncoordinate systems. The present work unifies and extends the previous findings\nthat vorticity is conserved in planar Euler flow, while in axisymmetric Euler\nrings it is the ratio of the vorticity to the distance from the symmetry axis\nthat is conserved. The unifying statement is that in any Euler flow, all\ncomponents of the vorticity tensor of a streamline coordinate system that are\nnormal to the streamline direction are conserved along streamlines. This is\ntrue for both two- and three-dimensional flows, whether the flow is\naxisymmetric or not, with or without swirl. What remains of the nonlinear\nconvective terms in the vorticity equation, after the mathematical\nsimplification, is the Lie derivative of the vorticity tensor with respect to\nfluid velocity. A temporal derivative is defined which, when set to zero,\nexpresses either the continuity or vorticity equation (excluding the viscous\nterm), depending upon the argument supplied to it.",
    "arxiv_id": "physics/0606187",
    "authors": [
      "T. S. Morton"
    ],
    "categories": [
      "physics.flu-dyn"
    ],
    "title": "A simplification of the vorticity equation and an extension of the   vorticity persistence theorem to three dimensions",
    "url": "https://arxiv.org/abs/physics/0606187"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1f0f5f6c-68ea-427e-97e9-a51afbaa2441",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}