{
  "id": "1811.03304",
  "version": "v1",
  "published": "2018-11-08T07:58:34.000Z",
  "updated": "2018-11-08T07:58:34.000Z",
  "title": "Towards a finite-time singularity of the Navier-Stokes equations",
  "authors": [
    "Keith Moffatt",
    "Yoshifumi Kimura"
  ],
  "comment": "37 pages, 28 figures, accepted for publication in Journal of Fluid Mechanics",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "A model is developed describing the approach to a finite-time singularity of the Navier-Stokes equations for two interacting vortices. The model is derived from a combination of the Biot-Savart law and an equation describing the evolution of the vortex core cross-sections. The maximum vorticity is attained within a finite time and increases as the square of the vortex Reynolds number. The manner in which vortex reconnection occurs at the apex of a pyramid, and singularity thereby averted, is described analytically.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-08T07:58:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "navier-stokes equations",
      "finite-time singularity",
      "vortex core cross-sections",
      "vortex reynolds number",
      "vortex reconnection occurs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}