{
  "id": "1906.06277",
  "version": "v1",
  "published": "2019-06-14T16:32:16.000Z",
  "updated": "2019-06-14T16:32:16.000Z",
  "title": "The origin of localized snakes-and-ladders solutions of plane Couette flow",
  "authors": [
    "Matthew Salewski",
    "John F. Gibson",
    "Tobias M. Schneider"
  ],
  "comment": "5 pages",
  "categories": [
    "physics.flu-dyn",
    "nlin.PS"
  ],
  "abstract": "Spatially localized exact solutions of plane Couette flow are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations. [PRL 104,104501 (2010)]. We demonstrate the mechanism by which these snaking solutions originate from well-known periodic states of the Taylor-Couette system. They are formed by a localized slug of Wavy-Vortex flow that emerges from a background of Taylor vortices via a modulational sideband instability. This mechanism suggests a deep connection between pattern-formation theory and Navier-Stokes flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-14T16:32:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "plane couette flow",
      "localized snakes-and-ladders solutions",
      "simpler pattern-forming partial differential equations",
      "well-known periodic states",
      "modulational sideband instability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}