{
  "id": "1605.04637",
  "version": "v1",
  "published": "2016-05-16T02:46:25.000Z",
  "updated": "2016-05-16T02:46:25.000Z",
  "title": "The arithmetic geometry of resonant Rossby wave triads",
  "authors": [
    "Gene S. Kopp"
  ],
  "comment": "19 pages, 3 figures",
  "categories": [
    "math.NT",
    "math-ph",
    "math.AG",
    "math.MP",
    "physics.flu-dyn"
  ],
  "abstract": "Linear wave solutions to the Charney-Hasegawa-Mima partial differential equation with periodic boundary conditions have two physical interpretations: Rossby (atmospheric) waves, and drift (plasma) waves in a tokamak. These waves display resonance in triads. In the case of infinite Rossby deformation radius, the set of resonant triads may be described as the set of integer solutions to a particular homogeneous Diophantine equation, or as the set of rational points on a projective surface. We give a rational parametrization of the smooth points on this surface, answering the question: What are all resonant triads? We also give a fiberwise description, yielding a procedure to answer the question: For fixed $r \\in \\mathbb{Q}$, what are all wavevectors $(x,y)$ that resonate with a wavevector $(a,b)$ with $a/b = r$?",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-16T02:46:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D41",
      "14G05",
      "76B65",
      "86A10",
      "11D45",
      "11G05",
      "11G35",
      "14G25",
      "14M20"
    ],
    "keywords": [
      "resonant rossby wave triads",
      "arithmetic geometry",
      "infinite rossby deformation radius",
      "charney-hasegawa-mima partial differential equation",
      "resonant triads"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}