{
  "id": "2109.09841",
  "version": "v1",
  "published": "2021-09-20T20:58:11.000Z",
  "updated": "2021-09-20T20:58:11.000Z",
  "title": "On the influence of gravity in the dynamics of geophysical flows",
  "authors": [
    "Daniele Del Santo",
    "Francesco Fanelli",
    "Gabriele Sbaiz",
    "Aneta Wróblewska-Kamińska"
  ],
  "comment": "Submitted. arXiv admin note: text overlap with arXiv:2005.04279",
  "categories": [
    "math.AP"
  ],
  "abstract": "In the present paper, we study a multiscale limit for the barotropic Navier-Stokes system with Coriolis and gravitational forces, for vanishing values of the Mach, Rossby and Froude numbers ($\\rm Ma$, $\\rm Ro$ and $\\rm Fr$, respectively). The focus here is on the effects of gravity: albeit remaining in a low stratification regime ${\\rm Ma}/{\\rm Fr}\\,\\rightarrow\\,0$, we consider scaling for the Froude number which go beyond the \"critical\" value $\\rm Fr\\,=\\,\\sqrt{\\rm Ma}$. The rigorous derivation of suitable limiting systems for the various choices of the scaling is shown by means of a compensated compactness argument. Exploiting the precise structure of the gravitational force is the key to get the convergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-20T20:58:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geophysical flows",
      "froude number",
      "gravitational force",
      "barotropic navier-stokes system",
      "low stratification regime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}