{
  "id": "1612.09009",
  "version": "v1",
  "published": "2016-12-28T23:46:23.000Z",
  "updated": "2016-12-28T23:46:23.000Z",
  "title": "An asymptotic model for the propagation of oceanic internal tides through quasi-geostrophic flow",
  "authors": [
    "Gregory L. Wagner",
    "Gwenael Ferrando",
    "William R. Young"
  ],
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "Starting from the hydrostatic Boussinesq equations, we derive a time-averaged `hydrostatic wave equation' that describes the propagation of inertia-gravity internal waves through quasi-geostrophic flow. The derivation uses a multiple-time-scale asymptotic method to isolate wave field evolution over intervals much longer than a wave period, assumes that the wave field has a well-defined and non-inertial frequency such as that of the mid-latitude semi-diurnal lunar tide, neglects nonlinear wave-wave interactions and makes no restriction on either the background density stratification or the relative spatial scales between the wave field and quasi-geostrophic flow. As a result the hydrostatic wave equation is a reduced model applicable to the propagation of large scale internal tides through the inhomogeneous and moving ocean. A numerical comparison with the linearized and hydrostatic Boussinesq equations demonstrates the validity of the hydrostatic wave equation and illustrates the manners of model failure when the quasi-geostrophic flow is too strong and the wave frequency is too close to inertial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-28T23:46:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasi-geostrophic flow",
      "oceanic internal tides",
      "hydrostatic wave equation",
      "asymptotic model",
      "hydrostatic boussinesq equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}