{
  "annotation_id": "8479e23d-7f66-4298-bf6b-38d51aa3e944",
  "date_created": "2026-03-02T18:01:14.147000Z",
  "date_modified": "2026-03-02T18:01:14.147000Z",
  "file_hash": "f55f3b4f5a4debe19b4018fcfd89ba5c7c90be5706eaadb850bf8b707829035c",
  "private": false,
  "record": {
    "abstract": "Marginally unstable Holmboe modes for smooth density and velocity profiles\nare studied. For a large family of flows and stratification that exhibit\nHolmboe instability, we show that the modes with phase velocity equal to the\nmaximum or the minimum velocity of the shear are marginally unstable. This\nallows us to determine the critical value of the control parameter R\n(expressing the ratio of the velocity variation length scale to the density\nvariation length scale) that Holmboe instability appears R=2. We then examine\nsystems for which the parameter R is very close to this critical value. For\nthis case we derive an analytical expression for the dispersion relation of the\ncomplex phase speed c(k) in the unstable region. The growth rate and the width\nof the region of unstable wave numbers has a very strong (exponential)\ndependence on the deviation of R from the critical value. Two specific examples\nare examined and the implications of the results are discussed.",
    "arxiv_id": "physics/0610258",
    "authors": [
      "Alexandros Alexakis"
    ],
    "categories": [
      "physics.flu-dyn",
      "physics.geo-ph"
    ],
    "doi": "10.1063/1.2730545",
    "title": "Marginally unstable Holmboe modes",
    "url": "https://arxiv.org/abs/physics/0610258"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "142bb25f-6734-41c0-a724-419aaba9b763",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}