{
  "annotation_id": "52c2311a-fbea-4cd3-9486-8e441a4bd229",
  "date_created": "2026-03-02T18:00:29.404000Z",
  "date_modified": "2026-03-02T18:00:29.404000Z",
  "file_hash": "331355eb5076e8a5d3c904696dddc9eac3c7cd8eb63aaa3599700fd3bb660b44",
  "private": false,
  "record": {
    "abstract": "A simple model is presented for the formation of rolling grain ripples on a\nflat sand bed by the oscillatory flow generated by a surface wave. An equation\nof motion is derived for the individual ripples, seen as \"particles\", on the\notherwise flat bed. The model account for the initial apperance of the ripples,\nthe subsequent coarsening of the ripples and the final equilibrium state. The\nmodel is related to physical parameters of the problem, and an analytical\napproximation for the equilibrium spacing of the ripples is developed. It is\nfound that the spacing between the ripples scale with the square-root of the\nnon-dimensional shear stress (the Shields parameter) on a flat bed. The results\nof the model are compared with measurements, and reasonable agreement between\nthe model and the measurements is demonstrated.",
    "arxiv_id": "patt-sol/9909006",
    "authors": [
      "K. H. Andersen"
    ],
    "categories": [
      "patt-sol",
      "cond-mat.stat-mech",
      "nlin.PS",
      "physics.flu-dyn"
    ],
    "title": "A Particle Model of Rolling Grain Ripples Under Waves",
    "url": "https://arxiv.org/abs/patt-sol/9909006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f4b414fa-1f15-41de-a65b-61d89856a977",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}