{
  "annotation_id": "73138166-9776-45b0-a335-b67bdc26b3ea",
  "date_created": "2026-03-02T18:00:28.854000Z",
  "date_modified": "2026-03-02T18:00:28.854000Z",
  "file_hash": "f7378c12cb5f6accb5bbfa6bb31d70f3a6f9199c98d36f60bdad30e2dbb24530",
  "private": false,
  "record": {
    "abstract": "A quasi-potential approximation to the Navier-Stokes equation for low\nviscosity fluids is developed to study pattern formation in parametric surface\nwaves driven by a force that has two frequency components. A bicritical line\nseparating regions of instability to either one of the driving frequencies is\nexplicitly obtained, and compared with experiments involving a frequency ratio\nof 1/2. The procedure for deriving standing wave amplitude equations valid near\nonset is outlined for an arbitrary frequency ratio following a multiscale\nasymptotic expansion of the quasi-potential equations. Explicit results are\npresented for subharmonic response to a driving force of frequency ratio 1/2,\nand used to study pattern selection. Even though quadratic terms are prohibited\nin this case, hexagonal or triangular patterns are found to be stable in a\nrelatively large parameter region, a fact that is in qualitative agreement with\nexperimental results.",
    "arxiv_id": "patt-sol/9701009",
    "authors": [
      "Wenbin Zhang",
      "Jorge Vinals"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1017/S0022112097005387",
    "journal_ref": "J. Fluid Mech. 341, 225 (1997).",
    "title": "Pattern formation in weakly damped parametric surface waves driven by   two frequency components",
    "url": "https://arxiv.org/abs/patt-sol/9701009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f1d37996-eadd-4232-aa02-e4a231c69806",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}