{
  "annotation_id": "d288e240-9e93-481f-8fb8-e73651567830",
  "date_created": "2026-03-02T18:01:14.574000Z",
  "date_modified": "2026-03-02T18:01:14.574000Z",
  "file_hash": "ad8586428b6cd975d08c3bac49079f61dc603d0ddcd1e76aa1784a3f30a692ba",
  "private": false,
  "record": {
    "abstract": "We adapt the statistical mechanics of the shallow-water equations to the case\nwhere the flow is forced at small scales. We assume that the statistics of\nforcing is encoded in a prior potential vorticity distribution which replaces\nthe specification of the Casimir constraints in the case of freely evolving\nflows. This determines a generalized entropy functional which is maximized by\nthe coarse-grained PV field at statistical equilibrium. Relaxation equations\ntowards equilibrium are derived which conserve the robust constraints (energy,\nmass and circulation) and increase the generalized entropy.",
    "arxiv_id": "physics/0611165",
    "authors": [
      "P. H. Chavanis",
      "B. Dubrulle"
    ],
    "categories": [
      "physics.flu-dyn"
    ],
    "doi": "10.1016/j.crhy.2006.01.007",
    "journal_ref": "C. R. Physique, 7, 422 (2006)",
    "title": "Statistical mechanics of the shallow-water system with a prior potential   vorticity distribution",
    "url": "https://arxiv.org/abs/physics/0611165"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f730ba23-9f45-41d7-8853-1369f2ea32a5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}