{
  "annotation_id": "06e65063-76e6-4b0c-bb85-0f01752048ac",
  "date_created": "2026-03-02T18:00:36.095000Z",
  "date_modified": "2026-03-02T18:00:36.095000Z",
  "file_hash": "ac2af0eb5a3d3f23416a055cb0c474d2adc2b1256c706e61f605b63736184b00",
  "private": false,
  "record": {
    "abstract": "Exact equations are derived that relate velocity structure functions of\narbitrary order with other statistics. \"Exact\" means that no approximations are\nused except that the Navier-Stokes equation and incompressibility condition are\nassumed to be accurate. The exact equations are used to determine the\nstructure-function equations of all orders for locally homogeneous but\nanisotropic turbulence as well as for the locally isotropic case. These\nequations can be used for investigating the approach to local homogeneity and\nto local isotropy as well as the balance of the equations and identification of\nscaling ranges.",
    "arxiv_id": "physics/0102055",
    "authors": [
      "Reginald J. Hill"
    ],
    "categories": [
      "physics.flu-dyn"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Mathematics of Structure-Function Equations of All Orders",
    "url": "https://arxiv.org/abs/physics/0102055"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1e054fa9-d072-4e7a-aee1-2f1491e6363f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}