{
  "annotation_id": "bce30a2a-2117-4aea-8d7d-9cbb156042e7",
  "date_created": "2026-03-02T18:00:57.120000Z",
  "date_modified": "2026-03-02T18:00:57.120000Z",
  "file_hash": "ef54f2b56e5b22e3431521bd5cc10704420e0300c7e88be0a368cc41dcd9a734",
  "private": false,
  "record": {
    "abstract": "Threshold amplitude of disturbance for transition to turbulence in a pipe\nPoiseuille flow is investigated. Based on the energy gradient theory, we argued\nthat the transition to turbulence depends on magnitudes of the energy gradient\nof mean flow and the disturbance energy. Furthermore, the threshold disturbance\nenergy required for turbulence transition is expressed as a function of the\ncomplementary angle to the energy angle which also characterizes the behaviour\nof the energy gradient of mean flow. With some mathematical treatments, the\nvariation of the threshold energy of disturbance versus the Reynolds number is\nobtained. Then, it is found for a fixed disturbance frequency that the\nnormalized amplitude of disturbance is scaled by Re with an exponent of -3/2\nfor the transition occurrence in a pipe. This value of exponent agrees well\nwith several recent results reported in the literature. Finally, the mechanism\nof transition to turbulence is suggested for different disturbance levels.",
    "arxiv_id": "physics/0502099",
    "authors": [
      "Hua-Shu Dou",
      "Boo Cheong Khoo",
      "Khoon Seng Yeo"
    ],
    "categories": [
      "physics.flu-dyn"
    ],
    "title": "Threshold amplitudes for transition to turbulence in a pipe",
    "url": "https://arxiv.org/abs/physics/0502099"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c9303475-8a9a-4faa-90d1-614e05cf7983",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}