{
  "annotation_id": "b73baf3e-6884-403a-a9e8-04854351b68a",
  "date_created": "2026-03-02T18:01:04.125000Z",
  "date_modified": "2026-03-02T18:01:04.125000Z",
  "file_hash": "12a95275a0f026c86ce2b9c46cd69da5ce9b04828d796b9c2f399e1df3748e98",
  "private": false,
  "record": {
    "abstract": "General stability criterions of two-dimensional inviscid parallel flow are\nobtained analytically for the first time. First, a criterion for stability is\nfound as $\\frac{U\u0027\u0027}{U-U_s}\u003e-\\mu_1$ everywhere in the flow, where $U_s$ is the\nvelocity at inflection point, $\\mu_1$ is eigenvalue of Poincar\\\u0027{e}\u0027s problem.\nSecond, we also prove a principle that the flow is stable, if and only if all\nthe disturbances with $c_r=U_s$ are neutrally stable. Finally, following this\nprinciple, a criterion for instability is found as $\\frac{U\u0027\u0027}{U-U_s}\u003c-\\mu_1$\neverywhere in the flow. These results extend the former theorems obtained by\nRayleigh, Tollmien and Fj{\\o}rtoft and will lead future works to investigate\nthe mechanism of hydrodynamic instability.",
    "arxiv_id": "physics/0512208",
    "authors": [
      "Liang Sun"
    ],
    "categories": [
      "physics.flu-dyn",
      "astro-ph",
      "physics.ao-ph",
      "physics.geo-ph"
    ],
    "title": "General stability criterion of two-dimensional inviscid parallel flow",
    "url": "https://arxiv.org/abs/physics/0512208"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ce149bcd-d9d3-43cf-854f-a8ed28191949",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}