dorsal/arxiv
View SchemaGeneral stability criteria for inviscid rotating flow
| Authors | Liang Sun |
|---|---|
| Categories | |
| ArXiv ID | physics/0603177 |
| URL | https://arxiv.org/abs/physics/0603177 |
| DOI | 10.1088/0143-0807/28/5/012 |
| Journal | Eur.J.Phys.28:889-896,2007 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
The general stability criteria of inviscid Taylor-Couette flows with angular velocity $\Omega(r)$ are obtained analytically. First, a necessary instability criterion for centrifugal flows is derived as $\xi'(\Omega-\Omega_s)<0$ (or $\xi'/(\Omega-\Omega_s)<0$) somewhere in the flow field, where $\xi$ is the vorticitiy of profile and $\Omega_s$ is the angular velocity at the inflection point $\xi'=0$. Second, a criterion for stability is found as $-(\mu_1+1/r_2)<f(r)=\frac{\xi'}{\Omega-\Omega_s}<0$, where $\mu_1$ is the smallest eigenvalue. The new criteria are the analogues of the criteria for parallel flows, which are special cases of Arnol'd's nonlinear criteria. Specifically, Pedley's cirterion is proved to be an special case of Rayleigh's criterion. Moreover, the criteria for parallel flows can also be derived from those for the rotating flows. These results extend the previous theorems and would intrigue future research on the mechanism of hydrodynamic instability.
{
"annotation_id": "22bd82c3-2e86-42d6-bdaa-b75abd0195a0",
"date_created": "2026-03-02T18:01:07.852000Z",
"date_modified": "2026-03-02T18:01:07.852000Z",
"file_hash": "26b828757c3ec45b7986e1b7d940ca93b0fbd3f30d917f1c2945da18bba73680",
"private": false,
"record": {
"abstract": "The general stability criteria of inviscid Taylor-Couette flows with angular\nvelocity $\\Omega(r)$ are obtained analytically. First, a necessary instability\ncriterion for centrifugal flows is derived as $\\xi\u0027(\\Omega-\\Omega_s)\u003c0$ (or\n$\\xi\u0027/(\\Omega-\\Omega_s)\u003c0$) somewhere in the flow field, where $\\xi$ is the\nvorticitiy of profile and $\\Omega_s$ is the angular velocity at the inflection\npoint $\\xi\u0027=0$. Second, a criterion for stability is found as\n$-(\\mu_1+1/r_2)\u003cf(r)=\\frac{\\xi\u0027}{\\Omega-\\Omega_s}\u003c0$, where $\\mu_1$ is the\nsmallest eigenvalue. The new criteria are the analogues of the criteria for\nparallel flows, which are special cases of Arnol\u0027d\u0027s nonlinear criteria.\nSpecifically, Pedley\u0027s cirterion is proved to be an special case of Rayleigh\u0027s\ncriterion. Moreover, the criteria for parallel flows can also be derived from\nthose for the rotating flows. These results extend the previous theorems and\nwould intrigue future research on the mechanism of hydrodynamic instability.",
"arxiv_id": "physics/0603177",
"authors": [
"Liang Sun"
],
"categories": [
"physics.flu-dyn",
"astro-ph",
"physics.ao-ph"
],
"doi": "10.1088/0143-0807/28/5/012",
"journal_ref": "Eur.J.Phys.28:889-896,2007",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "General stability criteria for inviscid rotating flow",
"url": "https://arxiv.org/abs/physics/0603177"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "4c069b5d-d192-44ab-82a6-72c748198903",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}