dorsal/arxiv
View SchemaStability of Plane-Parallel Vibrational Flow In a Two-Layer System
| Authors | Mikhail V. Khenner, Dmitrii V. Lyubimov, Tatyana S. Belozerova, Bernard Roux |
|---|---|
| Categories | |
| ArXiv ID | physics/9908007 |
| URL | https://arxiv.org/abs/physics/9908007 |
| DOI | 10.1016/S0997-7546(99)00143-0 |
Abstract
The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillation. There exists a simple basic state which corresponds to the unperturbed interface and plane-parallel unsteady counter flows; the properties of this state are examined. A linear stability problem for the interface is formulated and solved a) for both inviscid and b) for both viscous fluids. A transformation is found which reduces the linear stability problem under inviscid approximation to the Mathieu equation. The parametric resonant regions of instability associated with the intensification of capillary-gravity waves at the interface are examined and the results are compared to those found in the viscous case in a fully numerical investigation.
{
"annotation_id": "20b9c534-52f6-42ae-b3ca-48faf4a5cadf",
"date_created": "2026-03-02T18:01:24.837000Z",
"date_modified": "2026-03-02T18:01:24.837000Z",
"file_hash": "22b209776d4605413d1375e1878d405086d903e2b939a06aabf972e0e184776c",
"private": false,
"record": {
"abstract": "The stability of the interface separating two immiscible incompressible\nfluids of different densities and viscosities is considered in the case of\nfluids filling a cavity which performs horizontal harmonic oscillation. There\nexists a simple basic state which corresponds to the unperturbed interface and\nplane-parallel unsteady counter flows; the properties of this state are\nexamined. A linear stability problem for the interface is formulated and solved\na) for both inviscid and b) for both viscous fluids. A transformation is found\nwhich reduces the linear stability problem under inviscid approximation to the\nMathieu equation. The parametric resonant regions of instability associated\nwith the intensification of capillary-gravity waves at the interface are\nexamined and the results are compared to those found in the viscous case in a\nfully numerical investigation.",
"arxiv_id": "physics/9908007",
"authors": [
"Mikhail V. Khenner",
"Dmitrii V. Lyubimov",
"Tatyana S. Belozerova",
"Bernard Roux"
],
"categories": [
"physics.flu-dyn",
"physics.comp-ph"
],
"doi": "10.1016/S0997-7546(99)00143-0",
"title": "Stability of Plane-Parallel Vibrational Flow In a Two-Layer System",
"url": "https://arxiv.org/abs/physics/9908007"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "19271973-1b60-4c59-a095-9789fef553ed",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}