dorsal/arxiv
View SchemaParametric Autoresonance in Faraday waves
| Authors | Michael Assaf, Baruch Meerson |
|---|---|
| Categories | |
| ArXiv ID | physics/0506026 |
| URL | https://arxiv.org/abs/physics/0506026 |
| DOI | 10.1103/PhysRevE.72.016310 |
Abstract
We develop a theory of parametric excitation of weakly nonlinear standing gravity waves in a tank, which is under vertical vibrations with a slowly time-dependent ("chirped") vibration frequency. We show that, by using a negative chirp, one can excite a steadily growing wave via parametric autoresonance. The method of averaging is employed to derive the governing equations for the primary mode. These equations are solved analytically and numerically, for typical initial conditions, for both inviscid and weakly viscous fluids. It is shown that, when passing through resonance, capture into resonance always occurs when the chirp rate is sufficiently small. The critical chirp rate, above which breakdown of autoresonance occurs, is found for different initial conditions. The autoresonance excitation is expected to terminate at large amplitudes, when the underlying constant-frequency system ceases to exhibit a non-trivial stable fixed point.
{
"annotation_id": "032f379c-ac41-45a1-b008-753a2f0b89b5",
"date_created": "2026-03-02T18:01:00.794000Z",
"date_modified": "2026-03-02T18:01:00.794000Z",
"file_hash": "c8abd0c20f77a9327a1ed4bfcc54e03985f18fe8a58c4397f4aa9f350244ac2e",
"private": false,
"record": {
"abstract": "We develop a theory of parametric excitation of weakly nonlinear standing\ngravity waves in a tank, which is under vertical vibrations with a slowly\ntime-dependent (\"chirped\") vibration frequency. We show that, by using a\nnegative chirp, one can excite a steadily growing wave via parametric\nautoresonance. The method of averaging is employed to derive the governing\nequations for the primary mode. These equations are solved analytically and\nnumerically, for typical initial conditions, for both inviscid and weakly\nviscous fluids. It is shown that, when passing through resonance, capture into\nresonance always occurs when the chirp rate is sufficiently small. The critical\nchirp rate, above which breakdown of autoresonance occurs, is found for\ndifferent initial conditions. The autoresonance excitation is expected to\nterminate at large amplitudes, when the underlying constant-frequency system\nceases to exhibit a non-trivial stable fixed point.",
"arxiv_id": "physics/0506026",
"authors": [
"Michael Assaf",
"Baruch Meerson"
],
"categories": [
"physics.flu-dyn",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.72.016310",
"title": "Parametric Autoresonance in Faraday waves",
"url": "https://arxiv.org/abs/physics/0506026"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "fa087fff-d45f-4d9a-9a4d-0f8120252703",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}