Unstable surface waves in running water
| dc.creator | Hur, Vera Mikyoung | |
| dc.creator | Lin, Zhiwu | |
| dc.date | 2007-08-03 | |
| dc.date | 2007-11-28 | |
| dc.date.accessioned | 2026-07-07T08:45:12Z | |
| dc.date.available | 2026-07-07T08:45:12Z | |
| dc.description | We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for a general class of shear flows with inflection points and the maximal unstable wave number is found. Comparison to the rigid-wall setting testifies that free surface has a destabilizing effect. For a class of unstable shear flows, the bifurcation of nontrivial periodic traveling waves of small-amplitude is demonstrated at any wave number. We show the linear instability of small nontrivial waves bifurcated at an unstable wave number of the background shear flow. The proof uses a new formulation of the linearized water-wave problem and a perturbation argument. An example of the background shear flow of unstable small-amplitude periodic traveling waves is constructed for an arbitrary vorticity strength and for an arbitrary depth, illustrating that vorticity has a subtle influence on the stability of water waves. | |
| dc.description | 61 pages. Revised | |
| dc.identifier | https://arxiv.org/abs/0708.0541 | |
| dc.identifier | http://arxiv.org/abs/0708.0541 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142898 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Unstable surface waves in running water | |
| dc.type | text |