Self-similarity and recurrence in stability spectra of near-extreme Stokes waves
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910421197258752 |
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| author | Deconinck, Bernard Dyachenko, Sergey A. Semenova, Anastassiya |
| author_facet | Deconinck, Bernard Dyachenko, Sergey A. Semenova, Anastassiya |
| contents | We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree corner at the crest. The stability of these solutions with respect to coperiodic and subharmonic perturbations is studied, using new matrix-free numerical methods. We provide evidence for a plethora of conjectures on the nature of the instabilities as the steepest wave is approached, especially with regards to the self-similar recurrence of the stability spectrum near the origin of the spectral plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15481 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-similarity and recurrence in stability spectra of near-extreme Stokes waves Deconinck, Bernard Dyachenko, Sergey A. Semenova, Anastassiya Fluid Dynamics Mathematical Physics We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree corner at the crest. The stability of these solutions with respect to coperiodic and subharmonic perturbations is studied, using new matrix-free numerical methods. We provide evidence for a plethora of conjectures on the nature of the instabilities as the steepest wave is approached, especially with regards to the self-similar recurrence of the stability spectrum near the origin of the spectral plane. |
| title | Self-similarity and recurrence in stability spectra of near-extreme Stokes waves |
| topic | Fluid Dynamics Mathematical Physics |
| url | https://arxiv.org/abs/2404.15481 |