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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.17416 |
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| _version_ | 1866929554950455296 |
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| author | Ratliff, Daniel J. Trichtchenko, Olga Bridges, Thomas J. |
| author_facet | Ratliff, Daniel J. Trichtchenko, Olga Bridges, Thomas J. |
| contents | For Stokes waves in finite depth within the neighbourhood of the Benjamin-Feir stability transition, there are two families of periodic waves, one modulationally unstable and the other stable. In this paper we show that these two families can be joined by a heteroclinic connection, which manifests in the fluid as a travelling front. By shifting the analysis to the setting of Whitham modulation theory, this front is in wavenumber and frequency space. An implication of this jump is that a permanent frequency downshift of the Stokes wave can occur in the absence of viscous effects. This argument, which is built on a sequence of asymptotic expansions of the phase dynamics, is confirmed via energetic arguments, with additional corroboration obtained by numerical simulations of a reduced model based on the Benney-Roskes equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modulation leading to frequency downshifting of water waves in the vicinity of the Benjamin-Feir transition Ratliff, Daniel J. Trichtchenko, Olga Bridges, Thomas J. Fluid Dynamics For Stokes waves in finite depth within the neighbourhood of the Benjamin-Feir stability transition, there are two families of periodic waves, one modulationally unstable and the other stable. In this paper we show that these two families can be joined by a heteroclinic connection, which manifests in the fluid as a travelling front. By shifting the analysis to the setting of Whitham modulation theory, this front is in wavenumber and frequency space. An implication of this jump is that a permanent frequency downshift of the Stokes wave can occur in the absence of viscous effects. This argument, which is built on a sequence of asymptotic expansions of the phase dynamics, is confirmed via energetic arguments, with additional corroboration obtained by numerical simulations of a reduced model based on the Benney-Roskes equation. |
| title | Modulation leading to frequency downshifting of water waves in the vicinity of the Benjamin-Feir transition |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2410.17416 |