Nonlinear two-dimensional water waves with arbitrary vorticity
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929481846882304 |
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| author | Ionescu-Kruse, Delia Ivanov, Rossen |
| author_facet | Ionescu-Kruse, Delia Ivanov, Rossen |
| contents | We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed with the aid of the Dirichlet-Neumann operator and the Green function of the Laplace operator in the fluid domain. Moreover, we provide new explicit expressions for both objects.
The field of a point vortex and its interaction with the free surface is studied as an example. In the small-amplitude long-wave Boussinesq and KdV regimes, we obtain appropriate systems of coupled equations for the dynamics of the point vortex and the time evolution of the free surface variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear two-dimensional water waves with arbitrary vorticity Ionescu-Kruse, Delia Ivanov, Rossen Analysis of PDEs Mathematical Physics Pattern Formation and Solitons 35Q31, 35Q53 We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed with the aid of the Dirichlet-Neumann operator and the Green function of the Laplace operator in the fluid domain. Moreover, we provide new explicit expressions for both objects. The field of a point vortex and its interaction with the free surface is studied as an example. In the small-amplitude long-wave Boussinesq and KdV regimes, we obtain appropriate systems of coupled equations for the dynamics of the point vortex and the time evolution of the free surface variables. |
| title | Nonlinear two-dimensional water waves with arbitrary vorticity |
| topic | Analysis of PDEs Mathematical Physics Pattern Formation and Solitons 35Q31, 35Q53 |
| url | https://arxiv.org/abs/2409.00446 |