Towards eliminating the nonlinear Kelvin wake
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910628410556416 |
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| author | Keeler, Jack Binder, Benjamin Blyth, Mark |
| author_facet | Keeler, Jack Binder, Benjamin Blyth, Mark |
| contents | The nonlinear disturbance caused by a localised forcing moving at constant speed on the free surface of a liquid of finite depth is investigated using the forced Kadometsev-Petviashvili equation. The presence of a steady v-shaped Kelvin wave pattern downstream of the forcing is established for this model equation, and the wedge angle is characterised as a function of the Froude number. Inspired by this analysis, it is shown that the wake can be eliminated via a careful choice of the forcing distribution and that, significantly, the corresponding nonlinear wave-free solution is stable so that it could potentially be seen in a physical experiment. The stability is demonstrated via the numerical solution of an initial value problem for which the steady wave-free state is attained in the long-time limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards eliminating the nonlinear Kelvin wake Keeler, Jack Binder, Benjamin Blyth, Mark Fluid Dynamics Mathematical Physics The nonlinear disturbance caused by a localised forcing moving at constant speed on the free surface of a liquid of finite depth is investigated using the forced Kadometsev-Petviashvili equation. The presence of a steady v-shaped Kelvin wave pattern downstream of the forcing is established for this model equation, and the wedge angle is characterised as a function of the Froude number. Inspired by this analysis, it is shown that the wake can be eliminated via a careful choice of the forcing distribution and that, significantly, the corresponding nonlinear wave-free solution is stable so that it could potentially be seen in a physical experiment. The stability is demonstrated via the numerical solution of an initial value problem for which the steady wave-free state is attained in the long-time limit. |
| title | Towards eliminating the nonlinear Kelvin wake |
| topic | Fluid Dynamics Mathematical Physics |
| url | https://arxiv.org/abs/2410.01255 |