An introduction to the Zakharov equation for modelling deep water waves
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910048708460544 |
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| author | Stuhlmeier, Raphael |
| author_facet | Stuhlmeier, Raphael |
| contents | The Hamiltonian formulation of the water wave problem due to Zakharov, and the reduced Zakharov equation derived therefrom, have great utility in understanding and modelling water waves. Here we set out to review the cubic Zakharov equation and its uses in understanding deterministic waves in deep water. The background of this equation is developed and several applications are explored. Chief among these is an understanding of dispersion corrections and the energy exchange among modes. It is hoped that readers will be motivated to explore this powerful reformulation of the cubically nonlinear water wave problem for themselves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03539 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An introduction to the Zakharov equation for modelling deep water waves Stuhlmeier, Raphael Fluid Dynamics Atmospheric and Oceanic Physics 76-02, 76B15 The Hamiltonian formulation of the water wave problem due to Zakharov, and the reduced Zakharov equation derived therefrom, have great utility in understanding and modelling water waves. Here we set out to review the cubic Zakharov equation and its uses in understanding deterministic waves in deep water. The background of this equation is developed and several applications are explored. Chief among these is an understanding of dispersion corrections and the energy exchange among modes. It is hoped that readers will be motivated to explore this powerful reformulation of the cubically nonlinear water wave problem for themselves. |
| title | An introduction to the Zakharov equation for modelling deep water waves |
| topic | Fluid Dynamics Atmospheric and Oceanic Physics 76-02, 76B15 |
| url | https://arxiv.org/abs/2401.03539 |