Isobe-Kakinuma model for water waves as a higher order shallow water approximation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866917914087522304 |
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| author | Iguchi, Tatsuo |
| author_facet | Iguchi, Tatsuo |
| contents | We justify rigorously an Isobe-Kakinuma model for water waves as a higher order shallow water approximation in the case of a flat bottom. It is known that the full water wave equations are approximated by the shallow water equations with an error of order $O(δ^2)$, where $δ$ is a small nondimensional parameter defined as the ratio of the mean depth to the typical wavelength. The Green-Naghdi equations are known as higher order approximate equations to the water wave equations with an error of order $O(δ^4)$. In this paper we show that the Isobe-Kakinuma model is a much higher order approximation to the water wave equations with an error of order $O(δ^6)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1704_02419 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Isobe-Kakinuma model for water waves as a higher order shallow water approximation Iguchi, Tatsuo Analysis of PDEs We justify rigorously an Isobe-Kakinuma model for water waves as a higher order shallow water approximation in the case of a flat bottom. It is known that the full water wave equations are approximated by the shallow water equations with an error of order $O(δ^2)$, where $δ$ is a small nondimensional parameter defined as the ratio of the mean depth to the typical wavelength. The Green-Naghdi equations are known as higher order approximate equations to the water wave equations with an error of order $O(δ^4)$. In this paper we show that the Isobe-Kakinuma model is a much higher order approximation to the water wave equations with an error of order $O(δ^6)$. |
| title | Isobe-Kakinuma model for water waves as a higher order shallow water approximation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1704.02419 |