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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2409.17269 |
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| _version_ | 1866908981298987008 |
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| author | Kano, Tadayoshi |
| author_facet | Kano, Tadayoshi |
| contents | Approaching a sloping beach, shallow water surface waves of Airy get suddenly $ +\infty$ or $ -\infty$ propagation speed at the point of surface $x = x_0$, say, where the tangent $\varGamma_x$ of the surface $y = \varGamma$ "coincide" with that $b_x$ of the water-bottom $y = b(x)$, losing the cruising sound speed of propagation so high on a deep open sea. That is, the tunamis gain instantaneously a $ +\infty$ propagation speed just before the crest as $(\varGamma_x - b_x)(x) \to +0$, $x \to x_0\!-\!0$ , and a $ -\infty$ propagation speed just after the trough as $(\varGamma_x - b_x)(x) \to -0$, $x \to x_0\!-\!0$. We would have thus a big crush between the crest rushing forward and the trough rushing backward. This is a mathematical structure of tunamis "on" a sloping beach, in particular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17269 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tunamis on a deep open sea and on a sloping beach -- a mathematical theory Kano, Tadayoshi Analysis of PDEs Atmospheric and Oceanic Physics 35, 76 Approaching a sloping beach, shallow water surface waves of Airy get suddenly $ +\infty$ or $ -\infty$ propagation speed at the point of surface $x = x_0$, say, where the tangent $\varGamma_x$ of the surface $y = \varGamma$ "coincide" with that $b_x$ of the water-bottom $y = b(x)$, losing the cruising sound speed of propagation so high on a deep open sea. That is, the tunamis gain instantaneously a $ +\infty$ propagation speed just before the crest as $(\varGamma_x - b_x)(x) \to +0$, $x \to x_0\!-\!0$ , and a $ -\infty$ propagation speed just after the trough as $(\varGamma_x - b_x)(x) \to -0$, $x \to x_0\!-\!0$. We would have thus a big crush between the crest rushing forward and the trough rushing backward. This is a mathematical structure of tunamis "on" a sloping beach, in particular. |
| title | Tunamis on a deep open sea and on a sloping beach -- a mathematical theory |
| topic | Analysis of PDEs Atmospheric and Oceanic Physics 35, 76 |
| url | https://arxiv.org/abs/2409.17269 |