Well-posedness and potential-based formulation for the propagation of hydro-acoustic waves and tsunamis
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911854530396160 |
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| author | Dubois, Juliette Imperiale, Sébastien Mangeney, Anne Sainte-Marie, Jacques |
| author_facet | Dubois, Juliette Imperiale, Sébastien Mangeney, Anne Sainte-Marie, Jacques |
| contents | We study a linear model for the propagation of hydro-acoustic waves and tsunami in a stratified free-surface ocean. A formulation was previously obtained by linearizing the compressible Euler equations. The new formulation is obtained by studying the functional spaces and operators associated to the model. The mathematical study of this new formulation is easier and the discretization is also more efficient than for the previous formulation. We prove that both formulations are well posed and show that the solution to the first formulation can be obtained from the solution to the second. Finally, the formulations are discretized using a spectral element method, and we simulate tsunamis generation from submarine earthquakes and landslides. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17219 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness and potential-based formulation for the propagation of hydro-acoustic waves and tsunamis Dubois, Juliette Imperiale, Sébastien Mangeney, Anne Sainte-Marie, Jacques Analysis of PDEs Geophysics We study a linear model for the propagation of hydro-acoustic waves and tsunami in a stratified free-surface ocean. A formulation was previously obtained by linearizing the compressible Euler equations. The new formulation is obtained by studying the functional spaces and operators associated to the model. The mathematical study of this new formulation is easier and the discretization is also more efficient than for the previous formulation. We prove that both formulations are well posed and show that the solution to the first formulation can be obtained from the solution to the second. Finally, the formulations are discretized using a spectral element method, and we simulate tsunamis generation from submarine earthquakes and landslides. |
| title | Well-posedness and potential-based formulation for the propagation of hydro-acoustic waves and tsunamis |
| topic | Analysis of PDEs Geophysics |
| url | https://arxiv.org/abs/2404.17219 |