Internal waves in a 2D subcritical channel
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929721788334080 |
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| author | Li, Zhenhao Wang, Jian Wunsch, Jared |
| author_facet | Li, Zhenhao Wang, Jian Wunsch, Jared |
| contents | We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to outgoing data; this operator turns out to differ by a smoothing operator from the pullback by the ``bounce map'' for boundary data obtained by ray-tracing. As a consequence we obtain unique solvability of the inhomogeneous stationary scattering problem subject to an appropriate outgoing radiation condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14587 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Internal waves in a 2D subcritical channel Li, Zhenhao Wang, Jian Wunsch, Jared Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Spectral Theory 35L57, 86A05 We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to outgoing data; this operator turns out to differ by a smoothing operator from the pullback by the ``bounce map'' for boundary data obtained by ray-tracing. As a consequence we obtain unique solvability of the inhomogeneous stationary scattering problem subject to an appropriate outgoing radiation condition. |
| title | Internal waves in a 2D subcritical channel |
| topic | Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Spectral Theory 35L57, 86A05 |
| url | https://arxiv.org/abs/2411.14587 |