Wave topology brought to the coast
Since the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin plays a particular role, as it is a unidirectional mode filling a frequency gap between different wave band...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.043002 |
| _version_ | 1797210941085974528 |
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| author | A. Venaille P. Delplace |
| author_facet | A. Venaille P. Delplace |
| author_sort | A. Venaille |
| collection | DOAJ |
| description | Since the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin plays a particular role, as it is a unidirectional mode filling a frequency gap between different wave bands. The existence of such Kelvin waves is robust to changes in the boundary shape and in changes of the underlying model for the coast. This suggests a topological interpretation that has yet up to now remained elusive. Here we rectify the situation, by taking advantage of a reformulation of the shallow water dynamics that highlights an analogy with the celebrated Haldane model in condensed matter physics. For any profile of bottom topography, the number of modes that transit from one wave band to another in the dispersion relation is predicted by computing a first Chern number describing the topology of complex eigenmodes in a dual, simpler wave problem. |
| first_indexed | 2024-04-24T10:18:35Z |
| format | Article |
| id | doaj.art-9240b5d00ffd4bf2b74dcb05fa617bc6 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:18:35Z |
| publishDate | 2021-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-9240b5d00ffd4bf2b74dcb05fa617bc62024-04-12T17:14:30ZengAmerican Physical SocietyPhysical Review Research2643-15642021-10-013404300210.1103/PhysRevResearch.3.043002Wave topology brought to the coastA. VenailleP. DelplaceSince the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin plays a particular role, as it is a unidirectional mode filling a frequency gap between different wave bands. The existence of such Kelvin waves is robust to changes in the boundary shape and in changes of the underlying model for the coast. This suggests a topological interpretation that has yet up to now remained elusive. Here we rectify the situation, by taking advantage of a reformulation of the shallow water dynamics that highlights an analogy with the celebrated Haldane model in condensed matter physics. For any profile of bottom topography, the number of modes that transit from one wave band to another in the dispersion relation is predicted by computing a first Chern number describing the topology of complex eigenmodes in a dual, simpler wave problem.http://doi.org/10.1103/PhysRevResearch.3.043002 |
| spellingShingle | A. Venaille P. Delplace Wave topology brought to the coast Physical Review Research |
| title | Wave topology brought to the coast |
| title_full | Wave topology brought to the coast |
| title_fullStr | Wave topology brought to the coast |
| title_full_unstemmed | Wave topology brought to the coast |
| title_short | Wave topology brought to the coast |
| title_sort | wave topology brought to the coast |
| url | http://doi.org/10.1103/PhysRevResearch.3.043002 |
| work_keys_str_mv | AT avenaille wavetopologybroughttothecoast AT pdelplace wavetopologybroughttothecoast |