From the geometry of Foucault pendulum to the topology of planetary waves
The physics of topological insulators makes it possible to understand and predict the existence of unidirectional waves trapped along an edge or an interface. In this review, we describe how these ideas can be adapted to geophysical and astrophysical waves. We deal in particular with the case of pla...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Académie des sciences
2020-11-01
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| Series: | Comptes Rendus. Physique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.28/ |
| _version_ | 1827785151103369216 |
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| author | Delplace, Pierre Venaille, Antoine |
| author_facet | Delplace, Pierre Venaille, Antoine |
| author_sort | Delplace, Pierre |
| collection | DOAJ |
| description | The physics of topological insulators makes it possible to understand and predict the existence of unidirectional waves trapped along an edge or an interface. In this review, we describe how these ideas can be adapted to geophysical and astrophysical waves. We deal in particular with the case of planetary equatorial waves, which highlights the key interplay between rotation and sphericity of the planet, to explain the emergence of waves which propagate their energy only towards the East. These minimal ingredients are precisely those put forward in the geometric interpretation of the Foucault pendulum. We discuss this classic example of mechanics to introduce the concepts of holonomy and vector bundle which we then use to calculate the topological properties of equatorial shallow water waves. |
| first_indexed | 2024-03-11T16:14:58Z |
| format | Article |
| id | doaj.art-3135dbcfab5b4f26bd34adf95778582c |
| institution | Directory Open Access Journal |
| issn | 1878-1535 |
| language | English |
| last_indexed | 2024-03-11T16:14:58Z |
| publishDate | 2020-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Physique |
| spelling | doaj.art-3135dbcfab5b4f26bd34adf95778582c2023-10-24T14:21:43ZengAcadémie des sciencesComptes Rendus. Physique1878-15352020-11-0121216517510.5802/crphys.2810.5802/crphys.28From the geometry of Foucault pendulum to the topology of planetary wavesDelplace, Pierre0Venaille, Antoine1Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, FranceUniv Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, FranceThe physics of topological insulators makes it possible to understand and predict the existence of unidirectional waves trapped along an edge or an interface. In this review, we describe how these ideas can be adapted to geophysical and astrophysical waves. We deal in particular with the case of planetary equatorial waves, which highlights the key interplay between rotation and sphericity of the planet, to explain the emergence of waves which propagate their energy only towards the East. These minimal ingredients are precisely those put forward in the geometric interpretation of the Foucault pendulum. We discuss this classic example of mechanics to introduce the concepts of holonomy and vector bundle which we then use to calculate the topological properties of equatorial shallow water waves.https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.28/WavesCoriolis forceChern numbersGeometric phaseAstrophysical and geophysical flows |
| spellingShingle | Delplace, Pierre Venaille, Antoine From the geometry of Foucault pendulum to the topology of planetary waves Comptes Rendus. Physique Waves Coriolis force Chern numbers Geometric phase Astrophysical and geophysical flows |
| title | From the geometry of Foucault pendulum to the topology of planetary waves |
| title_full | From the geometry of Foucault pendulum to the topology of planetary waves |
| title_fullStr | From the geometry of Foucault pendulum to the topology of planetary waves |
| title_full_unstemmed | From the geometry of Foucault pendulum to the topology of planetary waves |
| title_short | From the geometry of Foucault pendulum to the topology of planetary waves |
| title_sort | from the geometry of foucault pendulum to the topology of planetary waves |
| topic | Waves Coriolis force Chern numbers Geometric phase Astrophysical and geophysical flows |
| url | https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.28/ |
| work_keys_str_mv | AT delplacepierre fromthegeometryoffoucaultpendulumtothetopologyofplanetarywaves AT venailleantoine fromthegeometryoffoucaultpendulumtothetopologyofplanetarywaves |