[De la géométrie du pendule de Foucault à la topologie des ondes planétaires]
La physique des isolants topologiques permet de comprendre et prédire l’existence d’ondes unidirectionnelles piégées le long d’un bord ou d’une interface. Nous décrivons dans cette revue comment ces idées peuvent être adaptées aux ondes géophysiques et astrophysiques. Nous traitons en particulier le cas des ondes équatoriales planétaires, qui met en lumière les rôles clés combinés de la rotation et de la sphéricité de la planète pour expliquer l’émergence d’ondes qui ne propagent leur énergie que vers l’est. Ces ingrédients minimaux sont précisément ceux mis en avant dans l’interprétation géométrique du pendule de Foucault. Nous discutons cet exemple classique de mécanique pour introduire les concepts d’holonomie et de fibré vectoriel que nous utilisons ensuite pour le calcul des propriétés topologiques des ondes équatoriales en eau peu profonde.
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.
Mots-clés : Ondes, Force de Coriolis, Nombre de Chern, Phase géométrique, Flots géophysiques et astrophysiques
Pierre Delplace 1 ; Antoine Venaille 1
CC-BY 4.0
@article{CRPHYS_2020__21_2_165_0,
author = {Pierre Delplace and Antoine Venaille},
title = {From the geometry of {Foucault} pendulum to the topology of planetary waves},
journal = {Comptes Rendus. Physique},
pages = {165--175},
publisher = {Acad\'emie des sciences, Paris},
volume = {21},
number = {2},
year = {2020},
doi = {10.5802/crphys.28},
language = {en},
}
TY - JOUR AU - Pierre Delplace AU - Antoine Venaille TI - From the geometry of Foucault pendulum to the topology of planetary waves JO - Comptes Rendus. Physique PY - 2020 SP - 165 EP - 175 VL - 21 IS - 2 PB - Académie des sciences, Paris DO - 10.5802/crphys.28 LA - en ID - CRPHYS_2020__21_2_165_0 ER -
Pierre Delplace; Antoine Venaille. From the geometry of Foucault pendulum to the topology of planetary waves. Comptes Rendus. Physique, Prizes of the French Academy of Sciences 2019, Volume 21 (2020) no. 2, pp. 165-175. doi : 10.5802/crphys.28. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.28/
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