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Comptes Rendus. Physique
From the geometry of Foucault pendulum to the topology of planetary waves
Comptes Rendus. Physique, Volume 21 (2020) no. 2, pp. 165-175.

Part of the special issue: Prizes of the French Academy of Sciences 2019

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.

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.

Published online:
DOI: 10.5802/crphys.28
Keywords: Waves, Coriolis force, Chern numbers, Geometric phase, Astrophysical and geophysical flows
Pierre Delplace 1; Antoine Venaille 1

1 Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Pierre Delplace; Antoine Venaille. From the geometry of Foucault pendulum to the topology of planetary waves. Comptes Rendus. Physique, 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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