From the geometry of Foucault pendulum to the topology of planetary waves

Abstract

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.

Short review for the Comptes Rendus - Physique (Académie des Sciences)

References in corpus (10)

• Topological Photonics
• Experimental realisation of the topological Haldane model
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Topological mechanics of gyroscopic metamaterials
• Topological Sound
• Topological Origin of Equatorial Waves
• Experimental Measurement of the Berry Curvature from Anomalous Transport
• Topological waves in fluids with odd viscosity
• Topological Sound and Flocking on Curved Surfaces
• Topological Gaseous Plasmon Polariton in Realistic Plasma

Cited by in corpus (3)

• Subwavelength Su-Schrieffer-Heeger topological modes in acoustic waveguides
• Topological Insights from State Manipulation in a Classical Elastic System
• Topological insulators and geometry of vector bundles