• Open Access

Wave topology brought to the coast

A. Venaille and P. Delplace
Phys. Rev. Research 3, 043002 – Published 1 October 2021

Abstract

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.

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  • Received 29 March 2021
  • Accepted 23 August 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.043002

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Venaille* and P. Delplace

  • Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France

  • *antoine.venaille@ens-lyon.fr
  • pierre.delplace@ens-lyon.fr

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Issue

Vol. 3, Iss. 4 — October - December 2021

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