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Article Dans Une Revue Physical Review Research Année : 2021

Wave Topology brought to the coast

Pierre Delplace

Résumé

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 an unidirectional mode filling a frequency gap between different bands of delocalized bulk modes. 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 the interplay between the Coriolis parameter that breaks time-reversal symmetry and a new parameter describing the gradient of bottom topography that breaks inversion symmetry. This leads to a fluid analogue of the celebrated Haldane model in condensed matter physics that is based on the same symmetries breaking, and allows for a new classification of coastal waves based on a correspondence between degeneracy points for bulk waves and a spectral flow for interface problems with varying topography.

Dates et versions

hal-02995334 , version 1 (09-11-2020)

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Antoine Venaille, Pierre Delplace. Wave Topology brought to the coast. Physical Review Research, 2021, ⟨10.1103/PhysRevResearch.3.043002⟩. ⟨hal-02995334⟩
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