Topological indices for shallow-water waves

Abstract: In this talk, I will apply tools from topological insulators to a fluid dynamics problem: the rotating shallow-water wave model with odd viscosity. The bulk-edge correspondence explains the presence of remarkably stable waves propagating towards the east along the equator and observed in some Earth oceanic layers. The odd viscous term is a small-scale regularization that provides a well defined Chern number for this continuous model where momentum space is unbounded. Equatorial waves then appear as interface modes between two hemispheres with a different topology. However, in presence of a sharp boundary there is a surprising mismatch in the bulk-edge correspondence: the number of edge modes depends on the boundary condition. I will explain the origin of such a mismatch using scattering theory and Levinson’s theorem. This talk is based on a series of joint works with Pierre Delplace, Antoine Venaille, Gian Michele Graf and Hansueli Jud.

mathematical physics

Audience: researchers in the discipline

( video )

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