Topological waves in geo- and astro-physical fluids
from a bulk-edge correspondence perspective

Pierre Delplace

CNRS, Ecole Normale Supérieure de Lyon

Continuous media, such as fluids, may host various trapped waves of topological origin,
e.g. similar to the unidirectional chiral edge states of a Chern insulator. In the absence of
a boundary, such trapped waves may still exist at “interfaces” if the fluid develops specific
gradients of physical quantities. In that case, their topological origin is well-defined despite
the absence of an underlying lattice. Geophysical and astrophysical fluids, namely
atmospheres, oceans and stars, are such continuous media that naturally develop
gradients of different kinds, such as density and rotation rate, which leads to various
trapped topological waves.
In this talk, I will introduce basic linear models that describe wave propagation in such
fluids and show how topology can help interpreting or predicting new wave behaviors.
From the perspective of a condensed matter physicist, I will discuss in particular the
topological description of unidirectional Equatorial waves that are responsible for the El
Nino phenomenon, and of Lamb waves whose recent prediction in the Sun might allow for
the first probe of the Sun’s core rotation rate.