# Topological Origin of Equatorial Waves

## TL;DR

This paper reveals that equatorial waves like Kelvin and Yanai modes have a topological origin, with their existence guaranteed by the Earth's rotation and the associated Chern number, linking climate dynamics to topological insulators.

## Contribution

It demonstrates a topological explanation for equatorially trapped waves, connecting geophysical fluid dynamics with topological phases of matter.

## Key findings

- Kelvin and Yanai waves are topologically protected due to Earth's rotation.
- The bulk Poincaré wave modes have a non-trivial Chern number of 2.
- Topology underpins the robustness of these oceanic and atmospheric waves.

## Abstract

Topology sheds new light on the emergence of unidirectional edge waves in a variety of physical systems, from condensed matter to artificial lattices. Waves observed in geophysical flows are also robust to perturbations, which suggests a role for topology. We show a topological origin for two celebrated equatorially trapped waves known as Kelvin and Yanai modes, due to the Earth's rotation that breaks time-reversal symmetry. The non-trivial structure of the bulk Poincar\'e wave modes encoded through the first Chern number of value $2$ guarantees existence for these waves. This invariant demonstrates that ocean and atmospheric waves share fundamental properties with topological insulators, and that topology plays an unexpected role in the Earth climate system.