Topological Origin of Geophysical Waves

Symmetries and topology are central to our understanding of physics. Topology explains the precise quantization of the Hall effect and the protection of surface states in topological insulators against scattering from disorder. However discrete symmetries and topology have so far played little role in thinking about the fluid dynamics of oceans and atmospheres. We show that, as a consequence of the rotation of the Earth that breaks time reversal symmetry, equatorially trapped Kelvin and Yanai waves have a topological origin, manifesting as edge modes in a rotating shallow water model. Thus the oceans and atmosphere of Earth naturally share basic physics with topological insulators. As equatorially trapped Kelvin waves in the Pacific ocean are an important component of the El Niño Southern Oscillation and the Madden-Julian Oscillation, our results demonstrate the topology plays a surprising role in Earth’s climate system. These and other geophysical waves of topological origin are protected against static perturbations by time scale separation from other wave modes that inhibits scattering.

A preprint describing this work can be found at URL https://arxiv.org/abs/1702.07583