Waves of Topological Origin in the Fluid Earth System and Beyond

Symmetries and topology are central to our understanding of physical systems. Topology, for instance, explains the precise quan/za/on of the Hall effect and the protec/on of surface states in topological insulators against scaIering from disorder or bumps. However discrete symmetries and topology have not, un/l recently, contributed much to our understanding of the fluid dynamics of oceans and atmospheres. In this talk I show that, as a consequence of the rota/on of the Earth that breaks /me reversal symmetry, equatorial Kelvin and Yanai waves emerge as topologically protected edge modes. The non-trivial topology of the bulk Poincare´ waves is revealed through their winding number in frequency - wavevector space. Bulk- interface correspondence then guarantees the existence of the two equatorial waves. I discuss our recent direct detec/on of the winding number in observa/ons of Earth’s stratosphere. Thus the oceans and atmosphere of Earth naturally share basic physics with topological insulators [1]. As equatorially trapped Kelvin waves in the Pacific ocean are an important component of El Nin~o Southern Oscilla/on, the largest climate oscilla/on on /me scales of a few years, topology plays a surprising role in Earth’s climate system. We also predict that waves of topological origin will arise in magne/zed plasmas [2]. The waves may appear in laboratory plasma experiments, and they may also arise in the solar system and beyond.

[1] Delplace, P., Marston, J. B. & Venaille, A. Topological origin of equatorial waves. Science 358, 1075–1077 (2017).

[2] Parker, J. B., Marston, J. B., Tobias, S. M. & Zhu, Z. Topological Gaseous Plasmon Polariton in Realis/c Plasma. Physical Review Le1ers 124, 195001 (2020)