Symmetries and topology are central to an understanding of physics. Topology explains the precise quantization of the Hall effect and the protection of surface states in topological insulators against scattering by non-magnetic impurities or bumps. Subsequent to the discovery of the quantum spin Hall effect, states of matter with different topological properties were classified according to the discrete symmetries of the system. Recently topologically protected edge excitations have been found in artificial lattice structures that support classical waves of various types. The interplay between discrete symmetries and the topology of fluid waves has so far played no role in the study of the dynamics of oceans and atmospheres. Here 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 equatorial edge modes in the rotating shallow water model. These unidirectional edge modes are guaranteed to exist by the non-trivial global structure of the bulk Poincar\’e modes encoded through the first Chern number of value $\pm2$, in agreement with the correspondence between behavior deep in the bulk and edge excitations of a physical system. Thus the oceans and atmospheres of Earth and other rotating planets naturally share fundamental properties with topological insulators, despite the absence of an underlying lattice. As equatorially trapped Kelvin waves are an important component of El Ni\~no Southern Oscillation, and Madden-Julian Oscillation, our results demonstrate the topology plays an unexpected 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 modes that inhibits scattering.
P. Delplace, J. Marston and A. Venaille
Mon, 27 Feb 17