Topological Structure of Moist Equatorial Waves

Abstract

Symmetries and topology have been actively introduced currently to characterize the mode structure of waves in various systems physics, giving rise to the concepts of topological insulators, topological superconductors and topological photonics, to name a few. Very recently, the equatorial wave systems have been described from a topological point of view by Delplace et. al. (Science 358, 1075-1077 (2017)). It was shown that the emergence of unidirectional edge waves (Yanai and Kelvin waves) can be attributed to the topological bound states. An f-plane model is used to connect the topological invariants, the Chern numbers, to the existence of these modes. We have extended this analysis by incorporating a beta plane model thereby including the Earth’s sphericity from beginning. Equatorial beta plane model renders the Poincare and Rossby waves also equatorially trapped. Further, the effect of moisture balance on the topology of the equatorial waveguide is examined. It is shown that the presence of a new eastward propagating mode within a low-frequency regime is similar to the observed MJO mode. We explained how moisture localizes these low-frequency unidirectional oscillations. The topological origin of moist waves is emphasized by relating their topological invariants, or Chern numbers. From this perspective, equatorial moist waves also show the strong similarities with bulk-edge correspondence encountered in quantum valley Hall effect and its classical analogues. Our study shows that the topological origin of MJO-like mode and its localization due to low-level moisture encode essential information of the tropical climatic systems.