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\begin{document}

\title{Topological Structure of Moist Equatorial Waves}



\author[1]{Kartheek Mamidi}%
\author[1]{Vincent Mathew}%
\affil[1]{Dept. of Physics}%


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  \date{May 26, 2024}


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\begin{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.%
\end{abstract}%



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