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Topological origin of equatorial waves. (English) Zbl 1404.86016
Summary: Topology sheds new light on the emergence of unidirectional edge waves in a variety of physical systems, from condensed matter to artificial lattices. Waves observed in geophysical flows are also robust to perturbations, which suggests a role for topology. We show a topological origin for two well-known equatorially trapped waves, the Kelvin and Yanai modes, owing to the breaking of time-reversal symmetry by Earth’s rotation. The nontrivial structure of the bulk PoincarĂ© wave modes encoded through the first Chern number of value 2 guarantees existence for these waves. This invariant demonstrates that ocean and atmospheric waves share fundamental properties with topological insulators and that topology plays an unexpected role in Earth’s climate system.

MSC:
86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics
57R20 Characteristic classes and numbers in differential topology
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