Topological origin of equatorial waves

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Science  24 Nov 2017:
Vol. 358, Issue 6366, pp. 1075-1077
DOI: 10.1126/science.aan8819

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Fluid waves with topological origins

Topological effects that arise from material boundaries are well known in solid-state physics and form the basis for topological insulators. Delplace et al. describe atmospheric and ocean waves that appear to have a similar topological origin (see the Perspective by Biello and Dimofte). The waves exist because of the symmetry-breaking nature of Earth's rotation, which allows certain fixed topological constraints on the system. These findings may be useful for understanding a wide variety of geophysical and astrophysical flows.

Science, this issue p. 1075; see also p. 990


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 Poincaré wave modes encoded through the first Chern number of value 2 guarantees the existence of 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.

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