Topological origin of equatorial waves

Abstract

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.

Topological Sound and Flocking on Curved Surfaces

“…This should be contrasted with many of the systems considered previously, which required a carefully designed metamaterial structured on an artificial lattice. The phenomenon reported here is akin to the one recently found in geophysical flows of oceans or the Earth's atmosphere, where equatorially trapped Kelvin waves were reinterpreted as topologically protected modes [39]. In that case, the flow is imposed externally by the Earth's rotation.…”

“…In a frame comoving with the flock, the finite curvature of the sphere plays a role similar to the Coriolis force that would be present for a passive fluid on a rotating sphere. In the case of the Earth's atmosphere, this has recently been shown to give a gapped sound spectrum and equatorially confined Kelvin and Yanai waves [59] that are topological in origin [39]. In our active system, no external flow or rotation needs to be imposed, and the absence of Galilean invariance allows for independent tuning of the material parameters (such as λ) in order to probe regimes that are not accessible to passive fluids.…”

“…In other words the propagation rate of long-wavelength density fluctuations is finite. This is a distinct property of active polar fluids, and it arises because the polarization field plays the dual role of the order parameter and flow velocity and is therefore subject to the same lensing effect that forces flow to move along geodesics on curved surfaces [29,39]. With a spectral gap opened, in Sec.…”

Linearly forced fluid flow on a rotating sphere

“…Conceptually, our analysis supports the view that non-equilibrium approaches can provide analytical insights into the dynamics of planetary flows (Delplace et al 2017) and atmospheres (Marston 2011(Marston , 2012. Moreover, in view of the recent successful application of phenomenological GNS models to active fluids (Dunkel et al 2013;S lomka & Dunkel 2017b), the results of this study can also help advance the understanding of active matter propagation on curved surfaces (Sanchez et al 2012;Sknepnek & Henkes 2015;Zhang et al 2016;Henkes et al 2018;Nitschke et al 2019) and in rotating frames (Löwen 2019).…”

Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection

“…Other examples include two-dimensional chiral materials (Tsai et al 2005;Nash et al 2015), isostatic lattices in two dimensions (Kane & Lubensky 2014) and photonic systems (Khanikaev & Shvets 2017). Recently it was observed that similar arguments apply to equatorial shallow water waves and used to confirm the presence of two types of low frequency eastward-propagating equatorially trapped waves, Kelvin and Yanai waves, separating bulk waves at higher positive and negative frequency (Delplace et al 2017;Tauber et al 2019). The theory predicts that both these boundary currents are robust, for example, with respect to topography.…”