Topological Signature of Stratospheric Poincare -- Gravity Waves

TL;DR

This paper reveals the topological nature of Poincare inertio-gravity waves in the stratosphere, predicting and confirming the existence of Kelvin and Yanai waves through analysis of reanalysis data, offering new insights into atmospheric wave behavior.

Contribution

It introduces the topological framework to understand stratospheric waves and demonstrates the existence of topologically protected equatorial waves using observational data.

Findings

Identification of vortex and anti-vortex in wave phase at high frequencies

Confirmation of trivial topology in lower-frequency planetary waves

Validation of topological predictions through ERA5 data analysis

Abstract

The rotation of the earth breaks time-reversal and reflection symmetries in an opposite sense north and south of the equator, leading to a topological origin for certain atmospheric and oceanic equatorial waves. Away from the equator the rotating shallow water and stably stratified primitive equations exhibit Poincare inertio-gravity waves that have nontrivial topology as evidenced by their strict superinertial timescale and a phase singularity in frequency-wavevector space. This non-trivial topology then predicts, via the principle of bulk-interface correspondence, the existence of two equatorial waves along the equatorial interface, the Kelvin and Yanai waves. To directly test the nontrivial topology of Poincare-gravity waves in observations, we examine ERA5 reanalysis data and study cross-correlations between the wind velocity and geopotential height of the mid-latitude stratosphere at the 50 hPa height. We find the predicted vortex and anti-vortex in the relative phase of the geopotential height and velocity at the high frequencies of the waves. By contrast, lower-frequency planetary waves are found to have trivial topology also as expected from theory. These results demonstrate a new way to understand stratospheric waves, and provide a new qualitative tool for the investigation of waves in other components of the climate system.