Topological Signature of Stratospheric Poincare -- Gravity Waves
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914718858346496 |
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| author | Xu, Weixuan Fox-Kemper, Baylor Lee, Jung-Eun Marston, J. B. Zhu, Ziyan |
| author_facet | Xu, Weixuan Fox-Kemper, Baylor Lee, Jung-Eun Marston, J. B. Zhu, Ziyan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_12191 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological Signature of Stratospheric Poincare -- Gravity Waves Xu, Weixuan Fox-Kemper, Baylor Lee, Jung-Eun Marston, J. B. Zhu, Ziyan Atmospheric and Oceanic Physics Mesoscale and Nanoscale Physics Fluid Dynamics Geophysics 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. |
| title | Topological Signature of Stratospheric Poincare -- Gravity Waves |
| topic | Atmospheric and Oceanic Physics Mesoscale and Nanoscale Physics Fluid Dynamics Geophysics |
| url | https://arxiv.org/abs/2306.12191 |