Topology of shallow-water waves on the rotating sphere

Autor:	Perez, Nicolas, Leclerc, Armand, Laibe, Guillaume, Delplace, Pierre
Rok vydání:	2024
Předmět:	Physics - Fluid Dynamics Astrophysics - Earth and Planetary Astrophysics Condensed Matter - Mesoscale and Nanoscale Physics Physics - Atmospheric and Oceanic Physics
Druh dokumentu:	Working Paper
Popis:	Topological properties of the spectrum of shallow-water waves on a rotating spherical body are established. Particular attention is paid to its spectral flow, i.e. the modes whose frequencies transit between the Rossby and inertia-gravity wavebands as the zonal wave number is varied. Organising the modes according to the number of zeros of their meridional velocity, we conclude that the net number of modes transiting between the shallow-water wavebands on the sphere is null, in contrast with the Matsuno spectrum. This difference can be explained by a miscount of zeros under the $\beta$-plane approximation. We corroborate this result with the analysis of Delplace et al (2017) by showing that the curved metric discloses a pair of degeneracy points in the Weyl symbol of the wave operator, non-existent under the $\beta$-plane approximation, each of them bearing a Chern number $-1$. Comment: 27 pages, 13 figures, 4 appendices
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.07655 Zobrazit plný text záznamu View this record from Arxiv