[A-CG40] Dynamics of Oceanic and Atmospheric Waves, Vortices, and Circulations

[ACG40-P01] Topological indices in rotating stratified fluid and bulk-edge correspondence

*Yohei Onuki¹, Antoine Venaille², Pierre Delplace² (1.Research Institute for Applied Mechanics, Kyushu University, 2.Laboratoire de Physique, ENS de Lyon)

Keywords:Topology, Rotating stratified fluid, Inertia-gravity wave, Kelvin wave

Inspired by pioneering work in the context of the quantum Hall effect, recent years have witnessed tremendous utility of topology to elucidate the emergence of unidirectional trapped modes in various geophysical fluid systems. The representative examples are the Kelvin and Yanai waves along the equator and the Lamb-like waves in the compressible atmosphere. In these prior studies, topological indices named the Chern numbers are computed from a bulk problem and corresponded to the number of wave modes trapped at an interface that separates a flow system into two parts. On the other hand, wave modes trapped at an external boundary, such as the coastal Kelvin wave, do not necessarily match with the bulk topology. This issue, known as the violation of bulk-edge correspondence, is resolved in the present study for a fundamental rotating stratified fluid model. Our novel contribution is introducing an auxiliary field to formally remove an incompressible constraint from the governing equations. This technique enables us to compose a complete set of fiber bundles in wave number space that exhibit nontrivial topology. The resulting Chern numbers successfully predict the existence of boundary modes, including the Kelvin wave, with respect to varying boundary conditions.

Reference:
- Onuki, Y., Venaille, A., & Delplace, P. (2023). Bulk-edge correspondence recovered in incompressible continuous media, submitted, arXiv:2311.18249.