[A-CG40] 海洋と大気の波動・渦・循環の力学

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

*大貫 陽平¹、Venaille Antoine²、Delplace Pierre² (1.九州大学 応用力学研究所、2.リヨン高等師範学校 物理学研究所)

キーワード：トポロジー、回転成層流体、慣性重力波、ケルビン波

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.