Topological nature of rotating convection

 

Rotation and convection are key features of the geophysical flow of planets, stars and galaxies. This work focuses on the topology of rotating convection. In topological physics, the junction of two materials with distinct topological invariants inevitably forms a boundary region, namely, the topologically protected edge states. After decades of their discovery, whether the robust sidewall modes in rotating convection are topologically protected remains a puzzle. By defining a Berry curvature in the complex wavenumber space of the non-Hermitian rotating convection system, we reveal that the interior modes can be characterized by a non-zero integer Chern number, confirming the topological origin [Zhang and Xie, 2024, J. Fluid Mech.]. Thus, bulk-boundary correspondence links the non-zero bulk Chern number and the robust wall modes. In addition, we define a winding number to visualize the topological nature of the fluid (cf. Figure below).

 

 

(Work with Prof. Furu Zhang.)