In this talk, I will apply tools from topological insulators to a fluid dynamics problem:the rotating shallow-water wave model with odd viscosity. The celebrated bulk-edge correspondence explains the origin of Kelvin waves that propagates in the Earth's ocean, towards the east and along the equator, with a remarkable stability. The odd viscous term is a small-scale regularization that leads to a well-defined Chern number for this continuous model where momentum space is unbounded. Equatorial waves then appear as interface modes between two hemispheres with a different topology. However, in presence of a sharp boundary, there is a surprising mismatch in the bulk-edge correspondence: the number of edge modes depends on the boundary condition. I will explain the origin of such a mismatch using scattering theory and Levinson’s theorem. This talk is based on a series of joint works with Pierre Delplace, Antoine Venaille, Gian Michele Graf and Hansueli Jud.