  We study the two-dimensional rotating shallow-water model describing Earth's
oceanic layers. It is formally analogue to a Schr\"odinger equation where the
tools from topological insulators are relevant. Once regularized at small scale
by an odd-viscous term, such a model has a well-defined bulk topological index.
However, in presence of a sharp boundary, the number of edge modes depends on
the boundary condition, showing an explicit violation of the bulk-edge
correspondence. We study a continuous family of boundary conditions with a rich
phase diagram, and explain the origin of this mismatch. Our approach relies on
scattering theory and Levinson's theorem. The latter does not apply at infinite
momentum because of the analytic structure of the scattering amplitude there,
ultimately responsible for the violation.
