  Bulk-edge correspondence is a cornerstone in topological physics,
establishing a connection between the number of unidirectional edge modes in
physical space and a Chern number, an integer that counts phase singularities
of the eigenmodes in parameter space. In continuous media, violation of this
correspondence has been reported when some of the frequency wavebands are
unbounded, resulting in weak topological protection of chiral edge states.
Here, we propose a strategy to reestablish strong bulk-edge correspondence in
incompressible rotating stratified flows, taking advantage of a natural cutoff
frequency provided by density stratification. The key idea involves the
introduction of an auxiliary field to handle the divergence-free constraint.
This approach highlights the resilience of internal coastal Kelvin waves near
vertical walls under varying boundary conditions.
