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Bulk-edge correspondence is a cornerstone in topological physics,establishing a connection between the number of unidirectional edge modes andthe topological invariants that describe bulk wave singularities. In continuousmedia, this correspondence can be violated, resulting in weak topologicalprotection of chiral edge states. Here, we propose a strategy to reestablishstrong bulk-edge correspondence in incompressible continuous media. The keyideas involve handling the divergence-free constraint through an auxiliaryfield and considering a physical mechanism that imposes a high-frequency cutoffof bulk waves. When applied to rotating stratified fluids, this approachhighlights the resilience of coastal Kelvin waves near vertical walls undervarying boundary conditions.

Bulk-edge correspondence recovered in incompressible continuous media