Kelvin's theorem is applied to the problem of Rossby waves impinging on large oceanic barriers containing gaps that are small compared to the scale of the wave. Kelvin's theorem implies that each island is turned from a barrier to a radiating antenna so that the wave transits the barrier chain with minimal reflection. Impinging wave packets as well as normal modes in closed basins are considered.

The steady flow around very large islands is considered. For the case of a long meridionally oriented island, Kelvin's theorem, extended to include dissipation, requires a recirculation region east of the island. The addition of a topographic “skirt” to the island, as a representation of coastal topography, significantly alters the circulation pattern and the flux of fluid around the island. Some of the more dramatic alterations of the flow are demonstrated with laboratory experiments.