On the trapping of wave energy round islands

It is shown that islands can trap long-wave energy in a way similar to the capture of a particle by an atomic nucleus. The frequencies of the captured waves form a discrete set, being determined by the shape of the island and the contours of the surrounding sea bed. If the depth at great distances tends to a constant value, the trapped modes must leak some energy to infinity, though the consequent rate of decay may be exceedingly small. The initial energy of the trapped modes may be absorbed from incident radiation of the same frequency or from a sharp pulse. The particular example of a rectilinear pulse incident on a circular island is discussed in some detail. The effect of the rotation of the Earth is to split the frequencies of a pair of waves progressing in opposite directions round the island. The splitting of the frequencies produces slow beats in the waves as seen at any fixed point. Slight asymmetry in the island induces a slow exchange of energy between each pair of progressive modes. The present investigation was suggested by the occurrence of regular oscillations having a period of 6 min and a beat period of about 3 h in long-wave records taken at Macquarie Island, in the Southern Ocean.