Resonance of long waves around a circular island and its relation to edge waves

Abstract

As long waves propagate over an island, wave energy can be trapped in the shallow water near the coastline due to the effect of refraction and diffraction. However, in some particular situations extremely huge near-shore waves can be excited due to the resonance of edge waves. This study focuses on the occurrence condition of the resonance phenomenon, and mainly investigates the effects of geometric parameters of underwater topography around island, especially the curvature of island profile. Based on an analytical solution of long waves over an idealized circular island, resonance of long waves around islands has been investigated. The island profile is described as a function with three independent parameters. The influences of average slope and curvature of island profile on the resonance frequency and amplification factor have been discussed. It is found that not only the average slope but also the curvature parameter greatly affects the resonance frequency and amplification factor of resonance peaks. The resonance frequency shifts to lower frequency with decrease of the average slope and increase of the curvature parameter of island profile. The milder slope and larger curvature parameter are associated with a larger resonance peak and a narrower resonance bandwidth. By comparison with the existing edge wave theory, the resonance peaks are confirmed to relate to edge waves. The resonance peaks appear when the frequency of incident long wave is close to the edge wave that the perimeter of island is an integral multiple of its wave length. An approach to estimate the resonance frequency considering the curvature of island profile is given, which agrees well with the result of the complex analytical solution.