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.

当长波传播到一个岛上时，由于折射和衍射的作用，波能会被困在海岸线附近的浅水中。但是，在某些特定情况下，由于边缘波的共振，可能会激发出巨大的近岸波。本研究关注共振现象的发生条件，主要研究岛屿周围水下地形的几何参数，尤其是岛屿剖面曲率的影响。基于理想圆形岛上长波的解析解，研究了长波在岛周围的共振。岛轮廓被描述为具有三个独立参数的函数。讨论了岛形轮廓的平均斜率和曲率对共振频率和放大因子的影响。发现不仅平均斜率而且曲率参数极大地影响共振频率和共振峰的放大因子。随着平均斜率的减小和岛形轮廓的曲率参数的增加，共振频率移至较低频率。较缓的斜率和较大的曲率参数与较大的共振峰和较窄的共振带宽有关。通过与现有的边波理论进行比较，可以确定共振峰与边波有关。当入射长波的频率接近边缘的波时，共振峰出现。边缘波是岛的周长是其波长的整数倍。给出了一种考虑孤岛曲率估算共振频率的方法，