Scattering of Surface Waves by a Conical Coral Reef

The most important mechanism responsible for the formation and shaping of coral cays is wave action. In this paper a study is presented with a view to making prediction model of the waves motion at the coral reef. For simplicity, a circular reef in a sea of constant depth is considered. Refracted and diffracted waves are calculated by the modified refraction-diffraction equation. This equation allows for steeper bottom slopes and energy dissipation due to wave breaking and bottom friction. The model gives a detailed distribution of wave energy around the reef and on the reef top. It was found that wave heights depend strongly on the reef size, bottom slope and water depth. Examples of the numerical calculations are shown and comparisons with observed reefs are given.