Study on the Set-up and Set-down Induced by Breaking Waves Over A Reef

Abstract

This paper proposes an equation to calculate breaking wave induced wave set-up and set-down along reef flat. The mathematical equation was derived based on the theory of radiation stress and the conservation of wave energy. The equation is primarily determined by several physical variables including the breaking wave index, the stable wave index, the attenuation coefficient of wave energy flux, and the flow velocity in the re-stabilization zone. A series of laboratory experiments were carried out to calibrate the theoretical equations. Specifically, the breaking wave index, the stable wave index, and the velocity over the reef flat were measured in the laboratory. The attenuation coefficient of wave energy flux in our theoretical equation was determined by calibration by comparing with the laboratory measured wave height. Furthermore, it has been put forward that the velocity based on cnoidal wave theory could be used to determine the velocity over the reef flat if there is no velocity measurement available. Overall, the proposed equation can provide satisfactory prediction of wave set-up and set-down along the reef flat.