Abstract
An extended refraction–diffraction equation [Massel, S.R., 1993. Extended refraction–diffraction equation for surface waves. Coastal Eng. 19, 97–126] has been applied to predict wave transformation and breaking as well as wave-induced set-up on two-dimensional reef profiles of various shapes. A free empirical coefficient α in a formula for the average rate of energy dissipation 〈ϵ b 〉=(αρgω/8π)( gh /C)(H 3/h) in the modified periodic bore model was found to be a function of the dimensionless parameter F c0=( g 1.25 H 0 0.5 T 2.5)/ h r 1.75, proposed by Gourlay [Gourlay, M.R., 1994. Wave transformation on a coral reef. Coastal Eng. 23, 17–42]. The applicability of the developed model has been demonstrated for reefs of various shapes subjected to various incident wave conditions. Assuming proposed relationships of the coefficient α and F c0, the model provides results on wave height attenuation and set-up elevation which compare well with experimental data.
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