To design a coastal structure constructed on a fringing reef, it is important to estimate not only wave height reduction but also wave setup and surf-beat distribution, because they can cause sea-level rise in front of the coastal structure, and increase wave force and wave overtopping rate on it. In this study, a series of numerical experiments is conducted by using a Boussinesq wave model to especially reveal the characteristics of surf-beat distribution, after the wave breaking model based on a one-equation turbulence model is modified through the verification with experimental results.
To design a coastal structure constructed on a fringing reef, it is important to estimate not only wave height reduction but also wave setup and surf-beat distribution, because they can cause sea-level rise in front of the coastal structure, and increase wave force and wave overtopping rate on it (e.g. Cheriton et al., 2016; Nwogu and Demirbilek, 2010). Miyaguni et al. (2008) suggested that Goda's diagrams (1975) could be also used to estimate wave overtopping for a reef coast while both the wave set-up and the sea-level rise due to surfbeat were taken into account for the design sea level. Hereby in this study, a series of numerical experiments is conducted by using a Boussinesq wave model to especially reveal the characteristics of surfbeat distribution which may have relations to wave height distribution.
The wave transformations on a fringing reef must be affected by wave shoaling and breaking on a front-slope connected to a reef flat (e.g. Young, 1989; Fang et al., 2017). Here the wave breaking model based on a one-equation turbulence model (Hirayama and Hiraishi, 2005) is adapted and modified through the verification with experimental results on a slope, then calculation results for wave height distribution on a fringing reef are compared with an experimental formula proposed by Takayama et al. (1977). Furthermore, both the wave set-up and the surf-beat which are calculated by using the Boussinesq wave model are also compared with a theoretical equation from deep water toward the shoreline (Longuet-Higgins, 1962) and an empirical equation within the surf zone on a sloping beach (Goda, 2009), respectively. However, it must be not expected that the high-order wave transformation would be reproduced in these numerical experiences because the fundamental equation of the Boussinesq wave model is derived by Madsen and S⊘rensen (1992). In addition to the above results reported in Hirayama and Aida (2016), in this paper, the distributions of normalized surf-beat heights in total 96 cases calculated on 3 types of fringing reef are compared among them focusing the Ursell number of conveyance waves.
