A multi-layer non-hydrostatic model is developed to investigate the solitary wave propagation and transformation on fringing reef profiles. Euler equations in terrain and surface-following coordinates is descretized by a combined finite-volume and finite-difference scheme. The fluxes at cell faces are estimated by central upwind scheme. A two-step predictor-corrector scheme is used for time stepping. The numerical model is verified by solitary wave propagation over constant water depth and transformation and breaking over a plane beach. Solitary wave transformation over idealized fringing reef profiles with or without reef crest is then numerically investigated.
Fringing reefs are commonly found along coastlines in the tropical and subtropical regions around the world. A typical fringing reef is characterized by a sloping (or composite) reef face with an abrupt transition to an inshore shallow reef platform extending toward the shoreline (Buckley et al., 2015; Fang et al., 2016). The tropical areas affected by many events of destructive waves generated by storms and tsunamis are often sheltered by fringing reefs (Roeber et al., 2010). Ferrario et al. (2014) revealed that coral reefs provide substantial protection against natural hazards by reducing wave energy by an average of 97%. Wave processes on coral reefs also play a major role in determining coral reef ecology (Buckley et al., 2015). Hence the accuracy of prediction of surface waves on fringing reefs has great engineering, ecological and environmental effects (Gourlay and Colleter, 2005; Yao et al., 2012).
It is a challenging task to simulate surface waves on fringing reefs because the associated hydrodynamics is more complex than that on common beaches (Nwogu and Demirbilek, 2010; Roeber, 2010; Yao et al., 2012; Fang et al., 2016). Phase-averaged spectral wave model SWAN was applied to describe wave transformation over fringing reefs by Filipot and Cheung (2012). They found that SWAN properly fitted the observed wave height and setup after fine tuning but failed to describe the nonlinear energy transfer toward the infra-gravity band that was observed in the laboratory and field studies. Buckley et al. (2014, 2015) reported that tuning the SWAN to best reproduce the observed wave height decay across a laboratory reef profile often resulted in a reduction in the accuracy of wave setup predictions. Recently developed shock-capturing Boussinesq models (Roeber et al., 2010; Shi et al., 2012; Yao et al., 2012; Fang et al., 2016; Fang et al., 2016; Kazolea et al., 2014) and depth-integrated non-hydrostatic models (Yamazaki et al., 2009; Fang et al., 2015ab) were successfully used to simulate wave propagation over fringing reef profiles. In these kinds of models, wave breaking is evaluated by shifting Boussinesq-type equations or depth-integrated Euler equations to nonlinear shallow water equations. However breaking criterion should be provided to initialize and cease breaking event. In addition, the velocity field is not available due to the depth-integrated nature of the governing equations. The above mentioned limitations could be overcome by using a multi-layer non-hydrostatic model as proved by Ai and Jin (2012); Ma et al. (2012) and Ma and Shi (2014).
