1DH Boussinesq modeling of wave transformation over fringing reefs

To better understand wave transformation process and the associated hydrodynamic characteristics over fringing coral reefs, we present a numerical study, which is based on one-dimensional (1D) fully nonlinear Boussinesq equations, of the wave-induced setups/setdowns and wave height changes over various fringing reef profiles. An empirical eddy viscosity model is adopted to account for wave breaking and a shock-capturing finite volume (FV)-based solver is employed to ensure the computational accuracy and stability for steep reef faces and shallow reef flats. The numerical results are compared with a series of published laboratory experiments. Our results show that with an appropriate treatment of boundary conditions and a fine-tuned eddy viscosity model, the full nonlinear Boussinesq model can give satisfactory predictions of the wave height as well as the mean water level over various reef profiles with different reef-flat submergences and reef-crest configurations under both monochromatic and spectral waves. The primary 1D wave transformation processes, including nonlinear shoaling, refection, breaking, generation of higher harmonics and infragravity waves, can also be reasonably captured. Finally, the model is applied to study the effects of reef-face slopes and profile shapes on the distribution of the wave height and mean water level over the fringing reefs