Numerical modeling of low-frequency wave dynamics over a fringing coral reef

Low-frequency (infragravity) wave dynamics on a fringing coral reef were investigated using the numerical model XBeach (Roelvink et al., 2009). First, the skill of the model was evaluated in one- and two-dimensions based on its predictions of short waves (0.04–0.2 Hz), infragravity waves (0.004–0.04 Hz) and water level measurements (tidal and wave setup) obtained during a 2009 field study at Ningaloo Reef in Western Australia. The model calibration was sensitive to friction coefficients for short waves and current/infragravity bed friction, which were assumed independent in this model study. Although the one-dimensional cross-shore model captured the gradients in the dominant hydrodynamic processes at the site, a high current/IG bed friction coefficient was required. This resulted in an overestimation and a phase lag between the observed and predicted wave setup signal. In the two-dimensional model, a lower (more realistic) current/infragravity wave friction coefficient was required to achieve optimum performance due to the presence of significant reef and lagoon mean flows in the model, which led to reduced setup across the reef. The infragravity waves were found to propagate from the surf zone across the reef in a dominantly cross-shore direction towards the shore, but with substantial frictional damping. The infragravity waves were strongly modulated also over the reef by tidal depth variations, primarily due to the variability in frictional dissipation rates when the total water depth over the reef varied. Two mean wave-driven circulation cells were observed in the study area, with cross-shore flow becoming more alongshore-dominated before exiting the system via the two channels in the reef. The results reveal that short waves dominated bottom stresses on the forereef and near the reef crest; however, inside the lagoon, infragravity waves become increasingly dominant, accounting up to 50% of the combined bottom stresses.

► Infragravity wave energy dominates swell wave energy over the reef and accounts for 50% of shear stresses locally.
► Model results both in 1D and 2D compare well to data for the duration of a swell event.
► In the two-dimensional model, a lower friction coefficient was required due to the presence of significant mean flows.
► IG waves are predominantly generated by the breakpoint mechanism and dissipated by friction.
► The infragravity waves were modulated by tidal depth variations, primarily due to the variability in frictional dissipation.