Long Wave Effects on Breaking Waves Over Fringing Reefs

Abstract

Modeling of wave energy transformation and breaking on fringing reefs is inherently difficult due to their unique topography. Prior methods of determining dissipation are based on empirical data from gently sloping beaches and offer only bulk energy dissipation estimates over the entire spectrum. Methods for deducing a frequency dependent dissipation have been limited to hypothesized linkages between dissipation and wave shape in the surf, and have used bulk dissipation models as a constraint on the overall dissipation for mild sloping beaches. However, there is no clear indication that the constraint on the overall level of dissipation is suitable for the entire reef structure. Using these constraints the frequency dependent dissipation rate can be deduced from laboratory data, taken at the Coastal and Hydraulics Laboratory, of wave transformation over reefs. The frequency dependent dissipation rate can then be integrated over the spectrum to derive an empirically-based counterpart to energy flux dissipation. Comparing the bulk energy dissipation estimates for the reef system to the frequency based method allows for the modification of wave breaking parameters in the frequency estimation, to better estimate total dissipation. Since this method is based on the Fourier transform of the time series data, it allows the dissipation to be found as a function of the frequency. This analysis shows that there is a correlation between the amount of energy in the low frequencies of the wave spectrum and certain characteristics of the frequency dependent dissipation coefficient.

Experimental and Numerical Studies on Wave Breaking Characteristics over a Fringing Reef under Monochromatic Wave Conditions

“…The results were compared with the laboratory experiments conducted by Demirbilek et al [ 37 ] and checked the dependency of the incipient breaker depth index, the breaking-intensity parameter, and the nonlinearity parameter on the measured data. Goertz et al [ 38 ] applied probabilistic bulk dissipation models to estimate wave energy dissipation on a reef structure by comparing the results to the two-dimensional laboratory experimental data under the irregular wave conditions but no one accurately estimated wave energy dissipation by breaking over the reef structure. Yao et al [ 39 ] conducted laboratory experiments of wave breaking over idealized fringing reef under the monochromatic wave conditions to understand the effects of reef-flat submergence and the fore-reef slope on the wave breaking characteristics.…”