Wave Dissipation Formulations in Frequency Domain Models

Incorporation of wave dissipation due to breaking in both time-domain and frequency domain models have long been a subject of study. Until recently, the formulation of wave breaking in frequency domain models have been based on lumped-parameter dissipation models based on a Rayleigh distribution function for the wave heights in the surf zone (Battjes and Janssen, 1978; Thornton and Guza, 1983). Modifications to improve the dissipation model include allowing for nonlinear energy transfer (Mase and Kirby, 1992), which leads to improvements in predictions of the skewness and asymmetry. Bredmose (2004) show how time- domain wave breaking models can be included in a frequency domain version of the Boussinesq model using a time-domain inversion of the roller model. However, frequency domain versions of the Boussinesq model tend to perform poorly until the waves are close to breaking. In this study, we will show how time-domain wave breaking models can be included in frequency domain models that are based on the mild-slope formulation. We will then compare the results of using such a breaking model to the empirical bulk-dissipation formulation. Comparisons will include wave height distributions, skewness, and asymmetry. We will also discuss implications of using different breaking models on sediment transport.