Application of a Consistent Nonlinear Mild-Slope Equation Model to Random Wave Propagation and Dissipation

In the context of actual surface wave conditions, the wave field is represented as a set of complex fluctuations that randomly change in both time and space, commonly known as “random waves.” These random waves can be expressed mathematically as a combination of multiple monochromatic waves, each having unique phases, directions, and amplitudes. Frequency-domain phase-resolving wave models have been shown to be robust predictors of random wave propagation provided the dispersive characteristics are valid for the range of water depths considered. Recently, a new dispersive nonlinear mild-slope equation model was developed by establishing a closer correspondence between the scaling of nonlinearity, horizontal depth variation, and modulation scale during the derivation process. In this work, this new model is augmented with a wave-breaking dissipation model using frequency-squared dissipation weighting over the wave spectrum. The new model and previous models are compared with laboratory data for accuracy in modeling the evolution of the random wave spectrum. Overall, the new model demonstrates improved agreement with results compared with the previously derived models. The additional nonlinear terms of the model, indicating the interaction effects between amplitude and amplitude change, correct the overprediction of wave spectral energy from prior models, especially at the lower frequencies of the shallowest gauges. Furthermore, the predictions of free surface elevation by the newly derived model are in excellent agreement with the observations at the shallowest gauge, primarily due to the alleviation of phase mismatch caused by the additional terms. Lastly, we provide the nonlinear modification to linear wavenumber on the basis of the additional nonlinearity.