An eddy viscosity model for two-dimensional breaking waves and its validation with laboratory experiments

Abstract

An eddy viscosity model to describe energy dissipation in two-dimensional breaking waves in deep water is implemented in a numerical model for the evolution of nonlinear surface waves and evaluated with experimental results. In the experiments, to develop a reliable eddy viscosity model, breaking waves are generated by both energy focusing and modulated wave groups. Local wave parameters prior to and following breaking are defined and then determined. Significant correlations between the pre-breaking and post-breaking parameters are identified and adopted in the eddy viscosity model. The numerical model detects automatically wave breaking onset based on local surface slope, determines pre-breaking local wave parameters, predicts post-breaking time and length scales, and estimates eddy viscosity to dissipate energy in wave breaking events. Numerical simulations with the model are performed and compared to the experiments. It is found that the model predicts well the total energy dissipation due to breaking waves. In addition, the computed surface elevations after wave breaking agree reasonably well with the measurements for the energy focusing (plunging) wave groups. However, for breaking wave groups due to modulational instability (plunging and spilling), a relatively large discrepancy between the surface elevation predictions and the experimental measurements is observed, in particular, at the downstream wave probe locations. This is possibly due to wave reflection and three-dimensionality in the experiments. To further validate the eddy viscosity model, the evolution of highly nonlinear irregular waves is studied numerically and the numerical solutions are compared with additional independent laboratory experiments for long-crested irregular waves. It is shown that the numerical model is capable of predicting the wave evolution subsequent to wave breaking.