Physical and Numerical Modeling of Wave-by-Wave Overtopping along a Truncated Plane Beach

Abstract

Wave-by-wave and cumulative overtopping data from fixed planar impermeable smooth beaches will be presented from random wave experiments and compared with predictions from two nonlinear shallow water equations (NLSWE) models, Australian National University and Geoscience Australia (ANUGA) and Simulating WAves till SHore (SWASH). These models have been tested and used by many researchers in various coastal processes studies. However, the capability of the models has not been tested when modeling wave-by-wave overtopping processes, and there is relatively limited validation for cumulative or time-averaged overtopping. The verified numerical models will be used to perform a parametric study on the relationship between overtopping and beach slope (β), which has not been well resolved in the literature. This paper shows that the models provide reliable estimates of nearshore wave transformation and run-up, which includes the shoreline motion on a nontruncated beach, with SWASH modeling wave shoaling accurately. For the experimental configuration of a beach that was truncated with a sharp vertical edge, ANUGA provided more reliable estimates of wave-by-wave and cumulative overtopping and predicted total overtopping volumes without bias and within a few percent on the average overall. For wave-by-wave and cumulative overtopping SWASH is sensitive to the bathymetry at the overtopping edge, under predicting total overtopping volumes by approximately 25% for a sharp vertical edge but overpredicting by approximately 20% for a flat crest followed by a downward slope. A detailed investigation indicated that partial reflection occurred at the overtopping edge in the SWASH model for some configurations of the bathymetry, which lead to overestimated depths but reduced durations for positive discharge. The influence of β on the ANUGA model run-up predictions and overtopping will be investigated and compared with empirical formulations. The ANUGA predictions for run-up were consistent with the empirical formulations for low β and were linearly proportional to β (tan β), but were proportional to β at a smaller power for a higher β, which differed from the relationship given in some empirical models. For a given beach crest elevation (zc) with a sharp vertical edge and fixed wave conditions, the numerical ANUGA model and empirical model predictions for overtopping were approximately linearly proportional to tan β, but the exact power varied depending on the chosen model. This was in contrast to some of the existing empirical models (when this dependency was explicit), but it was consistent with the analytical SWASH solution when written for positive volume flux (Vo) and deficit in the freeboard (R-zc) scaling. The numerical predictions from ANUGA agreed well with the empirical models. The modeling provided a new interpretation of the influence of the β on overtopping in the empirical EurOtop formulation, where the complete influence of β is not explicitly provided.