Random wave runup and overtopping a steep sea wall: Shallow-water and Boussinesq modelling with generalised breaking and wall impact algorithms validated against laboratory and field measurements

A semi-implicit shallow-water and Boussinesq model has been developed to account for random wave breaking, impact and overtopping of steep sea walls including recurves. At a given time breaking is said to occur if the wave height to water depth ratio for each individual wave exceeds a critical value of 0.6 and the Boussinesq terms are simply switched off. The example is presented of waves breaking over an offshore reef and then ceasing to break as they propagate inshore into deeper water and finally break as they run up a slope. This is not possible with the conventional criterion of a single onset of breaking based on rate of change of surface elevation which was also found to be less effective generally. The runup distribution on the slope inshore of the reef was well predicted. The model is tested against field data for overtopping available for Anchorsholme, Blackpool and corresponding 1:15 scale wave flume tests. Reflection of breaking waves impacting a steep sea wall is represented as a partial reversal of momentum flux with an empirically defined coefficient. Offshore to nearshore significant wave height variation was reasonably predicted although nearshore model spectra showed distinct differences from the experiments. The breaking wave shape described by a shape parameter was also not well represented as might be expected for such a simple model. Overtopping agreement between model, field and flume was generally good although repeatability of two nominally identical flume experiments was only within 25%. Different distributions of random phase between spectral components can cause overall overtopping rates to differ by up to a factor of two. Predictions of mean discharge by EurOtop methods were within a factor of two of experimental measurements.