In this paper, a Reynolds-averaged Navier–Stokes (RANS) equations solver, interFoam of OpenFOAM^®, is validated for wave interactions with a dike, including a promenade and vertical wall, on a shallow foreshore. Such a coastal defence system is comprised of both an impermeable dike and a beach in front of it, forming the shallow foreshore depth at the dike toe. This case necessitates the simulation of several processes simultaneously: wave propagation, wave breaking over the beach slope, and wave interactions with the sea dike, consisting of wave overtopping, bore interactions on the promenade, and bore impacts on the dike-mounted vertical wall at the end of the promenade (storm wall or building). The validation is done using rare large-scale experimental data. Model performance and pattern statistics are employed to quantify the ability of the numerical model to reproduce the experimental data. In the evaluation method, a repeated test is used to estimate the experimental uncertainty. The solver interFoam is shown to generally have a very good model performance rating. A detailed analysis of the complex processes preceding the impacts on the vertical wall proves that a correct reproduction of the horizontal impact force and pressures is highly dependent on the accuracy of reproducing the bore interactions.

Three open source wave models are applied in 2DV to reproduce a large-scale wave flume experiment of bichromatic wave transformations over a steep-sloped dike with a mildly-sloped and very shallow foreshore: (i) the Reynolds-averaged Navier–Stokes equations solver interFoam of OpenFOAM^® (OF), (ii) the weakly compressible smoothed particle hydrodynamics model DualSPHysics (DSPH) and (iii) the non-hydrostatic nonlinear shallow water equations model SWASH. An inter-model comparison is performed to determine the (standalone) applicability of the three models for this specific case, which requires the simulation of many processes simultaneously, including wave transformations over the foreshore and wave-structure interactions with the dike, promenade and vertical wall. A qualitative comparison is done based on the time series of the measured quantities along the wave flume, and snapshots of bore interactions on the promenade and impacts on the vertical wall. In addition, model performance and pattern statistics are employed to quantify the model differences. The results show that overall, OF provides the highest model skill, but has the highest computational cost. DSPH is shown to have a reduced model performance, but still comparable to OF and for a lower computational cost. Even though SWASH is a much more simplified model than both OF and DSPH, it is shown to provide very similar results: SWASH exhibits an equal capability to estimate the maximum quasi-static horizontal impact force with the highest computational efficiency, but does have an important model performance decrease compared to OF and DSPH for the force impulse.

This study comprises a detailed description of the individual overtopped bore impact processes against a vertical wall, situated on top of a dike. A twin peak force impact signal shape was observed with two distinct peaks during every impact. The two peaks were assigned consecutively to the dynamic components (thickness and velocity) or hydrostatic components (run-up of water at the wall) of the impacting bore. The two peaks were termed dynamic F1 and quasi-static F2 impact respectively. Based on available literature semi-empirical equations to describe either the dynamic F1 or quasi-static F2 impact force were investigated and the prediction accuracy evaluated using impact force data from large-scale experiments. The prediction accuracy of the dynamic F1 impacts was very low. The prediction accuracy of the quasi-static impact F2 was increased based on fitting the hydrostatic theory to the maximum run-up measurement at the wall. Based on these findings 80% of the maximum run-up height was effectively contributing to the maximum quasi-static force F2 on the wall. The results coincided well with previous small-scale studies (Chen et al. 2012). After deconstructing the process chain preceding an impact, using the physically most meaningful parameters to predict the impact force, evaluating on a range of existing approaches, and observing the scattered prediction results, it was concluded that the impact behavior is highly stochastic and statistical analysis would be more beneficial.

Wave overtopping is a critical parameter in the design of coastal defense structures. Nowadays, several empirical formulations based on small-scale experiments are available in the literature to predict the mean overtopping discharge at dikes on shallow foreshores. Although the accuracy of the predictions has improved due to each approach’s contributions, the formulations’ performance depends on their range of applicability. In engineering applications, it is important to know the performance and limitations of the different formulas. This work presents a new experimental dataset focused on very shallow and extremely shallow foreshore conditions for a range of foreshore slopes (i.e., 1/20, 1/35, 1/50, and 1/80) and relative water depths. The recent developments in wave overtopping research on very shallow and extremely shallow foreshore conditions have been reviewed using this dataset to reflect the existing uncertainties and challenges in the wave-overtopping literature. We find that predicting wave overtopping for extremely shallow foreshore conditions still requires improvement. Additional research is needed to understand the (residual) influence on the wave overtopping of the foreshore slope and relative magnitude of the infragravity wave height to the sea-swell wave height at the dike toe, especially for extremely shallow foreshore conditions. The variation in performance of the formulas for different foreshore slopes is demonstrated. Finally, some of the remaining uncertainties that need further exploration are discussed.

Groynes were constructed west of the Volta river mouth sand spit in Ghana to mitigate the local average beach retreat of 6 m/year. Even though severe swell events occurred during the construction of the first couple of groynes, the sand spit retreat of about 150 m over less than 1 year was surprising. An in-depth analysis was done by performing a hindcast over that year with the 2DH morphological model XBeach. It qualitatively reproduced the sand spit evolution as measured in situ. The governing processes of the severe erosion of the sand spit, in addition to the effect of the groynes, were identified to be a longshore sediment transport gradient and differences in overwash occurrence. A second hindcast, without groynes, has shown that the groynes were not the main cause. It also demonstrated that the beach, which was to be protected, has clearly benefitted from the construction of the groynes.

This paper introduces the 2D experiments conducted for the CREST project in the wave flume of Ghent University. The experiments focus on wave interactions with low-crested sea dikes fronted by a shallow foreshore and mildly to steeply sloping beaches, which is a very typical situation along the Belgian coast. Foreshore slopes of 1/20, 1/35, 1/50 and 1/80 were tested for a range of low to high energy wave conditions, a variation in wave steepness and two water levels. The main goal was to obtain a dataset in which the effects of the infragravity waves on the wave-structure interactions (i.e. wave overtopping and impact forces) can be studied. The tests included high spatial resolution surface elevation measurement tests, which is new for beaches including a dike in the inner surf zone. From the first results it became clear that the foreshore slope influences the wave transformation up to the dike toe. The influence is apparent comparing to existing (semi-) empirical models for prediction of the spectral wave period at the dike toe and wave overtopping at the dike crest. The high spatial resolution data show a steep increase in infragravity significant wave height in the very shallow area in front of the dike.