The work highlights the importance of directional spreading effects on wave overtopping estimation in shallow and mild sloping foreshores. Wave short-crestedness leads, in general, to a reduction of mean overtopping discharges on coastal structures. In the present work, the case of a sea dike with gentle foreshore in very and extremely shallow water conditions is analysed. Physical model tests have been carried out in order to investigate the effect of directional spreading on overtopping and incident wave characteristics. In the present experimental campaign, the effect of wave spreading has only been investigated for perpendicular wave attack. Results show that directional spreading is proved to cause a reduction of average discharge of sea dikes with gentle and shallow foreshore. Expressions for the reduction factor for directional spreading are derived, fitted on the tested database. The use of this reduction factor leads to more accurate prediction and avoids overtopping overestimation, however reduction-factor formulations are overtopping-formula depending.

Physical model experiments were conducted in a wave tank at Flanders Hydraulics Research, Antwerp, Belgium, to characterize the wave overtopping and impact force on vertical quay walls and sloping sea dike (1:2.5) under very oblique wave attack (angle between 45° and 80°). This study was triggered by the scarce scientific literature on the overtopping and force reduction due to very oblique waves since large reduction is expected for both when compared with the perpendicular wave attack. The study aimed to compare the results from the experimental tests with formulas derived from previous experiments and applicable to a Belgian harbor generic case. The influence of storm return walls and crest berm width on top of the dikes has been analyzed in combination with the wave obliqueness. The results indicate significant reduction of the overtopping due to very oblique waves and new reduction coefficients were proposed. When compared with formulas from previous studies the proposed coefficients indicate the best fit for the overtopping reduction. Position of the storm return wall respect to the quay edge rather than its height was found to be more important for preventing wave induced overtopping. The force reduction is up to approximately 50% for the oblique waves with respect to the perpendicular wave impact and reduction coefficients were proposed for two different configurations a sea dike and vertical quay wall, respectively.

Due to ongoing climate change, overtopping risk is increasing. In order to have effective countermeasures, it is useful to understand overtopping processes in details. In this study overtopping flow on a dike with gentle and shallow foreshores are investigated using a non-hydrostatic wave-flow model, SWASH (an acronym of Simulating WAves till SHore). The SWASH model in 2DV (i.e., flume like configuration) is first validated using the data of long crested wave cases with second order wave generation in the physical model test conducted. After that it is used to produce overtopping flow in different wave conditions and bathymetries. The results indicated that the overtopping risk is better characterized by the time dependent h (overtopping flow depth) and u (overtopping flow velocity) instead of h_max (maximum overtopping flow depth) and u_max (maximum overtopping flow velocity), which led to overestimation of the risk. The time dependent u and h are strongly influenced by the dike configuration, namely by the promenade width and the existence of a vertical wall on the promenade: the simulation shows that the vertical wall induces seaward velocity on the dike which might be an extra risk during extreme events.

Verwaest, T.; Houthuys, R.; Roest, B.; Dan, S., and Montreuil, A.-L., 2020. A coastline perturbation caused by natural feeding from a shoreface-connected ridge (headland Sint-André, Belgium). In: Malvárez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 701-705. Coconut Creek (Florida), ISSN 0749-0208. This paper explains how a local seaward perturbation, headland Sint-André, in the straight sandy coastline of Belgium can persist for centuries. The diffusive longshore transport gradients on the beach are counterbalanced by a sediment supply from off-shore via a shoreface-connected ridge. A UNIBEST-CL+ 1D coastline model is set up to describe the genesis of this coastline feature. From the size and shape of the perturbation and taking into account the diffusivity caused by the longshore transport gradients, the average sand supply from offshore is estimated to be 55,000 m3/year and it is hindcasted that the connection of the ridge to the coastline occurred between 300 and 400 years ago.

Estimation of wave overtopping over the crest of coastal structures is crucial to design effective and cost efficient countermeasures against storms. Semi-empirical formulas are often used for wave overtopping assessment, but they are not always applicable for complex structures which exist in reality (e.g. a storm wall on a dike in a shallow or very shallow foreshore). Detailed numerical models such as Eulerian and Lagrangian RANS models have potential to simulate overtopping of complex coastal structures with good accuracy. However such models require significant computational resources. The use of such models is often not feasible for the design of coastal structures, which often requires multiple iterations and model runs over a reasonably long period of time (e.g. wave trains with 1000 individual waves). In this paper we investigated the applicability of the simplified depth integrated wave transformation model SWASH for wave overtopping estimation of impermeable coastal structures in shallow foreshores. The validation results demonstrate the capability of SWASH to predict mean wave overtopping discharge with good accuracy compared to results from four different overtopping experimental campaigns (comprising 124 individual cases). The overall performance of SWASH to estimate mean wave overtopping discharge is as accurate as those obtained by semi-empirical equations in literature. However, in order to obtain accurate mean wave overtopping discharge with the SWASH model, the incident wave properties at the toe of the dike need to be accurately reproduced. For cases where this is not possible, a correction method is proposed in this paper. Detailed validation of the instantaneous wave overtopping also shows a good agreement with physical model data. In one example, a single, intensive overtopping event was not well resolved by the SWASH model and the instantaneous wave overtopping was under-predicted. However, this did not contribute significantly to the mean wave overtopping discharge. An additional advantage of the SWASH model is that specific coastal structure geometries can be modelled in SWASH if they are not covered by semi-empirical equations. Even in a case with rapidly varied flow (e.g. vertical wall on a dike) the model shows sufficient robustness. In this paper the details on the SWASH model configuration and post processing methods are outlined to enable the reader to reproduce reliable wave overtopping estimation over impermeable coastal structures in shallow foreshores.

Wave overtopping is one of the key parameters for designing coastal structures: the crest level is usually determined using admissible overtopping discharges. Several formulae already exist for wave overtopping assessment that predict the average overtopping discharge per meter width of the coastal defence, generally for deep or intermediate water depths at the toe of the dike. However, the process of wave overtopping on sea dikes with shallow and very shallow foreshore is not yet fully understood. Gentle foreshores in combination with (very) shallow water conditions lead to heavy wave breaking and a significant change of the wave spectra from offshore to the toe of the dike. The wave steepness is assumed as one of the main criteria to identify cases of severe wave breaking on shallow and very shallow foreshores. For these conditions, Van Gent's formula, generally used for wave overtopping with shallow foreshores, has been implemented and validated against experimental data. It is the purpose of this paper to show that Van Gent's formula overestimates the average overtopping discharge for cases of very shallow foreshores. Moreover the existing formula cannot be applied to cases with an emergent toe. The present work therefore introduces a new “equivalent slope” concept to obtain an estimation of average wave overtopping discharges on sea dikes with shallow and very shallow foreshores. This study uses data from CLASH database and experimental campaigns, specifically carried out at Flanders Hydraulics Research (Belgium), in order to validate this approach. Results indicate that this concept shows better performance compared to other empirical formulae, which suggests that the influence of the very shallow foreshore on the average wave overtopping discharge should be included.