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 composed 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 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.

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Understanding key flooding processes such as wave overtopping and overflow (i.e., water flows over a structure when the crest level of the structure is lower than the water level in front) is crucial for coastal management and coastal safety assessment. In port and harbour environments, waves are not only perpendicular to the coastal structure but also very oblique, with wavefronts almost perpendicular to the main infrastructures in the harbour docks. Propagation and wave–structure interaction of such perpendicular and (very) oblique waves need to be appropriately modelled to estimate wave overtopping properly. Overflow can also be critical for estimating flooding behind any coastal defence. In this study, such oblique and parallel waves (i.e., main wave direction is parallel to the structures) are modelled in a non-hydrostatic wave model and validated with physical model tests in the literature. On top, overflow is also modelled and validated using an existing empirical formula. The model gives convincing behaviours on the wave overtopping and overflow.

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Ongoing climate change is a significant threat to coastal communities. To understand potential risks during extreme storm events, detailed post-overtopping processes are investigated using DualSPHysics and SWASH with a newly developed approach. It is a calibrated-based wave generation: a target incident wave is first obtained from the validated SWASH model, and DualSPHysics creates the target incident wave by adjusting the offshore wave and bathymetry conditions. This one-way coupling process makes the DualSPHysics computation efficient enough to apply 3D simulation. With a vertical wall at the end of a room located at the end of the promenade in a mild and shallow foreshore, the present model shows a good correspondence on the wave force with the literature. After confirming the efficiency and accuracy of the present model, the 3D simulation with furniture inside the room was conducted and visualized with the state-of-the-art visualization technique. Based on the visualization, the potential risks during the extreme storm event are further discussed in this paper. The present work shows a further capability of DualSPHysics to deal with wave–object–structure interaction based on the latest developments in an efficient way. The developed model can be further used to understand the potential risks of ongoing climate change.

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As waves interact with the slopes of coral reefs and other steep bathymetry profiles, plunging breaking usually occurs where the free surface overturns and violent water motion is triggered. Resolving these surf zone processes pose significant challenges for conventional mesh-based hydrodynamic models, due to the rapidly-deforming nature of the free surface and associated flows. Yet the accurate prediction of these surf zone hydrodynamics is critical for predicting a wide range of nearshore processes driven by wave breaking (e.g., wave dissipation and energy transfers; mean water levels and currents; and wave runup). In this study we assess the ability of the mesh-free, Lagrangian particle-based numerical modelling approach Smoothed Particle Hydrodynamics (SPH) based on DualSPHysics, to simulate the fine-scale hydrodynamic processes driven by irregular wave transformation over a fringing reef profile, by comparing results against detailed experimental observations from a physical modelling study. To greatly improve the computational efficiency, the SPH model was coupled to the mesh-based multi-layer nonhydrostatic wave-flow model SWASH. With this coupled approach, SWASH was used to efficiently simulate the evolution of non-breaking waves from the wavemaker up to the fore reef slope, with the SPH model then used to simulate the detailed hydrodynamic processes over the reef from just offshore of the breakpoint to the shoreline. The SPH model was able to accurately reproduce the complex free surface deformations during plunging breaking, the spectral evolution of waves across the reef flat (including nonlinear wave shape), the mean water levels and currents, and wave runup at the shoreline. Using the long duration simulations (>400 wave periods), the model was able to reproduce the full range of wave motions over the reef (from sea-swell to infragravity frequencies), including the increasing dominance of low frequency waves towards the shoreline and the large cross-reef standing wave motions excited by the reef geometry.

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This work presents the results of an investigation on how wave overtopping at a near-vertical seawall at the back of a sandy foreshore is influenced by sequences of erosive storms. The experiments were carried out in the Large Wave Flume (GWK) at Leibniz University, Hannover (Germany). The tested layout consisted of a near-vertical 10/1 seawall and a sandy foreshore with an initial 1/15 slope. Three sequences of idealised erosive storms were simulated. Within each storm both the incident wave conditions and still water level were varied in time to represent high and low tide conditions. Each sequence started from a 1/15 configuration and the beach was not restored in between storms. The measurements included waves, beach profile, wave overtopping volumes. The profile of the beach was measured after each sea state tested. Wave overtopping at each stage of the tested storms was significantly influenced by bed changes. This was linked to the measured evolution of the beach. Measurements showed that a barred profile developed quickly at the start of each sequence, and scour developed at the toe of the structure during high water level conditions, while accretion or partial backfilling developed during low water level conditions. Due to these processes, the position of a sea state in the tested sequence is shown to be an important factor in determining the wave overtopping volume. Remarkably, when a weaker idealised storm followed a more energetic one, nearly the same level of overtopping was recorded. This is explained by the foreshore erosion, leading to increased water depths and wave heights at the toe of the structure. This finding allows to quantify and to explain the variability of wave overtopping in storms following one another at intervals shorter than the recovery time of the foreshore.

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The state-of-The-Art formulas for mean wave overtopping (q) assessment typically require wave conditions at the toe of the structure as input. However, for structures built either on land or in very shallow water, obtaining accurate estimates of wave height and period at the structure toe often proves difficult and requires the use of either physical modeling or high-resolution numerical wave models. Here, we follow Goda's method to establish an accurate prediction methodology for both vertical and sloping structures based entirely on deep-water characteristics-where the influence of the foreshore is captured by directly incorporating the foreshore slope and the relative water depth at the structure toe (htoe/Hm0,deep). Findings show that q decreases exponentially with htoe/Hm0,deep due to the decrease of the incident wave energy; however, the rate of reduction in q decreases for structures built on land or in extremely shallow water (htoe/Hm0,deep ≤ 0.1) due to the increased influence of wave-induced setup and infragravity waves-which act as long-period fluctuations in mean water level-generated by nonlinear wave transformation over the foreshore.

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Despite the widely recognized role of infragravity (IG) waves in many often-hazardous nearshore processes, spectral wave models, which exclude IG-wave dynamics, are often used in the design and assessment of coastal dikes. Consequently, the safety of these structures in environments where IG waves dominate remains uncertain. Here, we combine physical and numerical modeling to: (1) assess the influence of various offshore, foreshore, and dike slope conditions on the dominance of IG waves over those at sea and swell (SS) frequencies; and (2) develop a predictive model for the relative magnitude of IG waves, defined as the ratio of the IG-to-SS-wave height at the dike toe. Findings show that higher, directionally narrow-banded incident waves; shallower water depths; milder foreshore slopes; reduced vegetated cover; and milder dike slopes promote IG-wave dominance. In addition, the empirical model derived, which captures the combined effect of the varied environmental parameters, allows practitioners to quickly estimate the significance of IG waves at the coast, and may also be combined with spectral wave models to extend their applicability to areas where IG waves contribute significantly.

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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.

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Design criteria for coastal defenses exposed to wave overtopping are usually assessed by mean overtopping discharges and maximum individual overtopping volumes. However, it is often difficult to give clear and precise limits of tolerable overtopping for all kinds of layouts. A few studies analyzed the relationship between wave overtopping flows and hazard levels for people on sea dikes, confirming that one single value of admissible mean discharge or individual overtopping volume is not a sufficient indicator of the hazard, but detailed characterization of flow velocities and depths is required. This work presents the results of an experimental campaign aiming at analyzing the validity of the safety limits and design criteria for overtopping discharge applied to an urbanized stretch of the Catalan coast, exposed to significant overtopping events every stormy season. The work compares different safety criteria for pedestrians. The results prove that the safety of pedestrians on a sea dike can be still guaranteed, even for overtopping volumes larger than 1,000 L/m. Sea storms characterized by deep-water wave height between 3.6 and 4.5 m lead to overtopping flow depth values larger than 1 m and flow velocities up to 20 m/s. However, pedestrian hazard is proved to be linked to the combination of overtopping flow velocity and flow depth rather than to single maximum values of one of these parameters. The use of stability curves to assess people's stability under overtopping waves is therefore advised.

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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.

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Practitioners often employ diverse, though not always thoroughly validated, numerical models to directly or indirectly estimate wave overtopping (q) at sloping structures. These models, broadly classified as either phase-resolving or phase-averaged, each have strengths and limitations owing to the physical schematization of processes within them. Models which resolve the vertical flow structure or the full wave spectrum (i.e. sea-swell (SS) and infragravity (IG) waves) are considered more accurate, but more computationally demanding than those with approximations. Here, we assess the speed-accuracy trade-off of six well-known models for estimating q, under shallow foreshore conditions. The results demonstrate that: i) q is underestimated by an order of magnitude when IG waves are neglected; ii) using more computationally-demanding models does not guarantee improved accuracy; and iii) with empirical corrections to incorporate IG waves, phase-averaged models like SWAN can perform on par, if not better than, phase-resolving models but with far less computational effort.

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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.

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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.

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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.

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In this study we investigated the capabilities of the mesh-free, Lagrangian particle method (Smoothed Particle Hydrodynamics, SPH) to simulate the detailed hydrodynamic processes generated by both spilling and plunging breaking waves within the surf zone. The weakly-compressible SPH code DualSPHysics was applied to simulate wave breaking over two distinct bathymetric profiles (a plane beach and fringing reef) and compared to experimental flume measurements of waves, flows, and mean water levels. Despite the simulations spanning very different wave breaking conditions (including an extreme case with violently plunging waves on an effectively dry reef slope), the model was able to reproduce a wide range of relevant surf zone hydrodynamic processes using a fixed set of numerical parameters. This included accurate predictions of the nonlinear evolution of wave shapes (e.g., asymmetry and skewness properties), rates of wave dissipation within the surf zone, and wave setup distributions. By using this mesh-free approach, the model was able to resolve the critical crest region within the breaking waves, which provided robust predictions of the wave-induced mass fluxes within the surf zone responsible for the undertow. Within this breaking crest region, the model results capture how the potential energy of the organized wave motion is initially converted to kinetic energy and then dissipated, which reproduces the distribution of wave forces responsible for wave setup generation across the surf zone. Overall, the results reveal how the mesh-free SPH approach can accurately reproduce the detailed wave breaking processes with comparable skill to state-of-the-art mesh-based Computational Fluid Dynamics (CFD) models, and thus can be applied to provide valuable new physical insight into surf zone dynamics.@en

While the significance of infragravity waves (IG) in many—often-hazardous—nearshore processes is widely-recognized, many of the empirical and numerical models used in dike safety assessments do not (directly) consider their contribution. Here, we combine physical and numerical modelling to better understand the factors that contribute to the dominance of IG waves over higher-frequency waves at the dike toe. Findings show that IG-wave dominance increases as the ratio of local water depth to offshore significant wave height decreases. Therefore, it is critical that any tool used to assess the safety of dikes fronted by very and extremely shallow foreshores accurately describe IG-wave dynamics.

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In this study we assess the capabilities of the mesh-free, Lagrangian particle method (Smooth Particle Hydrodynamics, SPH) method to simulate the detailed hydrodynamic processes generated by both spilling and plunging breaking waves within the surf zone, and present how the approach can be used to predict a broad spectrum of hydrodynamic processes relevant to coastal applications where wave breaking is important. The weakly-compressible SPH code DualSPHysics was applied to simulate wave breaking over two bathymetric profiles (a plane beach and fringing reef) and compared to experimental flume measurements of waves, currents, and mean water levels. We demonstrate how the model can accurately reproduce a broad range of relevant hydrodynamic processes, ranging from the nonlinear evolution of wave shapes across the surfzone, wave setup distributions, mean current profiles and wave runup. We compare the surfzone predictions with results from other classes of wave models, and illustrate some of the advantages of the SPH approach (particularly in resolving the hydrodynamics above the wave trough). Overall, the results reveal how the mesh-free SPH approach can accurately reproduce the detailed wave breaking processes with comparable skill to state-of-the-art mesh-based Computational Fluid Dynamic models, and how it can be used as a valuable tool to develop new physical insight into surf zone processes.

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Overtopping bore impact forces on a dike mounted vertical wall were measured in similar large-scale (Froude length scale factor 1-to-4.3) and small-scale (Froude length scale factor 1-to-25) models. The differences due to scale effects were studied, by comparing the up-scaled force measurements from both models in prototype. It was noted that if a minimum layer thickness, velocity of the overtopping flow and water depth at the dike toe were maintained in the small-scale model, the resulting differences in impact force due to scale effects are within the range of differences due to non-repeatability and model effects.@en

An improved Relaxation Zone (RZ) method has been implemented in the meshless SPH-based DualSPHysics model. Final purpose of this work is to have a general wave generation scheme that allows coupling SPH-based models to other models, e.g. Eulerian based wave models, besides employing the RZ as alternative wave generation in SPH as a stand-alone scheme. Using RZ in SPH, the movement of the fluid particles is controlled by correcting their orbital velocity by means of a weighting function in a specified generation area. In the present work, the new technique is used to couple DualSPHysics to the non-hydrostatic wave-flow model SWASH. The results of RZ employed both as stand-alone wave generation technique and as coupling framework with SWASH model are validated for wave generation and wave reflection for monochromatic waves. Then, the method is tested successfully for generation and absorption of irregular waves. Finally, the coupling between DualSPHysics and SWASH using RZ is validated against experimental data concerning the wave flow impacts on vertical walls. A procedure for a proper design of the RZ (i.e. shape of the weighting function, size of the RZ) is described in the present work. Overall, the results indicate that the proposed improved RZ technique is among the most effective alternatives for wave generation in SPH-based models for coastal engineering application.

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