SWASH Model Research Articles

Nonlinear modelling of arrays of submerged wave energy converters

Studies of arrays of wave energy converters (WECs) with respect to power absorption and array interactions are often performed using linear models. However, nonlinear effects can be important and may change power estimates and optimal array designs. In this study, we have compared linear predictions of the behaviour of a shallowly submerged, buoyant point absorber with predictions from the nonlinear model SWASH with a WEC incorporated (WEC-SWASH). The latter was first comprehensively validated against 1:20 Froude scaled measured data from physical experiments. WEC-SWASH predictions of body motions and mean power absorption were generally in good agreement with measurements (absolute bias within 25%), although some discrepancies were observed in the body motions, especially when the device exhibited motion instabilities. The validated WEC-SWASH model was then compared with a linear frequency-domain model, as the latter is well-known and widely used because of its computational efficiency. Model comparisons were carried out for both an isolated WEC and small arrays (up to 5 devices). The mean power estimates from the linear model and WEC-SWASH for two representative wave farms showed good agreement for mild waves, with a difference of less than 5%. However, for larger waves, the disagreement increased to about 75 to 85% between the models (for the two wave farms tested). We found that array interactions for these arrays depend on wave amplitude and not just wave frequency. Furthermore, we discovered that the power take-off coefficients optimized using the linear model were not the optimum coefficients for the nonlinear model (WEC-SWASH).

An overtopping formula for shallow water vertical seawalls by SWASH

There is now wide evidence that phase-resolving numerical models can capture the general physics of the overtopping process even under complex hydrodynamics. Based on this outcome, an extensive parametric study has been carried out with the model SWASH, to develop a design formula that uniformly predicts the overtopping rate at vertical seawalls for both breaking and non-breaking wave conditions. The use of the numerical model has allowed to vary the experimental conditions smoothly, avoiding the typical limitation of laboratory experiments. Furthermore, particular tests have been performed to assess whether, and up to which extent, the mean overtopping discharge is affected by the low frequency components of the incident wave spectrum.The formula relates the overtopping rate to a new water level statistic, which represents the average of the highest one-fourth wave displacements at the toe of the wall; it has initially been derived for planar beaches and then extended to the case of slope varying foreshores. A comparison with an array of 200 laboratory experiments confirms that the new parametrization can reduce the scatter of data compared to the EurOtop equation.

A study of the non-linear properties and wave generation of the multi-layer non-hydrostatic wave model SWASH

Despite the increasing use of non-hydrostatic models in the study of wave processes in coastal regions, there is still limited understanding of the non-linear properties of the governing equations and how they improve with increased vertical resolution. In this study, the governing equations of the non-hydrostatic wave model SWASH are analysed and the linear and non-linear solutions up to third-order of all dependent variables are derived, considering one to four vertical layers. The analysis concludes that the model can achieve excellent non-linear properties with respect to the Stokes theory over a large range of water depths using only a few vertical layers. Furthermore, deriving solutions for all variables enables the formulation of improved wave generation and absorption boundary conditions for non-hydrostatic models. A well-known issue of non-linear wave models is related to the generation and propagation of spurious free waves, resulting to non-homogeneous wave fields. In this study, it is proven that by imposing the derived exact mathematical solutions of the governing equations at the model’s boundaries, the target first- and second-order wave profiles can be generated with high accuracy, while the spurious waves can be entirely eliminated.

Effect analysis of wooden fence width on wave transmission by SWASH model

Wooden fences, a permeable structure, have become a nature-based solution for supporting traditional structures to restore mangrove forests along the Mekong deltaic coasts. Even though prior studies have explored a number of hydraulic functions of these fences, an in-depth investigation into the influence of fence width on wave dissipation and damping is needed to consider. Therefore, this paper employs a numerical approach to thoroughly examine the impact of fence width on wave damping. The findings illustrate the substantial role of fence width in governing the dissipation of incoming waves. The correlation between the transmission coefficient and the fence width is established. This relationship also concludes that the larger the fence thicknesses, the lower the transmission coefficients. Notably, the study also identifies that the transmission coefficient experiences a slight decline beyond a certain width threshold.

Including the effect of depth-uniform ambient currents on waves in a non-hydrostatic wave-flow model

Currents can affect the evolution of waves in nearshore regions through altering their wavenumber and amplitude. Including the effect of ambient currents (e.g., tidal and wind-driven) on waves in phase-resolving wave models is not straightforward as it requires appropriate boundary conditions in combination with a large domain size and long simulation duration. In this paper, we extended the non-hydrostatic wave-flow model SWASH with additional terms that account for the influence of a depth-uniform ambient current on the wave dynamics, in which the current field can be taken from an external source (e.g., from observations or a circulation model). We verified the model ability by comparing predictions to results from linear theory, laboratory experiments and a spectral wave model that accounts for wave interference effects. With this extension, the model was able to account for current-induced changes to the wave field (i.e., changes to the wave amplitude, length and direction) due to following and opposing currents, and two classical examples of sheared currents (a jet-like current and vortex ring). Furthermore, the model captured the wave dynamics in the presence of strong opposing currents. This includes reflections of relatively small amplitude waves at the theoretical blocking point, and transmission of breaking waves beyond the theoretical blocking point for larger wave amplitudes. The proposed model extension allows phase-resolving models to more accurately and efficiently simulate the wave dynamics in coastal regions with tidal and/or wind-driven flows.

Optimising the wave attenuation of bamboo fences using the numerical wave model SWASH

Mangroves protect tropical coastlines from flooding and erosion, reducing flood risks along coastal communities worldwide. Nevertheless, mangrove forests have experienced considerable losses due to activities like urbanization and aquaculture, exposing coastal areas to wave attack. To restore mangroves at eroding coastlines, structures formed by bamboo poles and a brushwood filling are used to shelter the coast from waves, and create a favourable habitat for mangrove colonization. However, these structures often lose their brushwood filling during storms, resulting in high maintenance costs. This study proposes a new type of design to reduce maintenance expenses, consisting of only vertical bamboo poles without a filling of brushwood. Structure designs are evaluated for a case study in Demak, Indonesia, using the numerical wave model SWASH to predict wave attenuation through the structures. Field measurements and WaveWatch III data are analyzed to obtain the design conditions for the structures in Demak. SWASH is validated against laboratory experiments, and applied to investigate the optimum number of rows and their optimum spacing (in the direction of wave propagation). The model shows that for a structure consisting of two rows of bamboo poles, the transmission rate Et/Ei decreases from 75% to 55% when the row spacing in the wave direction is increased from sx = 0.42 m to sx = 5.8 m. Larger spacings do not result in less transmission, and at least three rows are needed to have a transmission rate lower than 50 % - a common wave reduction target used in restoration efforts with structures. This study thus identifies potential strategies to maximize wave attenuation by bamboo structures, which can be used to reduce wave attack along muddy coasts without the need of a brushwood filling. Hereby, it provides an economically and user friendly alternative with respect to the previous brushwood structure designs, as it requires less material costs and maintenance. In addition, this study presents a new method to schematize these kind of structures in SWASH in an efficient way.

TECHNOLOGY-DRIVEN APPROACH TO THE MODELLING AND DESIGN OF ARTIFICIAL SURF REEFS

Most coastal protection projects consider amenity outcomes. Increasingly, surf amenity has become an important consideration. Artificial reefs have been promoted as creating coastal protection, surf amenity and ecological outcomes, however, delivering artificial reefs that provide sustained improvement in wave quality for surfing has proven challenging. This paper presents a novel and technology-driven approach for the design of artificial surfing reefs using the Southern Ocean Surf Reef (SOSR) project as an Australian case study. This proposed artificial reef at Middleton Beach, Albany consists of a submerged rock reef structure, the design of which has resulted from extensive investigations to optimise its performance. Results found that the SWASH model, when combined with Wave peel tracks (WPT) technology, was a valuable tool for valuating breaking mechanics of artificial reef surf breaks and designing and optimising the reef shapes that can be verified in physical modelling.

INVESTIGATION OF DIRECTIONAL SPREADING EFFECT ON WAVE RUN-UP USING SWASH

In order to keep optimal safety of coastal lines, it is necessary to maintain an appropriate crest level of coastal dikes. This is designed based on wave run-up height and/or wave overtopping discharge. Therefore, it is important to estimate wave run-up and overtopping as accurate as possible. However, the influence of directional spreading on wave run-up and overtopping has not been fully understood yet. In this study, non-hydrostatic model SWASH (Zijlema et al., 2011) is used. First, we implemented a wave run-up model in SWASH in 2DV (flume like) and 3D (basin like). Then wave run-up are simulated for some different cases and compared to the existing empirical wave run-up formulas in literature (e.g. Holman, 1986 and Mase, 1989).

Overtopping at Vagueira sea defence using the SWASH model

A praia da Vagueira está localizada no Município de Vagos, distrito de Aveiro e é protegida por uma estrutura de defesa frontal aderente que foi requalificada em 2015, com alteamento da sua cota de coroamento para + 10 m (ZH), devido à ocorrência de inundações na zona por ela protegida. Para caracterizar o galgamento com a estrutura atual, aplicou-se o modelo numérico SWASH a uma secção desta estrutura, simulando-se os temporais ocorridos entre 1979 e 2018 que, segundo as fórmulas comumente utilizadas para este tipo de estrutura, dariam galgamentos significativos. Assim, nesta comunicação apresenta-se o modelo utilizado, as características da estrutura de defesa aderente e as condições de agitação e nível de mar utilizadas nas simulações. Os resultados obtidos com o SWASH são comparados com os resultados de várias fórmulas empíricas. Para todas as condições testadas, as fórmulas empíricas apresentam sempre caudais médios de galgamento não nulos, enquanto o SWASH apenas origina caudais médios de galgamento superiores a zero quando o espraiamento máximo não atinge o coroamento da estrutura. Consequentemente, a utilização dos resultados das fórmulas empíricas para a emissão de alertas pode conduzir a situações de alarme que não correspondem à realidade.

Применение численного моделирования для расчета ветрового волнения на Крюковском водохранилище

Purpose: testing the possibilities of using the SWAN wind wave model with input characteristics according to the data of the Krasnodar (Pashkovskiy) weather station for the Kryukovskiy reservoir. Materials and methods. The studies were carried out at the Kryukovskiy reservoir, taking into account the conditions of formation of the processes of en-vironment-improving potential formation of the territory in southern Russia, which guarantees the reliability and environmental safety of the facility operation under conditions of an in-creasing risk of natural and man-made disasters on the example of the Krasnodar Territory. Field studies and field tests were carried out according to the Kuban State Agrarian University methods. When modeling the surge overwash for two different profiles (Northern and Western water barrier dams), the SWAN model data in a one-dimensional version were compared with the data obtained by SP 38.13330.2012. Results. The SWASH model provides reliable results and is an adequate alternative calculation option. Wave field data, which provides a good foundation for further study of the climatic variability of wind waves in the Kryukovskiy reservoir have been obtained. Conclusions. As a result of surge overwash modeling for two profiles under study, it was found that on average, the marks of the existing water barrier dam slope are higher than the surge in the design storm, mainly by 0.55–0.75 m, however, at PK 9 + 00 it was revealed that the slope top elevation of the Northern water pro-tection dam corresponds to the overwash mark. Therefore, it is necessary to continue research on monitoring the engineering protection of the Kryukovskiy reservoir using mathematical modeling, which confirmed the effectiveness and information content of the applicable SWAN model at a relatively low cost.

Fully nonlinear investigation on energy transfer between long waves and short-wave groups over a reef

Long waves are amplified as short-wave groups shoal and break over reefs, therefore, having significant impacts on coastal inundation, structure stability, and sediment transport. This study investigated the cross-reef variation of long-wave energy exchange with short-wave group over a reef using fully nonlinear analysis of simulation results by the non-hydrostatic model SWASH. The objective was to elucidate the mechanisms of long-wave transformation under nonlinear short-wave group forcing over a reef, and to assess the consequences of simplifications in linear and weakly nonlinear analyses in this problem. The energy transfer between short and long waves is the work done by wave radiation stress on long waves, which is the product of radiation-stress gradient and long-wave velocity. Unlike conventional linear and weakly nonlinear analysis, the Stokes transport and long-wave modulation of local water depth are included in the fully nonlinear analysis. It was found that only the long-wave energy flux gradient predicted by the fully nonlinear analysis was balanced by the work done by wave radiation stress over a shallow reef. The fully nonlinear analysis showed that strict mass conservation has to be used to extract long wave velocity properly. In contrast, in linear and weakly nonlinear analysis, the long-wave velocity is extracted from single-point velocity measurements. The fully nonlinear analysis demonstrated that the generation and growth of incoming breakpoint-forced long waves overcame the dissipation of bound long waves in the surf zone, leading to amplification of incoming long-wave energy flux. This phenomenon occurred even when short waves mainly broke over the horizontal reef flat with large submergence, indicating that long-wave evolution is not locally controlled but dependent on wave spatial evolution history. Outgoing breakpoint-forced long waves were dissipated considerably during de-shoaling over the forereef due to substantial energy transfer to incoming short waves, though both of them are free waves. The phase coupling between outgoing long waves and incoming short-wave groups occurred at all frequencies at the breakpoint, which was found to be the main driving mechanism for the energy transfer. According to the fully nonlinear analysis, the reef-flat submergence may affect the long wave in a complex fashion, i.e. , reducing the submergence may enhance the energy transfer from short waves to long waves or suppress long-wave growth by increasing its frictional dissipation at the same time. • Long-wave energy balance is achieved with fully nonlinear analysis, but not linear and weakly nonlinear ones. • Strict mass conservation has to be used to extract long-wave velocity properly. • Long wave amplitude is dependent on short-wave spatial evolution history. • Radiation stress does positive work on incoming long waves in both shoaling and surf zones. • Substantial energy is transferred from outgoing free long waves to incident short waves during de-shoaling.

Numerical Simulation on Reduced Runup Height of Solitary Wave by Fixed Submerged and Floating Rectangular Obstacles

The wave runup height is one of the most important parameters for affecting the design of coastal structures such as dikes, revetments, and breakwaters. In this study, SWASH (Zijlema et al., 2011), a non-hydrostatic pressure numerical model, was used to analyze the effect of reducing The wave runup height of solitary waves by submerged and floating rectangular obstacles. It was confirmed that the SWASH model reproduces the propagation, breaking, and runup of solitary waves quite well. In addition, it was confirmed that the wave deformation of the solitary wave by submerged and floating rectangular obstacles was well reproduced. Finally, we conducted an examination of the effect of reducing the runup height of submerged and floating rectangular obstacles. Reduced runup heights are calculated and the characteristics of runup height reduction according to the dimensions of the obstacle were analyzed. The energy attenuation effect of the floating obstacle is greater than the submerged obstacle, and it is shown to be more effective in reducing the runup height.

Application of SWASH to Compute Wave Overtopping in Ericeira Harbour for Operational Purposes

This work aimed at testing the capability of the numerical model SWASH to be implemented in the prototype of the overtopping and flooding forecast system HIDRALERTA for Ericeira harbour. In contrast to the neural network NN_OVERTOPPING2, which is currently implemented in HIDRALERTA, SWASH is able to estimate the flood extension and wave propagation along the domain, which makes it a possible improvement to NN_OVERTOPPING2. The one-dimensional version of the SWASH model was implemented to simulate overtopping at two different profiles (antifer and tetrapods) and calibrated for three storms in 2019 by comparing the simulated overtopping discharge to NN_OVERTOPPING2 results. For the calibration, the Manning coefficient was used to represent the friction of the armour layer. Then, for operational purposes, four expressions to calculate the Manning coefficient were developed based on: the relative crest freeboard, the wave steepness, the incident wave angle and the type of armour layer. The expressions showed small errors between the calculated and calibrated Manning coefficients and highlighted the importance of the incident wave angle to obtain an accurate calibration. Despite an underestimation of the overtopping discharge in some cases, the SWASH model was found to provide overall good results when applied with calculated Manning coefficients and suitable to be implemented in HIDRALERTA.

Numerical study of cross-shore variations of bound super-harmonics over a single sandbar system

This study primarily investigates the capability of the one-dimensional mode of the SWASH model to reproduce bound super-harmonics resulted from self-coupling of the spectral peak. The model results were compared with an array of wave measurements along a straight perpendicular transect in west of Nowshahr Port in the Southern Caspian Sea. The wave model was calibrated during moderate conditions and the bispectral analysis was applied for model results and field measurements.It was revealed that the model can properly reproduce nonlinear waves experiencing significant shoaling as well as disappearing the couplings for breaking waves within stormy periods. Secondary and tertiary local peaks as results of self-coupling of the spectral peak could be found in the simulated wave spectra; however, erroneous intensive couplings were also represented by the model for very low energy conditions with no cross-shore wave transformation.The validated model results were used to investigate the variations of the bound triad interactions across the shore. It was found that the corresponding Ursell numbers for the most intensive positive couplings were in the range of 0.2–0.3. Also, it was concluded that the couplings may be drastically weakened before intensive wave breaking.

Non-hydrostatic modelling of the wave-induced response of moored floating structures in coastal waters

Predictions of the wave-induced response of floating structures that are moored in a harbour or coastal waters require an accurate description of the (nonlinear) evolution of waves over variable bottom topography, the interactions of the waves with the structure, and the dynamics of the mooring system. In this paper, we present a new advanced numerical model to simulate the wave-induced response of a floating structure that is moored in an arbitrary nearshore region. The model is based on the non-hydrostatic approach, and implemented in the open-source model SWASH, which provides an efficient numerical framework to simulate the nonlinear wave evolution over variable bottom topographies. The model is extended with a solution to the rigid body equations (governing the motions of the floating structure) that is tightly coupled to the hydrodynamic equations (governing the water motion). The model was validated for two test cases that consider different floating structures of increasing geometrical complexity: a cylindrical geometry that is representative of a wave-energy-converter, and a vessel with a more complex shaped hull. A range of wave conditions were considered, varying from monochromatic to short-crested sea states. Model predictions of the excitation forces, added mass, radiation damping, and the wave-induced response agreed well with benchmark solutions to the potential flow equations. Besides the response to the primary wave (sea-swell) components, the model was also able to capture the second-order difference-frequency forcing and response of the moored vessel. Importantly, the model captured the wave-induced response with a relatively coarse vertical resolution, allowing for applications at the scale of a realistic harbour or coastal region. The proposed model thereby provides a new tool to seamlessly simulate the nonlinear evolution of waves over complex bottom topography and the wave-induced response of a floating structure that is moored in coastal waters.

Phase resolving runup and overtopping field validation of SWASH

Time series of storm wave runup and overtopping observed on a sandy beach with a scanning LiDAR are compared with predictions of the phase-resolving numerical model SWASH 1D. SWASH is initialized 300 m offshore (8-m depth) with phase-resolved estimates of shoreward and seaward propagating waves, observed with a co-located pressure sensor-current meter. During 5 h of storm conditions (2.4-m significant wave height, 17-sec peak period, high tide) swash zone bed level erosion of 80 cm was observed with the LiDAR and included in SWASH simulations. Model offshore bathymetry is an ensemble of historical surveys. SWASH-predicted and LiDAR-observed runup time series are in-phase and coherent in both the sea-swell and infragravity frequency bands. Overtopping was intermittent and occurred only for the largest runups that were at suboptimal viewing angles. SWASH overpredicted by a factor of two the number of overtopping events observed with LiDAR and a single point pressure sensor. Phase-coupling between infragravity and sea swell waves at the offshore boundary and shoreline erosion both significantly affect model runup and overtopping. SWASH prediction misfits of 5%–6% in runup sea-swell and infragravity heights are encouragingly small given the uncertainty in underwater bathymetry, 1D dynamics assumption, and default model representations of wave breaking and bottom friction. • 4.5 h of simulated runup and overtopping from SWASH run on a 1D transect are compared to field observations. • Phase resolved offshore boundary conditions enable good agreement between modeled and observed runup time series. • Overtopping estimates agree within a factor of 2, with SWASH overpredicting.

Numerical Modelling of Wave Attenuation in Pile Breakwater

Pile breakwater is an artificial coastal structure consisting of closely spaced piles. Its benefits are similar to other coastal structures by attenuating the energy of the incoming wave. In this paper, the wave attenuation caused by the pile structure is investigated using a numerical model, namely the SWASH model. The model allows for simulating non-hydrostatic phenomena in coastal waters as driven by waves. The model setup is conducted in a rectangular wave flume with paddles to produce monochromatic waves on the left and the wave absorber on the other side. Several scenarios were carried out to determine the effect of variations in wave parameters. To deal with the efficiency of numerically modelled pile breakwater, we also investigate the transmission coefficient. We compare the result of the numerical model with experimental data, which took place in a wave flume at Balai Penelitian dan Pengembangan Pantai, Buleleng, Bali, Indonesia. The validation results demonstrate the capability of the SWASH Model to approximate the incident and transmitted wave height with good accuracy compared to experimental data.

Modeling the Evolution and Runup of Breaking Solitary and Solitary-Like Waves on Straight and Composite Slopes

Understanding the runup and inundation of long waves on coasts is of great importance for coastal community as flooding hazards are closely related to safety issues. For many years, solitary and solitary-like waves are frequently considered as a surrogate of extremely long waves for estimating runup and inundation. Since scaling issues are of concern when extending to real-world conditions, large-scale experiments for solitary waves on uniform beaches are reviewed and additional experiments for solitary waves on composite slopes are performed in this study. As such, those experimental data obtained from large-scale physical modeling can be used to validate numerical models and then to extend the range of parameters in terms of wave conditions and slope geometries which cannot be straightforwardly achieved in large-scale experimental works. Considering the computational efficiency, an open-source non-hydrostatic wave-flow model SWASH is used herein. Detailed model-data comparisons in terms of free surface elevation time series and maximum runup heights are carried out for long waves running up and down on beaches with different slope gradients to ensure the accuracy of the SWASH model for such applications. Finally, a simple method for estimating maximum shoreline excursion for solitary waves on a particularly designed composite slope is provided.

Simulation of 3D overtopping flow–object–structure interaction with a calibration-based wave generation method with DualSPHysics and SWASH

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.

Smoothed Particle Hydrodynamics simulations of reef surf zone processes driven by plunging irregular waves

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.