In spectral wave models, the nonlinear triad source term accounts for the transfer of energy to the bound higher harmonics. This paper presents an extension to commonly used spectral models that resolves the evolution of the bound wave energy by keeping track of the energy that has been bound by the triad interactions. This extension is referred to as the bound wave evolution (BWE) model. From this, the spatial evolution of the bound wave height is obtained, which serves as a proxy for the nonlinear wave shape. The accuracy of these bound wave heights, and thus wave shape predictions, is highly dependent on the accuracy of the triad source term. Therefore, in this study, the capability of the LTA and SPB triad formulations to capture the growth of the bound wave height is evaluated. For both of these formulations, it is found that slope dependent calibration parameters are required. Overall, despite being computationally more expensive, the SPB method proves to be significantly more accurate in predicting the bound wave evolution. In the shoaling zone, where the bound wave energy is dominated by triads, the BWE model is well capable of predicting the nonlinear wave’s shape. In the surf zone, however, where a combination of triads and wave breaking control the spectral evolution, the BWE model over-predicts the bound wave height. Nevertheless, this paper shows the promising capabilities of spectral models to predict the nonlinear wave shape.@en

Coastal wave forecasting over large spatial scales is essential for many applications (e.g., coastal safety assessments, coastal management and developments, etc.). This demand explains the necessity for accurate yet effective models. A well-known efficient modelling approach is the quadratic approach (often referred to as frequency-domain models, nonlinear mild-slope models, amplitude models, etc.). The efficiency of this approach stems from a significant modelling reduction of the original governing equations (e.g., Euler equations). Most significantly, the description of wave nonlinearity essentially collapses into a single mode coupling term determined by the quadratic interaction coefficients. As a result, it is expected that the efficiency achieved by the quadratic approach is accompanied by a decrease in prediction accuracy. In order to gain further insight into the predictive capabilities of this modelling approach, this study examines six different quadratic formulations, three of which are of the Boussinesq type and the other three are referred to as fully dispersive. It is found that while the Boussinesq formulations reliably predict the evolution of coastal waves, the predictions by the fully dispersive formulations tend to be affected by false developments of modulational instability. Consequently, the predicted wave fields by the fully dispersive formulations are characterized by unexpectedly strong modulations of the sea-swell part and associated unexpected infragravity response. The impact of the modulational instability on wave prediction based on the quadratic approach is further demonstrated using existing laboratory results of bichromatic and irregular wave conditions.

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Nearshore hydro- and morphodynamic data were collected during a field experiment under calm conditions, moderate conditions, and storm conditions with dune erosion in the collision regime. The experiment was conducted on the Sand Engine near Kijkduin, the Netherlands, from October 18, 2021, to January 7, 2022. Two artificial unvegetated dunes were constructed just above the high water line to measure storm erosion and dune impacts from higher water levels and waves. During the experiment, three storms occurred that resulted in significant erosion of both dunes. The collected hydrodynamic data include pressure sensor and velocimeter data along two cross-shore transects. The collected morphodynamic data include bathymetry and topography surveys, optical backscatter sensor data in the inner surf zone, and a continuous cross-shore line-scanning lidar data set of the dune face. This comprehensive data set can be used to (1) study relevant nearshore hydrodynamic and morphodynamic processes that occur during calm conditions, moderate conditions, and storm conditions with dune erosion in the collision regime, and (2) validate existing dune erosion models.@en

Spectral information of coastal waves and the associated statistical parameters (e.g., the significant wave height and mean wave period) over large spatial scales is essential for many applications (e.g., coastal safety assessments, coastal management and developments, etc.). This demand explains the necessity for accurate yet effective models. A well-known efficient modelling approach is the quadratic approach (often referred to as frequency-domain models, weakly nonlinear mild-slope models, amplitude models, etc.). The efficiency of this approach is achieved through modelling reduction of the original governing equations (e.g., Euler equations). Most significantly, wave nonlinearity is described solely by a single quadratic mode-coupling term. Therefore, doubts arise with regard to the predictive capabilities of the quadratic approach to reliably describe the nonlinear development of waves in the coastal environment where nonlinearity is typically significant. This study attempts to push the limit of the prediction capabilities of nonlinear coastal waves based on the quadratic approach. To this end, an optimization process is proposed, striving to extract the quadratic formulation which describes most adequately nonlinear wave developments over water depths and bathymetrical structures which characterize the coastal environment. The outcome is the model QuadWave1D: a fully dispersive quadratic model for coastal wave prediction in one-dimension. Based on a wide set of examples (including monochromatic, bichromatic and irregular wave conditions) and comparing to other representative quadratic formulations, it is found that QuadWave1D presents superior predictive capabilities of both the sea-swell components and the infragravity field.

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During extreme conditions, the transport of the wave-averaged suspended sediment concentrations in the inner surf zone affects dune erosion. Although large-scale laboratory experiments have provided insight in what drives these sediment concentrations, corresponding field data are lacking. To fill this gap, novel field observations of suspended sediment concentrations are compared to drivers that govern sediment suspension during storm conditions known from literature. A total of 128 time intervals of 20 min are analysed, spread over 10 different high water events with different hydrodynamic conditions. For each time interval, the wave-averaged (i.e. 20 min mean) suspended sediment concentration is computed and compared to three suspension drivers. The studied drivers are (1) bed shear due to near bed velocities that originate from mean currents in combination with wave-induced orbital flow, (2) the horizontal pressure gradients under steep wave fronts that increase the forces on the bed material, and (3) bore-induced turbulence that is generated at the free surface and reaches the bed. The derived bore-induced turbulence generates the greatest correlation with the mean suspended sediment concentrations (r = 0.74, p = 4.47E-23). Samples that deviate from this correlation correspond to time intervals with lower values of derived bore turbulence, less wave energy saturation in the inner surf zone, and stronger mean currents. The correlation with the mean suspended sediment concentrations increases when the shear stress originating from mean currents is used for these time intervals (r = 0.83, p = 1.63E-33). For time intervals during which more energetic conditions persist and the wave energy is saturated in the nearshore, bore turbulence was the dominant mechanism in stirring up sediment. The outcome of this study suggests that, based on the events analysed, dune erosion models may achieve more accurate results if computations of suspended sediment concentrations include a bore-induced turbulence term, or if already included, properly address the relative importance of bore-induced turbulence when compared to bed shearing.@en

A field campaign was carried out at a sheltered sandy beach with the aim of gaining new insights into the driving processes behind sheltered beach morphodynamics. Detailed measurements of the local hydrodynamics, bed-level changes and sediment composition were collected at a man-made beach on the leeside of the barrier island Texel, bordering the Marsdiep basin that is part of the Dutch Wadden Sea. The dataset consists of (1) current, wave and turbidity measurements from a dense cross-shore array and a 3 km alongshore array; (2) sediment composition data from beach surface samples; (3) high-temporal-resolution RTK-GNSS beach profile measurements; (4) a pre-campaign spatially covering topobathy map; and (5) meteorological data. This paper outlines how these measurements were set up and how the data have been processed, stored and can be accessed. The novelty of this dataset lies in the detailed approach to resolve forcing conditions on a sheltered beach, where morphological evolution is governed by a subtle interplay between tidal and wind-driven currents, waves and bed composition, primarily due to the low-energy (near-threshold) forcing. The data are publicly available at 4TU Centre for Research Data at: https://doi.org/10.4121/19c5676c-9cea-49d0-b7a3-7c627e436541 (Van der Lugt et al., 2023).@en

High-resolution wave measurements at intermediate water depth are required to improve coastal impact modeling. Specifically, such data sets are desired to calibrate and validate models, and broaden the insight on the boundary conditions that force models. Here, we present a wave data set collected in the North Sea at three stations in intermediate water depth (6–14 m) during the 2021/2022 storm season as part of the RealDune/REFLEX experiments. Continuous measurements of synchronized surface elevation, velocity and pressure were recorded at 2–4 Hz by Acoustic Doppler Profilers and an Acoustic Doppler Velocimeter for a 5-month duration. Time series were quality-controlled, directional-frequency energy spectra were calculated and common bulk parameters were derived. Measured wave conditions vary from calm to energetic with 0.1–5.0 m sea-swell wave height, 5–16 s mean wave period and W-NNW direction. Nine storms, i.e., wave height beyond 2.5 m for at least six hours, were recorded including the triple storms Dudley, Eunice and Franklin. This unique data set can be used to investigate wave transformation, wave nonlinearity and wave directionality for higher and lower frequencies (e.g., sea-swell and infragravity waves) to compare with theoretical and empirical descriptions. Furthermore, the data can serve to force, calibrate and validate models during storm conditions. Dataset: https://doi.org/10.4121/233f11ff-7804-4777-8b32-92c4606e56d8 Dataset License: CC-BY 4.0.

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Wave nonlinearity plays an important role in cross-shore beach morphodynamics and is often parameterized in engineering-type morphodynamic models through a nonlinear relationship with the Ursell number. It is not evident that the relationship established in previous studies also holds for sheltered sites with fetch-limited seas as they are more prone to effects of local winds and currents, the waves are generally steeper, and the beaches are typically reflective. This study investigates near-bed orbital velocity nonlinearity from wave records collected at two sheltered beaches in The Netherlands and contrasts them to earlier observations made along the exposed, wave-dominated North Sea coast. Our observations at sheltered beaches show that the Ursell number has comparable skill in predicting wave nonlinearity as it has on previously studied exposed coasts. However, the orbital velocities at sheltered coasts are more asymmetric for the same Ursell number than on exposed coasts. When exposed coast data were examined for moments with comparable high-steepness waves, a similar effect on asymmetry was observed. In addition, following and opposing winds were found to have a clear relationship with total nonlinearity, while they did not affect the phase between skewness and asymmetry at the sheltered beaches. Refitting the free parameters of an Ursell-based predictor improved the bias for the asymmetry parameterization. Whether this has implications for modeling of the magnitude of wave-nonlinearity-driven sediment transport using engineering type models is strongly dependent on the sediment transport formulation used, as these formulations depend on additional calibration coefficients too.

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Many sand spits are morphodynamically complex landforms, that are either analysed with complex and expensive computational models or at a conceptual level. Therefore, most case studies on spits in different environments are descriptive. A novel method based on the use of polar coordinates was devised to quantitatively analyse spit morphodynamics in a non-tidal, wind-dominated lake environment, using the Marker Wadden islands in Lake Markermeer, the Netherlands, as a case study. A high-resolution morphological data set allowed for the quantification of sedimentation processes around two spits, in two distinctive depth zones. Spit-platform growth is governed by alongshore currents that transport sediment over the spit-platform into deeper waters; the size of the spit-platform in turn affects the growth of the spit around the mean water level. Insight in this complex interplay of processes is crucial to understand spit behaviour in low-energy lake environments. At the Marker Wadden the submerged spit-platform grows during high energy wind events while the emerged spit part grows under mild to moderate energy conditions. With this new method we can quantitatively explore the role of different wave and flow conditions and predict spit growth direction in non-tidal, wind-dominated environments, beyond the level of conceptual descriptions.

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The coastline of Demak, Indonesia, has been eroding during the last 15 years. Coastal retreat in Demak is caused by a combination of mangrove deforestation and local subsidence due to groundwater extraction in the nearby city of Semarang. To restore the lost mangrove forest, permeable dams, consisting of bamboo poles with a brushwood filling, have been built to attenuate the waves, facilitate sedimentation at their land side, and thus create a suitable habitat for mangroves. However, existing designs required frequent brushwood maintenance. Therefore, a new type of design is proposed, consisting of only vertical bamboo poles without a filling of brushwood. Nevertheless, the hydrodynamic performance of this type of structure is not known. This study assesses the wave transformation through structures formed by bamboo poles for the physical conditions of Demak, Indonesia, with the numerical wave model SWASH. 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 different structure designs. 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. Even 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.@en

Infragravity (IG) waves are key drivers for coastal erosion and thus need to be properly included in process-based modelling of coastal hazards. Uncertainties remain regarding the offshore boundary conditions for these long waves. Typically, only bound IG waves are included at the boundary, which means that the possible contribution of free IG waves, such as those radiated from distant coastlines, is neglected. Recent studies however suggest that incoming free IG waves could be significant, particularly in semi-enclosed basins such as the North Sea where they could contribute to coastal hazards (e.g., Reniers et al., 2021, Rijnsdorp et al. 2021). The objective of this work is to improve the understanding of the incoming IG wave field along the Dutch coast. We will quantify how bound and free IG waves develop in intermediate water depths and assess in which conditions (onshore directed) free IG waves become significant.@en

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.

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The present work presents physical laboratory measurements of surface elevation and pore water pressures in a fine sand bed under bichromatic waves in a large-scale laboratory experiment. This was done at three cross-shore locations in the swash zone, with pressures being measured at different depths in the bed. The measurements show that the pore pressure signal decays and shifts with increased depth. These measurements are used to validate a practical model, based on the theory of Yamamoto et al. (1978, https://doi.org/10.1017/S0022112078003006) and Guest and Hay (2017, https://doi.org/10.1002/2016JC012257). The model corresponds well with the measurements (nRMSE < 0.2 and R² > 0.95 for most probes) and shows that a frequency-based model can reproduce the pressures in the bed, despite the bed being exposed during dry periods. Furthermore, the model provides the opportunity to calculate pressure gradients, both throughout the bed and at the bed surface. These modeled pressure gradients at the bed surface show that the vertical pressure gradient can have an important impact on the Shields parameter, thereby influencing sediment transport.

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Dune erosion during storm surges can lead to excessive damage to the dune system with devastating floods as a potential consequence. A risk assessment of areas protected by dunes can be facilitated by an understanding and description of the physical processes that take place. Field measurements, knowledge of underlying processes and numerical modelling have developed with time, which enabled a more comprehensive description and new predictive techniques. This review concerns dune erosion in the collision regime, and summarises relevant observations, describes underlying processes and explains existing models predicting dune erosion. Observations of dune erosion consist of field observations, laboratory experiments and manipulative field campaigns. The underlying physical processes that contribute to dune erosion are divided into processes that contribute to sediment transport due to hydrodynamic forcing, which occurs in the surf and swash zone, and sediment transport due to avalanching, which occurs in the swash zone, on the dune face and on the dune crest. The existing dune erosion models that are discussed here contain (empirical) equilibrium profile models and process-based models, which can both be a valuable tool for the risk assessment of storm surges. However, model uncertainties still remain, as specific processes are not yet fully understood and described. Examples are the influences of wave obliquity, sediment grain size, and vegetation on the dune face. By improving our knowledge through research and reducing these uncertainties, we can further improve our predictive models. This could eventually lead to more accurate predictions, more complete risk assessments, and sandy coastlines which are more resilient to excessive dune erosion and possible floods.@en

Grain size affects the rates of aeolian sediment transport on beaches. Sediment in coastal environments typically consists of multiple grain-size fractions and exhibits spatiotemporal variations. Still, conceptual and numerical aeolian transport models are simplified and often only include a single fraction that is constant over the model domain. It is unclear to what extent this simplification is valid and if the inclusion of multi-fraction transport and spatial grain-size variations affects aeolian sediment transport simulations and predictions of coastal dune development. This study applies the numerical aeolian sediment transport model AeoLiS to compare single-fraction to multi-fraction approaches for a range of grain-size distributions and spatial grain-size scenarios. The results show that on timescales of days to years, single-fraction simulations with the median grain size, D₅₀, often give similar results to multi-fraction simulations, provided the wind is able to mobilize all fractions within that time frame. On these timescales, vertical variability in grain size has a limited effect on total transport rates, but it does influence the simulation results on minute timescales. Horizontal grain-size variability influences both the total transport rates and the downwind bed grain-size composition. The results provide new insights into the influence of beach sediment composition and spatial variability on total transport rates toward the dunes. The findings of this study can guide the implementation of grain-size variability in numerical aeolian sediment transport models.

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Weyl rule of association, proposed by Hermann Weyl for quantum mechanics applications (Weyl, 1931), can be used to associate between the dispersion relation of water waves and a non-local pseudo-differential operator. The central result of this study is that this operator correctly approximates the Dirichlet-to-Neumann operator derived for linear waves over a slowly varying bathymetry. This opens the door to a formal use of Weyl's operational calculus, and consequently, allowing straightforward derivations and generalizations of water waves’ models over mild slopes. Specifically, within the framework of linear wave theory, the formulation based on Weyl rule of association provides a generalized mild-slope model which does not impose a limit on the spectral width. Most significantly, the mild-slope formulation based on Weyl rule of association allows to derive a general linear kinetic equation for which the widely used energy balance equation (the central equation of forecasting models such as SWAN and WAVEWATCH) serves as a special case. This result not only provides a formal link between the deterministic description (i.e., Euler equations) and the stochastic description (i.e., the energy balance equation), but also establishes the theoretical foundations for the statistical description of bathymetry-induced wave interferences. Such a statistical description is especially important over coastal waters, where through the interaction with the bathymetry, waves are rapidly scattered and tend to form focal zones and associated interference patterns.

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We present a fully coupled 2DV morphodynamic model, implemented in OpenFOAM^® that is capable of simulating swash-zone morphodynamics of sandy beaches. The hydrodynamics are described by the Reynolds-averaged Navier–Stokes (RANS) equations with a (Formula presented.) turbulence model and the Volume of Fluid (VoF) approach for discriminating between air and water. Sediment transport is described in terms of bedload and suspended load transport. We show that the default divergence scheme in OpenFOAM can become numerically unstable and lead to negative sediment concentrations, and propose a solution to avoid this problem. The model performance is assessed in terms of surface elevation, flow velocities, runup, suspended sediment concentrations, bed profile evolution and sediment transport volumes by comparing with measurements of field-scale (wave height of 0.6 m) solitary waves. The model shows reasonable agreement in terms of hydrodynamics and predicts the correct sediment transport volumes, although the deposition is predicted more onshore compared to the measurements. This is partially attributed to an overprediction of the runup. The model shows that the suspended sediment concentration displays a strong vertical dependence. These results show the potential of depth-resolving models in providing more insight into morphodynamic processes in the swash zone, particularly with respect to vertical structures in the flow and suspended sediment transport.

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A chenier is a beach ridge, consisting of sand and/or shells, overlying a muddy substrate. In this paper, we explore the cross-shore dynamics of cheniers in their ‘active’ phase, i.e. the phase between their formation and their landing on the shore and can no longer be reached by daily wave and tidal influences. While cheniers described in literature are known to only migrate onshore until they reach a stable position with their crest level above tidal influences, observations in Demak suggest the existence of an alternative stable state, highly dynamic on the short term, but stable on the longer term. To explore this alternative stable state, we developed an idealised chenier model to investigate cross-shore chenier dynamics under daily wave and tidal influences. The model is able to predict both onshore and offshore migration; onshore migration is mainly driven by wave action, while offshore migration is induced by a tidal phase lag, or the effect of the storm season. For certain combinations of waves, tide (incl. phase lag) and a storm season effect, the model predicts a dynamically stable chenier. In absence of a phase lag and storm season effect, the model yields a ‘classic’ stable chenier that welds onto the shoreline by onshore migration.

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To address the important research question of whether implicit (bottom friction) or explicit (stem drag) dissipation models are most appropriate for the prediction of wave attenuation due to aquatic vegetation, the Simulating Waves Nearshore (SWAN) spectral wave model has been extended with an explicit frequency-dependent dissipation model for submerged and emergent vegetation. The new explicit model is compared to existing explicit and implicit dissipation models in SWAN, and the distinguishing features of each of the dissipation models are quantified. The present work verifies the implementation of the new and existing dissipation models, outlines their distinguishing features, and compares model predictions against experimental data. The emphasis is on the transformation of the spectral wave periods Tm0;1 and Tm 1;0 over a canopy. Model evaluation based on academic and laboratory cases allows for recommendations regarding applicability of the three dissipation models, where the new method has the broadest applicability, since it bridges the gap in applicability between the other two dissipation models. The implementation of Jacobsen, McFall, and van der A (2019; A frequency distributed dissipation model for canopies; Coastal Engineering, 150, 135-146) is publicly available in SWAN version 41.31B.

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In sandy beach systems, the aeolian sediment transport can be governed by the vertical structure of the sediment layers at the bed surface. Here, data collected with a newly developed sand scraper is presented to determine high-resolution vertical grain size variability and how it is affected by marine and aeolian processes. Sediment samples at up to 2 mm vertical resolution down to 50 mm depth were collected at three beaches: Waldport (Oregon, USA), Noordwijk (the Netherlands) and Duck (North Carolina, USA). The results revealed that the grain size in individual layers can differ considerably from the median grain size of the total sample. The most distinct temporal variability occurred due to marine processes that resulted in significant morphological changes in the intertidal zone. The marine processes during high water resulted both in fining and coarsening of the surface sediment. Especially near the upper limit of wave runup, the formation of a veneer of coarse sediment was observed. Although the expected coarsening of the near-surface grain size during aeolian transport events was observed at times, the opposite trend also occurred. The latter could be explained by the formation and propagation of aeolian bedforms within the intertidal zone locally resulting in sediment fining at the bed surface. The presented data lays the basis for future sediment sampling strategies and sediment transport models that investigate the feedbacks between marine and aeolian transport, and the vertical variability of the grain size distribution.

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