Wave Run-up Research Articles

Fully-coupled hydroelastic modeling of a deformable wall in waves

The hydroelastic behavior of a vertical wall in periodic waves is investigated using a fully-coupled computational fluid dynamics (CFD) and computational solid mechanics (CSM) model. The present numerical model is verified against previous numerical and experimental results on wave evolution and structural displacement. Then the hydrodynamic characteristics and the structural responses of an elastic wall in periodic waves are parametrically investigated. It is demonstrated that wave reflection, run-up, and loading decrease as the wall becomes more flexible. The decreases also occur when the waves become shorter. With nonlinear wave propagation, both the displacement and the stress of the wall are larger in the shoreward direction than those in the seaward direction. The wall displacement has the same frequency as the exciting waves and the stress increases with the decrease of the ratio of the wave frequency to the wall’s natural frequency. Considering the effect of flexibility, empirical formulae are proposed for predicting the wave run-up, loading, and maximum displacement of the wall. Besides, the optimization of the flexible wall is conducted by taking into account both the defense performance (i.e., transmission coefficient) and the structural integrity (i.e., maximum von Mises stress). Finally, the effect of the material damping is studied, which shows that the material damping has a negligible effect on the interaction between periodic waves and the elastic structure. • The hydroelastic interaction between periodic waves and an elastic vertical wall is investigated using an advanced computational approach. • The structural stiffness and the ratio of the wave frequency to the wall’s natural frequency can largely affect the wave-wall interaction. • Empirical formulae are proposed for wave run-up, loading, and wall displacement in periodic waves. • Optimization of flexibility is performed considering the wave transmission and the stress within the vertical elastic wall. • The effect of the material damping is found to be negligible on periodic waves interacting with an elastic wall.

An optimized XGBoost-based machine learning method for predicting wave run-up on a sloping beach

Accurate and computationally efficient prediction of wave run-up is required to mitigate the impacts of inundation and erosion caused by tides, storm surges, and even tsunami waves. The conventional methods for calculating wave run-up involve physical experiments or numerical modeling. Machine learning methods have recently become a part of wave run-up model development due to their robustness in dealing with large and complex data. In this paper, an extreme gradient boosting (XGBoost)-based machine learning method is introduced for predicting wave run-up on a sloping beach. More than 400 laboratory observations of wave run-up were utilized as training datasets to construct the XGBoost model. The hyperparameter tuning through the grid search approach was performed to obtain an optimized XGBoost model. The performance of the XGBoost method is compared to that of three different machine learning approaches: multiple linear regression (MLR), support vector regression (SVR), and random forest (RF). The validation evaluation results demonstrate that the proposed algorithm outperforms other machine learning approaches in predicting the wave run-up with a correlation coefficient (R2) of 0.98675, a mean absolute percentage error (MAPE) of 6.635%, and a root mean squared error (RMSE) of 0.03902. Compared to empirical formulas, which are often limited to a fixed range of slopes, the XGBoost model is applicable over a broader range of beach slopes and incident wave amplitudes.•The optimized XGBoost method is a feasible alternative to existing empirical formulas and classical numerical models for predicting wave run-up.•Hyperparameter tuning is performed using the grid search method, resulting in a highly accurate machine-learning model.•Our findings indicate that the XGBoost method is more applicable than empirical formulas and more efficient than numerical models.

Monitoring interdecadal coastal change along dissipative beaches via satellite imagery at regional scale

Abstract Coastal morphological changes can be assessed using shoreline position observations from space. However, satellite-derived waterline (SDW) and shoreline (SDS; SDW corrected for hydrodynamic contributions and outliers) detection methods are subject to several sources of uncertainty and inaccuracy. We extracted high-spatiotemporal-resolution (~50 m-monthly) time series of mean high water shoreline position along the Columbia River Littoral Cell (CRLC), located on the US Pacific Northwest coast, from Landsat missions (1984–2021). We examined the accuracy of the SDS time series along the mesotidal, mildly sloping, high-energy wave climate and dissipative beaches of the CRLC by validating them against 20 years of quarterly in situ beach elevation profiles. We found that the accuracy of the SDS time series heavily depends on the capability to identify and remove outliers and correct the biases stemming from tides and wave runup. However, we show that only correcting the SDW data for outliers is sufficient to accurately measure shoreline change trends along the CRLC. Ultimately, the SDS change trends show strong agreement with in situ data, facilitating the spatiotemporal analysis of coastal change and highlighting an overall accretion signal along the CRLC during the past four decades.

Automated Extraction of a Depth-Defined Wave Runup Time Series From Lidar Data Using Deep Learning

Wave runup observations are key data for understanding coastal response to storms. Lidar scanners are capable of collecting swash elevation data at high spatial and temporal resolution in a range of environmental conditions. Efforts to develop automated algorithms that effectively separate returns off of the beach and the sea surface are complicated by environmental noise, thus requiring time-intensive data quality control or manual digitization. In this study, a fully convolutional neural network (FCNN) was trained and validated on 966 30-minute lidar linescan time-series of the beach and swash zone and tested on an additional 99 30-minute linescan time-series to improve the automated classification of lidar returns off of the beach and water, facilitating the extraction of a depth-defined wave runup time-series. Lidar returns were classified as beach or water, beach points at each cross-shore location were interpolated through time, creating a time-varying beach elevation surface that was used to calculate instantaneous swash depths. Runup was defined as the most landward position of 3-cm water depth through time. Overall, the runup time-series determined using the manually- and ML-digitized beach-water interface agreed well (0.02 m RMSD 3-cm contour location, and 0.06 m RMSD 2% runup exceedance elevation R2%). The trained model was found to be robust to noise and moderate data gaps and applicable in a range of wave conditions. Results demonstrate the potential of the ML model to replace manual data processing steps and significantly reduce the time and effort required to extract the instantaneous runup location from lidar linescan time-series.

Performance Evaluation of DualSPHysics and COMCOT Programs through Numerical Testing for Simulating Tsunami Propagation and Overtopping on Seawalls

A tsunami is a destructive wave that can cause massive damage to coastal infrastructure. One of the disaster mitigation measures that can be chosen is the construction of coastal protection infrastructure, such as a seawall. Seawalls play a crucial role in protecting coastal areas as they can reduce wave energy and minimize the impact of tsunami-induced damage. However, during the 2011 Japan tsunami, the seawall built in Taro city failed as it proved to be less effective in handling the tsunami waves. The research conducted aims to model the propagation and overtopping of tsunami waves on the seawall, initially carried out through physical laboratory experiments, and later transformed into numerical test models using the Smoothed Particle Hydrodynamics (SPH) method and the Cornell Multigrid Coupled Tsunami (COMCOT) model. In this study, the parameters being compared include wave height, wave propagation, and overtopping on the seawall under two scenarios : the run-up of solitary waves on a shore without a seawall and the overtopping condition with a seawall using the Solitary Wave generation type, following the experiments conducted by Huang et al en 2022. Several parameters in the laboratory case study should be considered to expand our understanding of the systematically discussed tsunami propagation and overtopping processes and evaluate the capabilities of the SPH and COMCOT models.

Prediction of the Wave Run-Up on Pile Breakwaters

Prediction of the Wave Run-Up on Pile Breakwaters

A Comparative Study of Lstm and Tcn Models for Wave Runup Prediction

A Comparative Study of Lstm and Tcn Models for Wave Runup Prediction

Detection of Landslides and Tsunamis in Douglas Channel and Gardner Canal, British Columbia

In 1975, an underwater landslide in Kitimat Arm at the northern end of Douglas Channel, British Columbia (Figure 1a), triggered tsunami waves that were observed to reach a height of over 8 m at the head of the inlet, destroying a dock and a newly built barge terminal (Bornhold, 1983). Elsewhere in the Douglas Channel region, seafloor deposits attest to previous submarine landslide events (Conway et al., 2012; Stacey et al., 2019), and subaerial landslides of various sizes regularly occur (Maynard et al., 2017). Landslide-generated tsunamis are increasingly recognized as a substantial hazard worldwide, with the potential for extreme wave runup and localized damage, particularly in narrow, steep-sided bays and inlets. In most cases it is not possible to prevent landslides from occurring; however, mitigation efforts can include early landslide detection and the development of tsunami early warning systems using real-time data.

Time domain boundary element modeling of coupled interaction between ocean wave and elastic bridge pier

High-rising bridge pylons or piers in coastal site are flexible enough to induce obvious interaction effect against ocean waves which could alter the dynamic properties and affect the resultant structural response. This study proposes a time domain boundary element approach to investigate the instantaneous coupled interaction between ocean wave and flexible structure with arbitrary geometry. The boundary element theory is integrated with Euler-Bernoulli element following a time integration scheme. The simple Green function associated with perturbation expansion is employed to build the time-invariant hydrodynamic matrix and Newmark method with additional numerical damping is used to integrate the structural response. The proposed approach is validated against both of a benchmark experiment and a previous frequency-domain approach. The interaction effects on structural dynamic properties as well as simultaneous structural response, wave run-up and surface pressure are characterized. The computational efficiency and stability are discussed. Results show that interaction effect might alter the fundamental period and damping ratio and affects the structural response considerably. The proposed approach shows both favorable accuracy and efficiency and could provide more transient information which is absent in previous frequency domain approaches.

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.

Extreme Coastal Water Levels Evolution at Dakar (Senegal, West Africa)

Increasingly, it is reported that the coastline of the Dakar region is affected by coastal flooding due to extreme water levels during wave events. Here, we quantify the extreme coastal water levels as well as the different factors contributing to coastal flooding during the period 1994–2015. Severe water levels reach values of 1.78 m and increase by 8.4 mm/year. The time spent above this threshold has already increased by 1.7 over the study period and will increase by 2100 to 8 times with 0.4 m mean sea level rise and up to 20 times with 0.8 m in the IPCC low and high greenhouse gas emission scenarios, respectively. Tide is the main contributor to the extremes when combined with large wave runup, due to wave breaking which contributes to 38% of the increase in extreme events while sea level rises to 44%. Our results show that because of its prominent location, Dakar region is affected by waves coming from the Northern and Southern Hemispheres with contrasted evolutions: wave runup events increase faster (7 mm/year) during austral winter due to a maximum of the South Atlantic storm activity, and have a decreasing trend (−3 mm/year) during boreal winter (December, January, February) driven by the evolution of corresponding climate modes.

Low dispersion finite volume/element discretization of the enhanced Green–Naghdi equations for wave propagation, breaking and runup on unstructured meshes

We study a hybrid approach combining a finite volume (FV) and a finite element (FE) method to solve a fully-nonlinear and weakly-dispersive depth averaged wave propagation model. The FV method is used to solve the underlying hyperbolic shallow water system, while a standard P1 finite element method is used to solve the elliptic system associated to the dispersive correction. We study the impact of several numerical aspects: the impact of the reconstruction used in the hyperbolic phase; the representation of the FV data in the FE method used in the elliptic phase and their impact on the theoretical accuracy of the method; the well-posedness of the overall method. For the first element we proposed a systematic implementation of an iterative reconstruction providing on arbitrary meshes up to third order solutions, full second order first derivatives, as well as a consistent approximation of the second derivatives. These properties are exploited to improve the assembly of the elliptic solver, showing dramatic improvement of the finale accuracy, if the FV representation is correctly accounted for. Concerning the elliptic step, the original problem is usually better suited for an approximation in H(div) spaces. However, it has been shown that perturbed problems involving similar operators with a small Laplace perturbation are well behaved in H1. We show, based on both heuristic and strong numerical evidence, that numerical dissipation plays a major role in stabilizing the coupled method, and not only providing convergent results, but also providing the expected convergence rates. Finally, the full mode, coupling a wave breaking closure previously developed by the authors, is thoroughly tested on standard benchmarks using unstructured grids with sizes comparable or coarser than those usually proposed in literature.

Numerical investigation of wave run-up and load on heaving cylinder subjected to regular waves

The heaving cylinder is widely used in various floating structures, and the wave run-up height and wave forces are essential parameters to be considered in the design. This paper uses OpenFOAM to numerically simulate the wave run-up and wave load of the heaving cylinder by solving the Reynolds-averaged Navier-Stokes equation. The wave run-up of the heaving cylinder is decomposed into the relative run-up height and the absolute run-up height compared with the fixed cylinder, in which the phase difference between the absolute wave run-up curve and the cylindrical motion curve is the important factor. The different wave conditions are considered, including the short wave, resonance wave and long wave. The results show that the dimensionless maximum run-up height of the heaving cylinder changes nonlinearly with the incident wave frequency. In the range of about 23% of the resonance frequency of the heaving cylinder, the increase of the relative run-up height should be considered with the reason of resonance and phase differences. The dimensionless horizontal wave force increases nonlinearly with the increased scattering parameters. The fixed and heaving cylinder results differ significantly from the theoretical value when the ka value is larger than 0.25.

Probabilistic analysis of irregular wave runup on a fixed and truncated surface-piercing vertical cylinder

This paper presents a numerical and experimental study on irregular wave runup on a fixed and truncated surface-piercing vertical cylinder. The numerical model was set up based on the incompressible two-phase flow solver in the open-source toolbox OpenFOAM. The model was successfully validated against the experimental data on both regular and irregular incident wave and wave runup. We analyse the characteristics of the runup spectrum against different kpHs and kpD, where kp is the wave number at peak frequency, Hs is the significant wave height and D is the diameter of the cylinder. A new method is proposed to predict the distribution of runup height. In this method, the average height of the highest one-third of all wave runup R1/3 is calculated based on the expansion of an empirical formula proposed in Cao et al., (2017). Then the non-dimensional runup height R/R1/3 is fitted into a two-parameter Weibull distribution, where the shape parameter and scale parameter are provided as a function of kpHs and kpD based on the interpolation of the experimental and numerical data. Based on the fitted Weibull distribution, the runup height at any cumulative probability can be determined. This newly proposed method is validated against the numerical and experimental data on the 2% excess wave runup height R2%, and the deviations are found to be within ±15% for most of the cases. Finally, a sensitivity analysis is conducted to demonstrate that the model uncertainty is within 15%.

Numerical Analysis on Influences of Emergent Vegetation Patch on Runup Processes of Focused Wave Groups

During severe weather, the runup of the devasting surges and waves can cause extensive damages to the coastal facilities and results in significant loss of life. Therefore, it becomes necessary to find reliable measures to reduce the wave runup in coastal regions. As a natural barrier to the shorelines, coastal vegetation has great potential to attenuate wave runup and to prevent the coastal communities from extreme floodings and huge land loss. This study numerically discusses the influences of the emergent vegetation patch on the runup processes of extreme wave groups by applying a nonhydrostatic flow solver. Influences of the major factors, i.e., water depth, peak wave period, significant wave height, and density and length of the vegetation patch, are analyzed in detail. Research findings indicate that the presence of the emergent vegetation patch can substantially dissipate most of the incident wave energy and effectively reduce the maximum wave runup heights of extreme wave groups at the sloped beach. It is hoped that the research results of this study will be helpful to the design of coastal soft protection measures.

Modeling wave processes in a reef-lagoon-channel system based on a Boussinesq model

The reef-lagoon-channel system is very typical on the low-lying reef-lined coasts in tropical and subtropical areas. Comparing to the well-studied one-dimensional horizontal (1DH) fringing reefs, little is known about the alongshore wave runup variation and its implication for coastal flooding in such a two-dimensional horizontal (2DH) reef configuration. To better understand the wave processes in an idealized reef-lagoon-channel system, a numerical model is presented in this study, which is based on a set of fully nonlinear Boussinesq equations. Wave breaking is addressed by a shock-capturing scheme and bottom friction is formulated by the Manning frictional law. The adopted model is first validated by a published laboratory dataset in view of wave spectrum, wave height, wave setup, mean current as well as wave runup on the back-reef beach. Subsequently, the effects of hydrodynamic (incident wave height, incident wave period, reef-flat wave level) and reef morphological (fore-reef slope, cross-shore reef-flat width, channel width and frictional coefficient) parameters that are not fully considered by the laboratory experiments are investigated through the numerical simulations. Finally, the model is used to analyze the infragravity (IG) wave resonant modes in the system, and the effects of channel on such modes are also demonstrated.

Hydrodynamic characteristics of an immersed horizontal plate in front of the steep revetment

In order to reduce the wave run-up on the steep revetment, an immersed horizontal plate is proposed to install in front of the steep revetment. The horizontal plate and the steep revetment are collectively regarded as an integrated coastal protection structure. Based on the OpenFOAM open-source software package, the hydrodynamic characteristics of the integrated structure are systematically studied. Firstly, the performances of the numerical model are well verified by comparing the predicted results with the corresponding experimental data for waves interaction with a single-layer plate-type breakwater. The verified model is applied to simulate waves interaction with an immersed horizontal plate in front of the steep revetment. The influences of the submerged depth of the plate and the distance from the plate to the toe of the revetment are discussed under the different wave conditions. The typical pressure distributions on the horizontal plate are also studied. In addition, the vortex structures in the vicinity of the plate and the revetment are displayed to further analyze the distributions of wave energy dissipation intensity. The predicted results indicate that it is a good way in practice to effectively restrain wave run-up by installing an immersed horizontal plate in front of the steep revetment.

3D Flooding Maps as Response to Tsunami Events: Applications in the Central Sicilian Channel (Southern Italy)

The assessment of the vulnerability of a site to tsunami events should take into consideration the geomorphological setting, which is strongly determined by the stratigraphic framework of the area. Lampedusa island is located in the central portion of the Sicilian Channel (Mediterranean Sea, Italy), where a significant incidence of tsunamis (with wave runup above 15 m) caused by earthquakes and submarine landslides has been historically documented. This work shows the geomorphological and stratigraphic differences between the western and south-eastern sectors of Lampedusa island. This update to the geological characterization of the island was used to create 3D flooding maps according to runup steps of 5 m, 10 m, and 15 m, thus showing a homogeneous involvement of the south-eastern sector of Lampedusa. Furthermore, our study aims to provide a geomorphological-stratigraphic base for a mathematical-statistical model to create coastal flooding maps due to tsunami waves. As such, this tool is useful for evaluation of strategic infrastructure for the security of the island and the improvement of risk management in civil protection.

Novel sediment sampling method provides new insights into vertical grain size variability due to marine and aeolian beach processes

AbstractIn 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.

A Novel BEM–FEM Scheme for the Interaction of Water Waves with Multiple Vertical Cylinders in the Presence of Currents

The interaction of waves and currents with marine structures finds interesting applications, including the study of offshore and shoreline protection systems, as in the case of permeable breakwaters. The latter systems exhibit various benefits, including a decrease in wave run-up, reflected wave energy and load excitation, allowing for the propagation of part of the incident flow to the lee side, facilitating the improvement of water quality in the protected areas. The present work focuses on the modelling and numerical simulation of wave fields, interacting with arrays of vertical cylinders in the presence of currents. The problem is treated in the framework of potential theory in the frequency domain, assuming waves of small steepness, in conjunction with boundary integral formulation. Numerical results are presented and discussed, concerning the structure of the reflected and transmitted 3D flow fields, making the model suitable for optimization purposes; however, it presents increased computational cost. On the other hand, for small current velocities the problem can be approximately considered on the horizontal plane, modelled by the 2D Helmholtz equation with variable coefficients, which is numerically treated by a coupled BEM–FEM scheme. Numerical examples are presented, demonstrating that the latter model is cost-efficient, providing reasonable predictions, and can be used for the preliminary study of the hydrodynamic characteristics of the considered configurations and the support of the design.