Wave Run-up Research Articles

Remotely induced storm effects on the coastal flooding along the southwest coast of India

The southwest coast of India is exposed to long-period swells propagated from the South Indian Ocean during pre- and post-monsoon seasons. Although swells from the Southern Ocean and Atlantic Ocean were identified in the North Indian Ocean, their existence and impact along the southwest coast of India were not well investigated. On 19 March 2019, the Valiyathura-Shangumukham coastal stretch along the southwest coast of India experienced an unexpected coastal inundation without having a prompt forecast/warning, and not induced by a storm/cyclone in its vicinity. The present study investigates the causative forces of this inundation and estimates the wave runup and inundation. The study reveals that an unusual swell system was developed in the Indian-Atlantic-Southern Oceans (IASO) interface during 10–12 March and propagated towards the southwest coast of India. The measured wave spectra off Varkala clearly depicts the presence of long-period swells (Tp>18 s), which dominantly occurred as single-peaked. Wave modelling has been carried out to characterize the wave transformation associated with the “IASO interface swells” along the southern Kerala coast. A wave runup of up to 0.93 m height and a coastal inundation of up to 83 m onshore have been estimated during this event.

Wave Overtopping and Flooding Costs in the Pre-Design of Longitudinal Revetments

Wave overtopping, mainly caused by growing coastal erosion processes, directly affects populations, causing coastal flooding and potential damages. This work aims to develop the relationship between overtopping phenomena and their impact costs through an approach that considers wave runup, corresponding overtopping events, their flow volume and related flooding costs. Herewith, it is possible to evaluate the relationship between the structure construction and maintenance costs and the consequent costs due to overtopping and flooding damages, leading to the design of optimised coastal structures solutions. To apply the proposed approach, a real case study on the Portuguese northwest coast (Ovar municipality) was analysed, evaluating overtopping and flooding data recorded by the Portuguese Environment Agency (APA), allowing costs per unit flooded volume to be estimated. Then, future scenarios were predicted to assess the influence of climate change, discuss intervention scenarios and evaluate the uncertainty of economic parameters’ evolution. The proposed methodological approach represents a step forward in the estimative of coastal overtopping and flooding impacts, leading to increasing the knowledge about flooding and overtopping costs and optimised mitigation measures in artificialised coastal areas, where coastal defence works (longitudinal revetments) are present. This approach fills a gap in knowledge regarding this type of forecast in a medium- to long-term perspective.

Grain-scale investigation of swash zone sediment transport on a gravel beach using DEM-MPS coupled scheme

ABSTRACT Sediment transport in the swash zone directly affects beach changes such as shoreline recession; thus, detailed understandings of sediment transport mechanisms are necessary to accurately estimate the short-time scales sediment transport rate. However, these detailed mechanisms under runup waves have not been elucidated because of the complex solid-gas-liquid multiphase turbulence flow. In this study, we attempt to numerically investigate the sediment grain-scale mechanism to overcome the shortcomings of experimental measurements and the free surface treatment in many numerical simulations. The gravel transport process on a sloped beach under regular waves was simulated using a 2D coupled model of the discrete element method (DEM) and a modified moving particle semi-implicit (MPS) method; a sub-model was built into the DEM-MPS model to improve fluid volume conservation. After validating the simulated performance by comparing it to a previous experiment, the gravel motions were investigated for turbulence and inner beach structure. The Shields number, estimated using the drag force distribution, revealed that significant turbulence contributed to onshore gravel transport near the rundown limit. The inter-gravel contact structure inside the beach explained the decrease in offshore sediment transport during backwash as increased resistance to gravel motions resulting from beach compaction.

Three-phase flow simulation of beach erosion induced by breaking solitary waves

A three-phase (air, water, and sediment) flow computational-fluid-dynamics model based on OpenFOAM was used in the present work to simulate the beach erosion induced by breaking solitary waves. The simulation results were first validated by comparing them against experimental measurements. The simulated time series of the surface elevation and pore pressure, as well as the simulated beach profile after erosion, compared fairly well with the experiment. The simulation results showed that the wave runup and rundown processes were accompanied by distinct hydrodynamics and sediment transport characteristics. The hydrodynamics in the runup stage is featured by a weaker flow before the wave breaking and a stronger one afterward, which then gradually weakens toward the runup limit. The hydrodynamics in the rundown stage is featured by a generally weaker flow compared to the runup stage. The flow is also stronger before the hydraulic jump and weaker afterward. A flow reversal and the exfiltration process are captured by the numerical model at the end of the rundown stage. The sediment transport in the runup stage is featured by an intense rate but a short duration, while the sediment transport in the rundown stage is much slower but has a longer duration. As a result, the total amounts of the transported sediment in the runup and rundown stages were comparable to each other. Finally, a discussion on the limitations of the numerical model and possible modifications to further improve the model in the future is presented.

Determination of Current and Future Extreme Sea Levels at the Local Scale in Port-Bouët Bay (Côte d’Ivoire)

The Port-Bouët Bay shoreline is threatened by extreme sea level (ESL) events, which result from the combination of storm tide, wave run-up, and sea level rise (SLR). This study provides comprehensive scenarios of current and future ESLs at the local scale along the bay to understand the evolution of the phenomenon and promote local adaptation. The methodological steps involve first reconstructing historical storm tide and wave run-up data using a hydrodynamic model (D-flow FM) and the empirical model of Stockdon et al. Second, the Generalized Pareto Distribution (GPD) model fitted to the Peaks-Over-Thresholds (POT) method is applied to the data to calculate extreme return levels. Third, we combine the extreme storm tide and wave run-up using the joint probability method to obtain the current ESLs. Finally, the current ESLs are integrated with recent SLR projections to provide future ESL estimates. The results show that the current ESLs are relatively high, with 100-year return levels of 4.37 m ± 0.51, 4.97 m ± 0.57, and 4.48 m ± 0.5 at Vridi, Petit-Bassam, and Sogefiha respectively. By end-century, under the SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios, the future SLR is expected to increase the current ESLs by 0.49 m, 0.62 m, and 0.84 m, respectively. This could lead to a more frequent occurrence of the current 100-year return period, happening once every 2 years by 2100, especially under SSP5-8.5. The developed SLR scenarios can be used to assess the potential coastal flood risk in the study area for sustainable and effective coastal management and planning.

Wave Runup Prediction and Alongshore Variability on a Pocket Gravel Beach under Fetch-Limited Wave Conditions

Most empirical equations used for wave runup predictions have been developed from measurements at straight sandy beaches in unlimited fetch environments. While there are empirical equations to predict wave runup on gravel beaches, they have not been tested for prediction of wave runup on pocket gravel beaches, in limited-fetch environment, which can be found around Mediterranean. This paper addresses this lack of measurements on this type of beaches and examines the alongshore variability of wave runup. Wave runup measurements were made using video observations along 3 cross-sectional profiles on the pocket beach of Ploče, Croatia. The measurements have shown that the wave runup can vary for about 71% even around the centerline of the pocket beach. This variability is due to beach orientation and alignment of beach profiles to the prevailing wave direction, as well as difference in beach slope. Comparison of wave runup predictions from five well-known empirical equations and field measurements showed significant underprediction (up to NBIAS = −0.33) for energetic wave events, and overall high scatter (up to NRMSE = 0.38). The best performing wave runup equation was used for further refinement outside the original parameter space by including the Goda wave peakedness parameter (Qp). The newly developed empirical equation for wave runup reduced the NBIAS to 0 and the NRMSE by 31% compared to the original equation (developed equation metrics: R = 0.91, NBIAS = 0, NRMSE = 0.2, HH = 0.2 on the study site). This empirical equation can potentially be used for design of coastal structures and artificial beaches in similar environments, but further measurements are needed to test its applicability to a range of forcing and environmental conditions.

Benchmarking a two-way coupled coastal wave–current hydrodynamics model

Wave–current interaction phenomena are often represented through coupled model frameworks in ocean modelling. However, benchmarking of these models is scarce, revealing a substantial research challenge. We seek to address this through a selection of cases for coupled wave–current interaction modelling. This comprises a series of analytical and experimental test cases spanning three diverse conditions of wave run-up, one scenario of waves opposing a current flow, and a 2-D arrangement of waves propagating over a submerged bar. We simulate these through coupling the spectral wave model, Simulating WAves Nearshore (SWAN), with the coastal hydrodynamics shallow-water equation model, Thetis, using the Basic Model Interface (BMI) structure. By comparing calibrated versus default parameter settings we identify and highlight calibration uncertainties that emerge across a range of potential applications. Calibrated model results exhibit good correlation against experimental and analytical data, alongside benchmarked wave–current model predictions, where available. Specifically, inter-model comparisons show equivalent accuracy. Finally, the coupled model we developed as part of this work showcases its ability to account for wave–current effects, in a manner extensible to other coupled processes through BMI and applicable to more complex geometries.

Short-crested wave-current forces around a concentric multiple-cylinder structure

ABSTRACT The potential flow theory is used to develop a new analytical method to solve the diffraction problem of short-crested incident waves with uniform current acting on a concentric multiple-cylinder system. The influence of uniform current on the hydrodynamic performance of the concentric structure is discussed. The incident angle and speed of the currents have a significant influence on the short-crested wave force and run-up on the concentric structure, i.e. the wave force and wave run-up increase significantly when wave and uniform current directions are the same, while decreasing when in the opposite direction of the wave and uniform current. Additionally, the effects of parameters such as the current incidence angle, current speed, porous-effect parameters, number of perforated walls, and short-crestedness of regular waves on the hydrodynamic performance of the concentric structures are valuated by numerical experiments. It is observed that as the number of permeable walls increases, wave load on the impermeable internal cylinder gradually decreases and the wave surface around is more even. This study is expected to provide theoretical guidance for the design of nearshore architecture.

Short-Crested Wave–Current Forces on a Concentric System with an ARC Exterior Porous Wall

In this study, the potential flow theory is adopted to develop an analytical solution to the diffraction problem of a short-crested wave–current incident on a concentric system consisted of an arc exterior wall and interior cylinder. The influence of the uniform current on the hydrodynamic performance of the concentric structure is primarily discussed. The incident angle and speed of the uniform current significantly influence the short-crested wave force and run-up on the concentric structure. Specific parametric conditions are obtained, under which the wave structure can resonate, and the resonance phenomenon may be more pronounced when the wave and current have the same incidence direction. Furthermore, semi-enclosed structures are highly sensitive to the direction of wave incidence, thereby triggering certain limitations in engineering applications. This study is expected to contribute as theoretical guidance to nearshore architecture designs.

Free Long-Wave Transformation in the Nearshore Zone through Partial Reflections

Abstract Long waves play an important role in coastal inundation and shoreline and dune erosion, requiring a detailed understanding of their evolution in nearshore regions and interaction with shorelines. While their generation and dissipation mechanisms are relatively well understood, there are fewer studies describing how reflection processes govern their propagation in the nearshore. We propose a new approach, accounting for partial reflections, which leads to an analytical solution to the free wave linear shallow-water equations at the wave-group scale over general varying bathymetry. The approach, supported by numerical modeling, agrees with the classic Bessel standing solution for a plane sloping beach but extends the solution to arbitrary alongshore uniform bathymetry profiles and decomposes it into incoming and outgoing wave components, which are a combination of successively partially reflected waves lagging each other. The phase lags introduced by partial reflections modify the wave amplitude and explain why Green’s law, which describes the wave growth of free waves with decreasing depth, breaks down in very shallow water. This reveals that the wave amplitude at the shoreline is highly dependent on partial reflections. Consistent with laboratory and field observations, our analytical model predicts a reflection coefficient that increases and is highly correlated with the normalized bed slope (bed slope relative to wave frequency). Our approach shows that partial reflections occurring due to depth variations in the nearshore are responsible for the relationship between the normalized bed slope and the amplitude of long waves in the nearshore, with direct implications for determining long-wave amplitudes at the shoreline and wave runup.

Investigation of higher-harmonic wave loads and low-frequency resonance response of floating offshore wind turbine under extreme wave groups

When floating offshore wind turbines (FOWT) encounter extreme waves in operation, it is a highly nonlinear system involving floater motion and extreme wave–structure interactions. The behavior is crucial for floating offshore wind turbine safety. With the aid of a high-fidelity CFD solver, a harmonic separation method through a ‘Stokes-like’ formulation was adopted to obtain the parameters for each harmonic response. The present study focuses on analyzing higher harmonic load, dynamic motion response, and tension load of the mooring line the DeepCwind semi-submersible FOWT. The results show that the higher-harmonic wave load cannot be ignored in the extreme marine environment, the second harmonic can be over 16% of the linear wave load, and the third harmonic can be over 10% of the linear wave load with large wave steepness. The duration of a focused wave crest interaction with the platform is a short process of only 1.4 s in model scale, corresponding to about 10 s for the prototype. The wave runup at the upstream column is larger than the other columns, and the flow velocity is double that of the wave without the floater in presence. The dynamic response of the floater contains two phases, ’forced oscillations’ is identified to be drag-driven from odd harmonics, and ’free decay’ mainly comes from second-order difference-frequency influence from even harmonics. The properly normalized wave forces of surge and heave motion are not influenced by steepness kpAlinear. For surge motion, the total motion mainly comes from the nonlinear low frequency component. For pitch motion, the linear response is dominant in small kpAlinear. When the steepness kpAlinear increases gradually, the second-order low-frequency response of pitch motion will increase rapidly and dominate the total response.

Foredune defending role: Vulnerability and potential risk through combined satellite and hydrodynamics approach

The paper presents an approach to assessing potential risks for coastal areas, where the foredune acts as the first and main line of defense against storm surges. The local correction technique for satellite data via morphodynamics and hydrodynamics features, applicable for the southern part of the Baltic Sea was developed. The proposed combination of regionally adapted height of the wave run-up and the surge height made it possible to clarify the width of the beach through analyzing ESA Sentinel-2a satellite images. Using digitized shorelines from ESA Sentinel-2a imagery as a reference, together with the results of modeling the near-hydrodynamic conditions, a study of the beach width dynamics between measurements was performed. This is due to the regularity of satellite data being affected by cloud cover and the period of circulation. Identifying hot spots on the shore made it possible to establish areas with a significant excess in the repeatability of small dry beach width and, correspondingly, the erosion rate. The hot spots were detected within the Curonian Spit protective dune ridge, identifying the vulnerable areas, which are able to serve as breach points to flooding. The hydrological analysis of the flood zones under storms of varying frequency was performed, and predictions were made regarding the regional sea level rise by BACC and Team (2015) regional climate analysis. The work shows the possibilities of combining hydrodynamic and hydrological modeling, satellite observations into a single forecasting and assessment system, which allows to analyze and model risks of various origins. The results obtained can significantly improve the existing models or become the background for the integrated coastal zone management system, especially in protected natural areas.

Observations of extreme wave runup events on the US Pacific Northwest coast

Abstract. Extreme, tsunami-like wave runup events in the absence of earthquakes or landslides have been attributed to trapped waves over shallow bathymetry, long waves created by atmospheric disturbances, and long waves generated by abrupt breaking. These runup events are associated with inland excursions of hundreds of meters and periods of minutes. While the theory of radiation stress implies that nearshore energy transfer from the carrier waves to the infragravity waves can also lead to very large runup, there have not been observations of runup events induced by this process with magnitudes and periods comparable to the other three mechanisms. This work presents observations of several runup events in the US Pacific Northwest that are comparable to extreme runup events related to the other three mechanisms. It also discusses possible generation mechanisms and shows that energy transfer from carrier waves to bound infragravity waves is a plausible generation mechanism. In addition, a method to predict and forecast extreme runup events with similar characteristics is presented.

Development of a typhoon wave overtopping prediction model based on an artificial neural network

In this study, an artificial neural network (ANN) model for the typhoon wave overtopping was developed using the database by a numerical wave flume simulation. The developed ANN model is effective for saving calculation time largely. The accuracy of the model is also approached to over 95% of the numerical simulation. This accuracy was evaluated by the correlation coefficient and the root mean square error with the target data of the numerical simulation and output of the ANN model. This model quickly produces the mean wave overtopping rate, maximum wave run-up height, maximum wave overtopping depth and velocity at the middle point in the coastal road without high-fidelity numerical model and high-computing resources. It means that the typhoon warning system including the ANN models is powerful and useful rather than only the monitoring warning system currently in use.

Experimental investigation on the wave-oscillating buoy interaction and wave run-up on the buoy

The interaction between a wave and an oscillating buoy is complex, and it directly affects the stability, working state, and efficiency of the buoy. In this study, an experimental investigation of the interaction between a wave and an oscillating buoy (including wave breaking, wave run-up, and the relative motion between waves and buoys) is conducted under constant power take-off (PTO) values. The wave conditions selected in the experiment are all obtained from measured data on the Qingdao coast, China. The experimental results show that when the wave steepness is greater than 0.0597, there is an obvious wave breaking in front of the oscillating buoy and that the steepness of the critical wave decreases with an increase in PTO. When the relative damping force is 0.101. In addition, an empirical formula based on the wave steepness, the PTO value, and the wave run-up is proposed in accordance with the M5’ model tree. The results obtained in this study contribute to an increased understanding of the development of wave energy from buoys. In turn, this improvement in understanding will inform the design and deployment of buoys in real-life scenarios.

Novel approach for predicting wave run-up on natural beaches

The evaluation of wave run-up on beaches is of significant importance since it is used in different coastal engineering and management applications, including the assessment of beach morphology, the determination of erosion and flooding risk, and the design and maintenance of coastal structures. The main aim of this paper is to present a new method of wave run-up prediction, which is intended to be applicable to the various types of natural beaches. A single formulation was established for beaches, which were categorised as dissipative, reflective and intermediate. This comprehensive parametric run-up model, which included both wave set-up and swash excursion, was specifically developed to represent the wide-ranging conditions experienced in the swash zone in terms of beach conditions. The run-up model included a means to account for obliquely incident waves, varying foreshore sediment characteristics and the infiltration/exfiltration processes during swash events; it also used fitting parameters to account for other site-specific conditions. The novel run-up model produced comparable results to other parametric models, and showed good correlation with laboratory data and limited field data. However, while the model was deemed suitable to be adopted at varying coastal sites, field data are required for implementation to yield meaningful output.

Numerical investigation of effects of artificial excavation pit on transformation and runup processes of tsunami-like wave over fringing reef

In recent years, excavating materials from the reef flat gradually becomes the main source of sand and aggregate for the coral-lined coasts in tropical and subtropical regions, especially the low-laying atoll islands. These artificial excavation pits are bound to have significant impacts on the wave hydrodynamics over the fringing reefs. However, effects of the excavation pit on the hydrodynamic characteristics of tsunami-like wave over the fringing reef are few studied. To fill the knowledge gap of previous research, effects of artificial excavation pit on the transformation and runup processes of tsunami-like wave over the fringing reef have been systematically investigated in this study based on a high-resolution two-phase flow model. Effects of several main factors are carefully discussed. Research results indicate that the presence of excavation pit can have noticeable influences on the wave transformation and runup processes of tsunami-like wave over the fringing reef. Complex interactions between the breaking surge bore and the water body in the excavation pit can be observed. The complicated flow field in the pit can dissipate more wave energy and result in a lower maximum wave runup height. However, the local wave height near the pit in most situations can be amplified. It is hoped that the research findings can broaden the understandings on the wave hydrodynamics over the fringing reef with the artificial excavation pit.

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.