Irregular Wave Runup Research Articles

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%.

Improvement of empirical formulas to estimate the reduction effects by berms on irregular wave runup over a dune-berm coast

This study formulates the reduction effects of a sandy berm on irregular wave runup over a dune-berm coast. The numerical experiments by Park and Cox (2016) are closely re-examined to develop an empirical formula describing the variability of reduction effects of a sandy berm over a broad range of conditions. Based on a sequence of regression analyses, the reduction effects are expressed as a reduction factor in terms of normalized berm width, normalized surge level, and wave steepness in deep water. The comparison with the numerical experiments demonstrates that the regression formula can satisfactorily reproduce the variability of the reduction effects over the range of numerical experiments. The analysis of prediction uncertainty demonstrated that the derived formula reproduced the reduction effects observed in the numerical experiments with negligible bias and a 90% confidence interval of approximately ±20% relative error. In addition, conversion formulas between representative runup values based on different statistical definitions are derived to enable consistent comparisons between them. The proposed reduction formula is implemented into three empirical runup models that are applicable to the quick estimations of irregular wave runup on a dune-berm coast: the models by Park and Cox (2016), Stockdon et al. (2006), and Mase et al. (2013). Consistent comparisons were conducted among the empirical predictions and numerical experiments based on the statistical conversion formulas. Combined with the proposed reduction formula, all three models well reproduced the normalized 2% runup in the numerical experiments over a wide range of conditions. On the other hand, the uncertainty in the runup prediction appeared in different forms depending on the selected model. When the proposed reduction formula was implemented in the modified Park and Cox (2016) and modified Stockdon et al. (2006) models, the uncertainty was described by a log-normal distribution of the error ratio between the empirical predictions and numerical experiments. Quantitatively, these two models predicted 90% of the normalized runup on a dune within a range of relative error of less than approximately 20–30%. When the proposed reduction formula was combined with the model by Mase et al. (2013), the uncertainty followed a normal distribution of the residual error between the empirical predictions and numerical experiments. On the normalized runup, the model prediction indicated a small conservative bias (+0.05) and a root-mean-square error of 0.13.

Estimation of Irregular Wave Runup on Intermediate and Reflective Beaches Using a Phase-Resolving Numerical Model

Accurate wave runup estimations are of great interest for coastal risk assessment and engineering design. Phase-resolving depth-integrated numerical models offer a promising alternative to commonly used empirical formulae at relatively low computational cost. Several operational models are currently freely available and have been extensively used in recent years for the computation of nearshore wave transformations and runup. However, recommendations for best practices on how to correctly utilize these models in computations of runup processes are still sparse. In this work, the Boussinesq-type model BOSZ is applied to calculate runup from irregular waves on intermediate and reflective beaches. The results are compared to an extensive laboratory data set of LiDAR measurements from wave transformation and shoreline elevation oscillations. The physical processes within the surf and swash zones such as the transfer from gravity to infragravity energy and dissipation are accurately accounted for. In addition, time series of the shoreline oscillations are well captured by the model. Comparisons of statistical values such as R2% show relative errors of less than 6%. The sensitivity of the results to various model parameters is investigated to allow for recommendations of best practices for modeling runup with phase-resolving depth-integrated models. While the breaking index is not found to be a key parameter for the examined cases, the grid size and the threshold depth, at which the runup is computed, are found to have significant influence on the results. The use of a time series, which includes both amplitude and phase information, is required for an accurate modeling of swash processes, as shown by computations with different sets of random waves, displaying a high variability and decreasing the agreement between the experiment and the model results substantially. The infragravity swash SIG is found to be sensitive to the initial phase distribution, likely because it is related to the short wave envelope.

Numerical Simulation of Wave Runup and Overtopping for Short and Long Waves Using Staggered Grid Variational Boussinesq

In designing a numerical tool for simulating a wide variety of water waves, i.e. short to long waves, an accurate and robust wave model and numerical implementation are needed. Dispersion and nonlinearity are the two most important physical aspects that should be modeled accurately. To be applicable to simulate many coastal engineering applications, the numerical scheme should be capable of simulating wave runup and overtopping. In this paper, we extend the capability of a Boussinesq-type model called Variational Boussinesq (VB) model for simulating the runup and overtopping of water waves. To that end, the vertical layer of the fluid is modeled continuously by a linear combination of three functions. If two of these three functions have been incorporated in the previous numerical approximation called the SVB model, this paper discusses the improvement of SVB model by incorporating all the three functions. This approach improve the dispersive property of the SVB model due to its ability to simulate short waves up to kd = 20, compared to the previous model which was only up to kd = 7, where k denotes wave number and d water depth. Furthermore, the model is implemented numerically by using the staggered conservative scheme. In the new implementation, the model is switched to the non-dispersive Shallow Water Equations (SWE) when dealing with a dry area for runup and overtopping phenomena. The new implementation is tested against analytical solutions of soliton propagation and standing wave phenomenon; moreover, it is also tested against experimental data from hydrodynamic laboratories for simulating solitary wave breaking above a sloping bottom, composite beach, and in a structure for simulating overtopping phenomenon. The implementation is also tested against experimental data for simulating irregular wave propagation and runup above a fringing reef. The results of numerical simulation agree quite well with experimental data.

Numerical Study of the Impact of Climate Change on Irregular Wave Run-up Over Reef-Fringed Coasts

Wave hydrodynamics over fringing reefs is largely controlled by the reef surface roughness and hydrodynamic forcing. It is believed that climate change will result in a net increase in the water depth over the reef flat, a degrading of the surface roughness of coral reefs and changes in extreme incident wave heights. For an accurate assessment of how climate change affects the safety of reef-fringed coasts, a numerical study of the impact of climate change on irregular wave run-up over reef-fringed coasts was carried out based on a Boussinesq wave model, FUNWAVE-TVD. Validated with experimental data, the present model shows reasonable prediction of irregular wave evolution and run-up height over fringing reefs. Numerical experiments were then implemented based on the anticipated effects of climate change and carried out to investigate the effects of sea level rise, degrading of the reef surface roughness and increase of extreme incident wave height on the irregular wave run-up height over the back-reef beach respectively. Variations of run-up components (i.e., spectral characteristics of run-up and mean water level) were examined specifically and discussed to better understand the influencing mechanism of each climate change-related effect on the run-up.

Study of irregular wave run-up over fringing reefs based on a shock-capturing Boussinesq model

This paper presents the results of a parametric study of irregular wave run-up over fringing reefs using the shock-capturing Boussinesq wave model Funwave-TVD to better understand the role of fringing reefs in the mitigation of wave-driven flooding. Laboratory experiments were newly performed with a typical fringing reef profile and typical hydrodynamic conditions to validate the model. Experimental data shows irregular wave run-ups are dominated by the low-frequency motions and confirms the run-up resonant phenomenon over the back-reef slope, which has been revealed in previous numerical studies. It is demonstrated that irregular wave evolution and run-up over fringing reefs are reasonably reproduced by the present model with a proper grid size. However, the infragravity run-up height and highest 2% run-up height over the back-reef slope are under-predicted due to the underestimation of the infragravity wave height over the reef flat. The validated model was then utilized to model irregular wave transformations and run-ups under different conditions. Through a series of numerical experiments, the effects of key hydrodynamic and reef geometry parameters, including the reef flat width, water depth over the reef flat, fore-reef slope angle and back-reef slope angle, on the irregular wave run-up were investigated. Variations of spectral components of irregular wave run-ups were examined to better understand the physical process underlying the effect of each parameter.

Irregular wave propagation with a 2DH Boussinesq-type model and an unstructured finite volume scheme

The application and validation, with respect to the transformation, breaking and run-up of irregular waves, of an unstructured high-resolution finite volume (FV) numerical solver for the 2D extended Boussinesq-type (BT) equations of Nwogu (1993) is presented. The numerical model is based on the combined FV approximate solution of the BT model and that of the nonlinear shallow water equations (NSWE) when wave breaking emerges. The FV numerical scheme satisfies the desired properties of well-balancing, for flows over complex bathymetries and in presence of wet/dry fronts, and shock-capturing for an intrinsic representation of wave breaking, that is handled as a shock by the NSWE. Several simulations and comparisons with experimental data show that the model is able to simulate wave height variations, mean water level setup, wave run-up, swash zone oscillations and the generation of near-shore currents with satisfactory accuracy.

Coastal Sediment Transport Modeling for Engineering Applications

AbstractAn effort has been made to improve quantitative understanding of beach morphology and stone structural damage progression and to develop a simple and robust model that is suited for engineering applications. The effort for the last 10 years has produced the cross-shore numerical model CSHORE, which is presently limited to the case of alongshore uniformity and uniform cohesionless sediment including sand, gravel, and stone. CSHORE consists of the following components: a combined wave and current model based on time-averaged continuity, cross-shore and longshore momentum, wave energy or action, and roller energy equations; a sediment transport model for suspended load and bed load; a permeable layer model to account for porous flow and energy dissipation; formulas for irregular wave run-up; a probabilistic model for an intermittently wet and dry zone on impermeable and permeable bottoms for the purpose of predicting wave overwash of a dune and armor layer damage progression, respectively; a drag for...

Irregular wave runup statistics on plane beaches: Application of a Boussinesq-type model incorporating a generating–absorbing sponge layer and second-order wave generation

Efficient absorption of reflected waves at the offshore boundary is a prerequisite for the accurate physical or theoretical modelling of long-duration irregular wave runup statistics at uniform, gently sloped beaches. This paper presents an implementation of the method suggested by Zhang et al. (2014) to achieve reflected wave absorption and simultaneous generation and propagation of incident waves in an existing numerical wave flume incorporating a moving boundary wavemaker. A generating–absorbing layer is incorporated within this 1DH hybrid Boussinesq-nonlinear shallow water equation model such that inshore-travelling incident waves, encompassing bound-wave structure approximately correct to second order, propagate unhindered while offshore-travelling reflected waves are absorbed. Once validated, the method is used to compile random wave runup statistics on uniform beach slopes broadly representative of dissipative, intermediate, and reflective beaches. Analyses of the individual runup time series, ensemble statistics and comparison to an empirical formula based on experimental runup data suggest that the main aspects of runup observed in the field are properly represented by the model. Existence of an upper limit on maximum runup is investigated using a simple extreme-value statistical analysis. Spectral saturation is examined by considering ensemble-averaged swash spectra for three representative beach slopes subject to incident waves with two different offshore significant wave heights. All spectra show f−4 roll-off at high frequencies in agreement with many previous field studies. The effect is also investigated of the swash motions preceding one particular extreme runup event on the eventual maximum runup elevation.

WAVE RUNUP ON DIKES AND BEACHES

In the United States, the Federal Emergency Management Agency (FEMA) is in the process of updating its coastal flood risk maps in order to determine which locations are threatened by storm surge and wave action. These maps require the prediction of extreme wave runup. A method for predicting the runup height along the entire coast must be robust, reliable, and applicable to many different coastal features. Kobayashi et al. (2008) developed a time-average probabilistic model that predicts wave runup statistics instead of the time series of shoreline elevation. This numerical cross-shore model, CSHORE, is extended to the wet-dry zone above the still water level to predict irregular wave runup on impermeable dikes and gentle impermeable slopes. To show the CSHORE's capability in predicting runup on beaches with different geometries, the computed results from the model are compared to measured data from a variety of experiments. CSHORE is tested against 40 wave runup tests on an impermeable dike on a barred beach, 97 wave runup tests on an impermeable dike with a gently sloping beach, and 120 tests for wave runup on gentle uniform slopes. The measured 2% and 1% exceedence runup heights are predicted within errors of about 20%. The spectral significant wave height, Hmo, and a representative period are used for input to CSHORE.
 The measured and computed cross-shore variations of Hmo are also computed and compared to measured data to show the capabilities and limitations of CSHORE in regards to predicting to wave transformation. Both the spectral period, Tm-1,0, and the peak period Tp at x = 0 are adapted as representative periods used in CSHORE to assess the period effect in CSHORE. The tested CSHORE is ready for practical applications such as FEMA's coastal flood mapping, and is a good practical choice because it can be used to predict beach and dune profile changes.

Wave Transformation and Runup on Dikes and Gentle Slopes

ABSTRACT Kobayashi, N.; Pietropaolo, J.A., and Melby, J.A., 2013. Wave transformation and runup on dikes and gentle slopes. Coastal flood-risk mapping requires the prediction of wave runup and overtopping of dikes and beaches. The cross-shore numerical model CSHORE is adjusted to predict irregular wave runup on impermeable dikes. The model is compared with 137 wave runup tests and 97 wave overtopping tests. The seaward boundary of the computation is taken at the location where wave setup is negligible. The spectral period and peak period at this boundary location are specified as input. The model predicts the measured cross-shore variation of the spectral significant wave height on the barred and sloping beaches in front of the dikes. The measured 2% and 1% exceedence runup heights are predicted within errors of about 20% for the spectral period used as input to CSHORE. The model predicts the threshold of wave overtopping, but the minor wave overtopping rates can be predicted only within a factor of 10. T...

Influence of the nonlinearity on statistical characteristics of long wave runup

Abstract. Runup of long irregular waves on a plane beach is studied experimentally in the water flume at the University of Warwick. Statistics of wave runup (displacement and velocity of the moving shoreline and their extreme values) is analyzed for the incident wave field with the narrow band spectrum for different amplitudes of incident waves (different values of the breaking parameter Brσ). It is shown experimentally that the distribution of the shoreline velocity does not depend on Brσ and coincides with the distribution of the vertical velocity in the incident wave field as it is predicted in the statistical theory of nonlinear long wave runup. Statistics of runup amplitudes shows the same behavior as that of the incident wave amplitudes. However, the distribution of the wave runup on a beach differs from the statistics of the incident wave elevation. The mean sea level at the coast rises with an increase in Brσ causing wave set-up on a beach, which agrees with the theoretical predictions. At the same time values of skewness and kurtosis for wave runup are similar to those for the incident wave field and they might be used for the forecast of sea floods at the coast.

Shock-capturing Boussinesq model for irregular wave propagation

In this paper, a shock-capturing numerical model, based on the combined solution of Boussinesq and nonlinear shallow water equations is validated with respect to the transformation, breaking and runup of irregular waves. Boussinesq equations are applied where dispersive and nonlinear effects are both relevant, assuring an appropriate description of wave propagation from intermediate to shallow waters. Nonlinear shallow water equations are used where dispersion is negligible; their shock-capturing features, exploited by the application of the finite volume method, enable an intrinsic representation of wave breaking and swash zone oscillations. No case by case calibration or tracking algorithms are required. Comparisons with experimental data show that the model is able to simulate wave height variations, mean water level setup, wave runup, and the generation of nearshore currents accurately.

Statistical estimates of characteristics of long-wave run-up on a beach

A run-up of irregular long sea waves on a beach with a constant slope is studied within the framework of the nonlinear shallow-water theory. This problem was solved earlier for deterministic waves, both periodic and pulse ones, using the approach based on the Legendre transform. Within this approach, it is possible to get an exact solution for the displacement of a moving shoreline in the case of irregular-wave run-up as well. It is used to determine statistical moments of run-up characteristics. It is shown that nonlinearity in a run-up wave does not affect the velocity moments of the shoreline motion but influences the moments of mobile shoreline displacement. In particular, the randomness of a wave field yields an increase in the average water level on the shore and decrease in standard deviation. The asymmetry calculated through the third moment is positive and increases with the amplitude growth. The kurtosis calculated through the fourth moment turns out to be positive at small amplitudes and negative at large ones. All this points to the advantage of the wave run-up on the shore as compared to a backwash at least for small-amplitude waves, even if an incident wave is a Gaussian stationary process with a zero mean. The probability of wave breaking during run-up and the applicability limits for the derived equations are discussed.

Numerical simulation of wave transformation and runup incorporating porous media wave absorber and turbulence models

A numerical wave tank is first established using the Navier–Stokes equations and the VOF method assuming laminar flow. The standard k– ε, realizable k– ε and RNG k– ε turbulent models are then incorporated to the numerical tank. An effective numerical method for wave absorption utilizing the energy-dissipating property of porous media is also included. To validate the accuracy of the proposed models, the propagation of a solitary wave, where analytical solution is available for comparison, is first simulated. This is followed by the simulation of irregular wave runup on a composite seawall, wave propagation over submerged bars and wave refraction and diffraction over an elliptic shoal, where experimental data are available for comparison. All computed results agree well with either the analytical solution or the experimental data.

Artificial neural networks for predicting maximum wave runup on rubble mound structures

Accurate prediction of maximum wave runup on breakwaters is a vital issue for determining crest level of coastal structures. In practice, traditional regression-based empirical model, recommended by the “Coastal Engineering Manual”, as well as the “Manual on the use of rock in hydraulic engineering”, is widely used. However, use of these approaches brings additional restrictive assumptions such as linearity, normality (Gaussian distributed variables), variance constancy (homoscedasticity) etc. This paper focuses on the prediction of maximum wave runup elevation through artificial neural networks (ANNs), which has no restrictive assumptions. Out of 261 irregular wave runup data of Van der Meer and Stam, 100 randomly chosen data points are used for training the model. The remaining data are exploited for testing purposes. This study has two objectives: (1) to develop ANN models and search their applicability to estimate maximum wave runup elevation on breakwaters; (2) to compare widely used empirical model with these models. For these purposes, different ANN models are constructed and trained with their own topology. The performance of the ANN models is tested against the same testing data, none of which is employed in the training. It is found that ANN technique gives more accurate results and the extent of accuracy can be affected by the structure of ANNs.

Time-Averaged Probabilistic Model for Irregular Wave Runup on Permeable Slopes

A time-averaged probabilistic model is developed to predict irregular wave runup statistics on permeable slopes such as cobble beaches and revetments. The cross-shore variations of the mean and standard deviation of the free surface elevation and horizontal fluid velocities above and inside a porous layer are predicted using the time-averaged continuity, momentum, and energy equations. The mean and standard deviation of the shoreline elevation measured by a runup wire are estimated from the predicted mean and standard deviation of the free surface elevation. The wave runup height above the mean water level, including wave setup, is assumed to be given by the Rayleigh distribution. The wave reflection coefficient is estimated from the wave energy flux remaining at the still water shoreline. This computationally efficient model is shown to be in fair agreement with 57 small-scale tests conducted on 1∕5 and 1∕2 permeable slopes situated inside surf zones on impermeable gentle slopes.

Run-up of tsunamis and long waves in terms of surf-similarity

In this paper we review and re-examine the classical analytical solutions for run-up of periodic long waves on an infinitely long slope as well as on a finite slope attached to a flat bottom. Both cases provide simple expressions for the maximum run-up and the associated flow velocity in terms of the surf-similarity parameter and the amplitude to depth ratio determined at some offshore location. We use the analytical expressions to analyze the impact of tsunamis on beaches and relate the discussion to the recent Indian Ocean tsunami from December 26, 2004. An important conclusion is that extreme run-up combined with extreme flow velocities occurs for surf-similarity parameters of the order 3–6, and for typical tsunami wave periods this requires relatively mild beach slopes. Next, we compare the theoretical solutions to measured run-up of breaking and non-breaking irregular waves on steep impermeable slopes. For the non-breaking waves, the theoretical curves turn out to be superior to state-of-the-art empirical estimates. Finally, we compare the theoretical solutions with numerical results obtained with a high-order Boussinesq-type method, and generally obtain an excellent agreement.

Swash overtopping and sediment overwash on a truncated beach

New experimental laboratory data are presented on swash overtopping and sediment overwash on a truncated beach, approximating the conditions at the crest of a beach berm or inter-tidal ridge-runnel. The experiments provide a measure of the uprush sediment transport rate in the swash zone that is unaffected by the difficulties inherent in deploying instrumentation or sediment trapping techniques at laboratory scale. Overtopping flow volumes are compared with an analytical solution for swash flows as well as a simple numerical model, both of which are restricted to individual swash events. The analytical solution underestimates the overtopping volume by an order of magnitude while the model provides good overall agreement with the data and the reason for this difference is discussed. Modelled flow velocities are input to simple sediment transport formulae appropriate to the swash zone in order to predict the overwash sediment transport rates. Calculations performed with traditional expressions for the wave friction factor tend to underestimate the measured transport. Additional sediment transport calculations using standard total load equations are used to derive an optimum constant wave friction factor of f w = 0.024. This is in good agreement with a broad range of published field and laboratory data. However, the influence of long waves and irregular wave run-up on the overtopping and overwash remains to be assessed. The good agreement between modelled and measured sediment transport rates suggests that the model provides accurate predictions of the uprush sediment transport rates in the swash zone, which has application in predicting the growth and height of beach berms.

Simulation and prediction of swash oscillations on a steep beach

This paper presents numerical simulations and analytical predictions of key aspects of swash oscillations on a steep beach. Simulations of the shoreline displacement based on bore run-up theory are found to give excellent agreement with recent experimental data for regular waves, wave groups and random waves. The theory is used to derive parameters that predict the onset of swash saturation and the spectral characteristics of the saturated shoreline motion. These parameters are again in good agreement with the measured laboratory data and are also consistent with previous experimental data. Simulation of irregular wave run-up using a series of overlapping monochromatic swash events is found to reproduce typical features of swash oscillations and can accurately describe both the low and high frequency spectral characteristics of the swash zone. In particular, the low frequency components of the run-up can be modelled directly using a sequence of incident short wave bores, with no direct long wave input to the numerical simulations. This suggests that wave groupiness must be accounted for when modelling shoreline oscillations.