Measured and modeled wave overtopping on a natural beach

The rate of wave overtopping of a barrier beach is measured and modeled. Unique rate of wave overtopping field data are obtained from the measure of the Carmel River, California, lagoon filling during a time when the lagoon is closed-off with no river inflow. Volume changes are based on measured lagoon height changes applied to a measured hypsometric curve. Wave heights and periods are obtained from directional wave spectra data in 15 m fronting the beach. Beach morphology was measured by GPS walking surveys. Three empirical overtopping models by Van der Meer and Janssen (1995), Hedges and Reis (1998) and Pullen et al. (2007) with differing parameterizations on wave height, period and beach slope and calibrated using extensive laboratory data obtained over plane, impermeable beaches are applied in a quasi-2D manner and compared with the field observations. Three overtopping events are considered when morphology data were available less than 2 weeks prior to the event. The models are tuned to fit the data using a reduction factor to account for beach permeability, berm characteristics, non-normal wave incidence and surface roughness influence. In addition, the run-up model by Stockdon et al. (2006) based on field data is examined and found to underestimate run-up as the calculated values were too small to predict any of the observed overtopping. The three overtopping models performed similarly well with values of 0.72–0.87 for the two narrow-banded wave cases, with an average reduction factor of 0.78. The European model (Pullen et. al., 2007) performed best overall and in particular for the case of the broad-banded, double peaked wave spectrum.     

Core made of geotextile sand containers for rubble mound breakwaters and seawalls: Effect on armour stability and hydraulic performance

A systematic armour stability and the hydraulic performance, including wave reflection, wave transmission, experimental study in the twin-wave flumes of Leichtweiss-Institute (LWI) is performed on a geocore breakwater and a conventional rubble mound breakwater in order to comparatively determine the wave run-up and wave overtopping. The geocore breakwater consists of a core made of sand-filled geotextile containers (GSC) covered by an armour made of rock. The geocore is more than an order of magnitude less permeable than the quarry run core of a conventional breakwater. As expected, the core permeability substantially affects the armour stability on the seaside slope, the wave transmission and the wave overtopping performance. Surprisingly, however, wave reflection and hydraulic stability of the rear slope are less affected. Formulae for the armour stability and hydraulic performance of the geocore breakwater are proposed, including wave reflection, transmission, run-up and overtopping.     

Wave transmission by overtopping due to random waves

Experimental studies of wave transmission by overtopping for a smooth impermeable breakwater with 1:1.5 slope under both regular and random waves were conducted. A resulting relationship between the transmission coefficient (determined by wave height and wave period) and a breakwater height above mean water level normalized with the height of wave run-up measured directly by capacity wave meter is reported. Meanwhile, their discrepancies in both regular and random waves are also discussed in this study. The authors find also that the transmitted significant wave period by overtopping of random waves may be much longer than those of the incoming wave. This characteristic is especially prominent and probably creates the oscillation phenomenon in the wave basin at the back of breakwater when the breakwater height (above mean water level) to water depth ratio is greater than 0.23 and the incoming wave period is longer than 8 sec.     

Laboratory experiments on wave transmission by overtopping

Laboratory experiments with regular waves were used to investigate wave transmission by overtopping for a smooth, impermeable breakwater with a 1-in-4 slope.A resulting relationship between the transmission coefficient and a breakwater height above mean sea level normalized with a theoretical wave run-up height is reported in this paper.     

Predictions on Irregular Wave run-up and Overtopping

A series of hydraulic model tests are carried out to investigate random wave run-up and overtopping on smooth, impermeable single slope and composite slope. Based on analysis of the influences of wave steepness, structure slope, incident wave angle, width of the berm and water depth on the berm and the wave run-up, empirical formulas for wave run-up on dike are proposed. Moreover, empirical formula on estimating the wave run-up on composite slope with multiple berms is presented for practical application of complex dike cross-section. The present study shows that the influence factors for wave overtopping are almost the same as those for wave run-up and the trend of the wave overtopping variation with main influence parameters is also similar to that for wave run-up. The trend of the wave overtopping discharge variations can be well described by two main factors, i.e. the wave run-up and the crest freeboard of the structure. A new prediction method for wave overtopping discharge is proposed for random waves. The proposed prediction formulas are applied to case study of over forty cases and the results show that the prediction methods are good enough for practical design purposes.     

Wave run-up on bermed coastal structures

Reliable estimation of wave run-up is required for the effective and efficient design of coastal structures when flooding or wave overtopping volumes are an important consideration in the design process. In this study, a unified formula for the wave run-up on bermed structures has been developed using collected and existing data. As data on berm breakwaters was highly limited, physical model tests were conducted and the run-up was measured. Conventional governing parameters and influencing factors were then used to predict the dimensionless run-up level with 2% exceedance probability. The developed formula includes the effect of water depth which is required in understanding the influence of sea level rise and consequent changes of wave height to water depth ratio on the future hydraulic performance of the structures. The accuracy measures such as RMSE and Bias indicated that the developed formula is more accurate than the existing formulas. Additionally, the new formula was validated using field measurements and its superiority was observed when compared to the existing prediction formulas. Finally, the new design formula incorporating the partial safety factor was introduced as a design tool for engineers.     

Numerical analysis of wave overtopping of rubble mound breakwaters

The paper describes the results of a two-dimensional (2-D) numerical modelling investigation of the functionality of rubble mound breakwaters with special attention focused on wave overtopping processes. The model, COBRAS-UC, is a new version of the COBRAS (Cornell Breaking Waves and Structures) based on the Volume Averaged Reynolds Average Navier–Stokes (VARANS) equations and uses a Volume of Fluid Technique (VOF) method to capture the free surface. The nature of the model equations and solving technique provides a means to simulate wave reflection, run-up, wave breaking on the slope, transmission through rubble mounds, overtopping and agitation at the protected side due to the combined effect of wave transmission and overtopping. Also, two-dimensional experimental studies are carried out to investigate the performance of the model. The computations of the free surface and pressure time series and spectra under regular and irregular waves, are compared with the experimental data reaching a very good agreement. The model is also used to reproduce instantaneous and average wave overtopping discharge. Comparisons with existing semi-empirical formulae and experimental data show a very good performance. The present model is expected to become in the near future an excellent tool for practical applications.     

Benchmark computations of wave run-up on single cylinder and four cylinders by naoe-FOAM-SJTU solver

The benchmark simulations of wave run-up on a fixed single truncated circular cylinder and four circular cylinders are presented in this paper. Our in-house CFD solver naoe-FOAM-SJTU is adopted which is an unsteady two-phase CFD code based on the open source package OpenFOAM. The Navier-Stokes equations are employed as the governing equations, and the volume of fluid (VOF) method is applied for capturing the free surface. Monochromatic incident waves with the specified wave period and wave height are simulated and wave run-up heights around the cylinder are computed and recorded with numerical virtual wave probes. The relationship between the wave run-up heights and the incident wave parameters are analyzed. The numerical results indicate that the presented naoe-FOAM-SJTU solver can provide accurate predictions for the wave run-up on one fixed cylinder and four cylinders, which has been proved by the comparison of simulated results with experimental data.     

Wave run-up on cylindrical and cone shaped foundations for offshore wind turbines

During the last decade, several offshore wind-farms were built and offshore wind energy promises to be a suitable alternative to provide green energy. However, there are still some engineering challenges in placing the foundations of offshore wind turbines. For example, wave run-up and wave impacts cause unexpected damage to boat landing facilities and platforms. To assess the forces due to wave run-up, the distribution of run-up around the pile and the maximum run-up height need to be known. This article describes a physical model study of the run-up heights and run-up distribution on two shapes of foundations for offshore wind turbines, including both regular and irregular waves. The influence of wave steepness, wave height and water depth on run-up is investigated. The measured run-up values are compared with applicable theories and previous experimental studies predicting run-up on a circular pile.     

Layer thicknesses and velocities of wave overtopping flow at seadikes

Seadikes often fail due to wave overtopping and a failure of the landward slope. Therefore, these aspects have to be taken into account for the design of seadikes. In present design, the calculation of the crest height of seadikes is essentially based on using a design water level and the corresponding wave run-up height. An average overtopping rate is generally considered for wave overtopping which can not account for the stresses and other effects due to extreme individual overtopping events. Landward slope design is more or less based on experience. It can be concluded from failure analysis that dike failures on the landward slope are rather initiated by individual overtopping events, in particular by the related overtopping flow velocities and layer thicknesses which are relevant for the prediction of erosion, infiltration and slip failure. Therefore, overtopping flow velocities and layer thicknesses are required in addition to average overtopping rates as hydraulic boundary conditions for the geotechnical stability analysis of seadikes.The objective of the present paper is the theoretical and experimental determination of overtopping flow velocities and layer thicknesses on the seaward slope, the dike crest and the landward slope of a seadike. Overtopping parameters are derived on the basis of small scale model tests which are required for the design of the landward slope and to avoid dike failures by wave overtopping in the future. For the prediction of the layer thicknesses and the velocities of the overtopping flow on the seaward slope, the dike crest and the landward slope, a set of theoretical formulas is derived and validated by hydraulic scale model tests.     

Forecast of wave run-up on coastal structure using offshore wave forecast data

In this paper, first we introduce the wave run-up scale which describes the degree of wave run-up based on observed sea conditions near and on a coastal structure. Then, we introduce a simple method which can be used for daily forecast of wave run-up on a coastal structure. The method derives a multiple linear regression equation between wave run-up scale and offshore wind and wave parameters using long-term photographical observation of wave run-up and offshore wave forecasting model results. The derived regression equation then can be used for forecasting the run-up scale using the offshore wave forecasting model results. To test the implementation of the method, wave run-up scales were observed at four breakwaters in the East Coast of Korea for 9 consecutive months in 2008. The data for the first 6 months were used to derive multiple linear regression equations, which were then validated using the run-up scale data for the remaining 3 months and the corresponding offshore wave forecasting model results. A comparison with an engineering formula for wave run-up is also made. It is found that this method can be used for daily forecast and warning of wave run-up on a coastal structure with reasonable accuracy.     

Derivation of unified wave overtopping formulas for seawalls with smooth,impermeable surfaces based on selected CLASH datasets

A set of unified formulas for prediction of the mean rate of wave overtopping at coastal structures with smooth, impermeable surfaces have been derived through the analysis of the selected CLASH datasets. The mean wave overtopping rate is expressed as the function of the significant wave height at the structural toe and the relative freeboard. The formulas are applicable for both vertical walls and inclined seawalls with smooth transition between them. The formulas are simple but cover the full range of water depth from the shoreline to deep water. The effects of the toe depth and the seabed slope on wave overtopping rate are duly incorporated in the formulas. Prediction performance of the new formulas is better than the EurOtop formulas for both vertical walls and inclined seawalls.     

Prototype measurements and small-scale model tests of wave overtopping at shallow rubble-mound breakwaters: the Ostia-Rome yacht harbour case

The paper presents the comparison between the results of small-scale model tests and prototype measurements of wave overtopping at a rubble-mound breakwater. The specific structure investigated is the west breakwater of the yacht harbour of Rome at Ostia (Italy) and is characterized by a gentle seaward slope (1/4) and by a long, shallow foreshore. The laboratory tests firstly aimed at carefully reproducing two measured storms in which overtopping occurred and was measured. The tests have been carried out in two independent laboratories, in a wave flume and in a wave basin, hence using a two-dimensional (2-D) and a three-dimensional (3-D) setup. In the 2-D laboratory tests no overtopping occurred during the storm reproductions; in the 3-D case discharges five to ten times smaller than those observed in prototype have been measured. This indicates the existence of model and scale effects. These effects have been discussed on the basis of the results of several parametric tests, which have been carried out in both laboratories, in addition to the storm reproductions, varying wave and water level characteristics. Final comparison of all the performed tests with 86 prototype measurements still suggests the existence of scale and model effects that induce strong underestimation of overtopping discharge at small scale. The scale reproduction of wave breaking on the foreshore, together with the 3-D features of the prototype conditions and the absence of wind stress in the laboratory measurements, have been individuated as the main sources of scale and model effects. The paper also provides a comparison between the data and a largely used formula for wave overtopping discharges in the presence of structures similar to the one at hand. The suitable value of a roughness factor that appears in that formula is investigated and good agreement is found with other recent researches on rubble-mound breakwaters.     

Numerical study on cnoidal wave run-up around a vertical circular cylinder

A finite element model of Boussinesq-type equations was set up, and a direct numerical method is proposed so that the full reflection boundary condition is exactly satisfied at a curved wall surface. The accuracy of the model was verified in tests. The present model was used to further examine cnoidal wave propagation and run-up around the cylinder. The results showed that the Ursell number is a nonlinear parameter that indicates the normalized profile of cnoidal waves and has a significant effect on the wave run-up. Cnoidal waves with the same Ursell number have the same normalized profile, but a difference in the relative wave height can still cause differences in the wave run-up between these waves. The maximum dimensionless run-up was predicted under various conditions. Cnoidal waves hold entirely distinct properties from Stokes waves under the influence of the water depth, and the nonlinearity of cnoidal waves enhances rather than weakens with increasing wavelength. Thus, the variations in the maximum run-up with the wavelength for cnoidal waves are completely different from those for Stokes waves, and there are even significant differences in the variation between different cnoidal waves.     

Laboratory study of combined wave overtopping and storm surge overflow of a levee

Combined wave overtopping and storm surge overflow of a levee with a trapezoidal cross section was studied in a two-dimensional laboratory wave/flow flume at a nominal prototype-to-model length scale of 25-to-1. The goal of this study was to develop design guidance in the aftermath of Hurricane Katrina. Time series of water depth at two locations on the levee crown and flow thickness at five locations on the landward-side slope were measured along with horizontal velocity near the landward edge of the crown. New equations are presented for average overtopping discharge, distribution of instantaneous discharge, and distribution of individual wave volumes. Equations are also given for mean flow thickness, RMS wave height, mean velocity, and velocity of the wave front down the landward-side slope.     

Three-dimensional investigations of wave overtopping on rubble mound structures

To study the influence of wave obliquity and directional spreading on wave overtopping of rubble mound breakwaters a total of 736 three-dimensional model tests were carried out at Aalborg University. The results of these tests are presented and analysed in this paper yielding a new empirical reduction factor to describe the influence of wave obliquity and directional spreading on the average wave overtopping discharges. The study shows that perpendicularly incident, long-crested waves result in conservative values of the overtopping discharge for the tested cross-section.     

Numerical simulation of irregular wave overtopping against a smooth sea dike

Based on the filtered Navier-Stokes equations and Smagorinsky turbulence model,a numerical wave flume is developed to investigate the overtopping process of irregular waves over smooth sea dikes.Simulations of fully nonlinear standing wave and regular wave’s run-up on a sea dike are carried out to validate the implementation of the numerical wave flume with wave generation and absorbing modules.To model stationary ergodic stochastic processes,several cases with different random seeds are computed for each specified irregular wave spectrum.It turns out that the statistical mean overtopping discharge shows good agreement with empirical formulas,other numerical results and experimental data.     

Wave run-up on slender circular cylindrical foundations for offshore wind turbines in nonlinear random waves

A practical method for estimating the wave run-up height on a slender circular cylindrical foundation for wind turbines in nonlinear random waves is provided. The approach is based on the velocity stagnation head theory and Stokes second order wave theory by assuming the basic harmonic wave motion to be a stationary Gaussian narrow-band random process. Comparisons are made with measurements by De Vos et al. (2007), and some of the highest wave run-up events that were predicted agree with those measured.     

Spatial distribution of wave overtopping water behind coastal structures

Spatial distribution of random wave overtopping water behind coastal structures was investigated using a numerical model based on Reynolds-Averaged Navier-Stokes solver (RANS) and Volume of Fluid (VOF) surface capturing scheme (RANS-VOF). The computed spatial distributions of wave overtopping water behind the structure agree well with the measurements by Pullen et al (2008) for a vertical wall and Lykke Andersen and Burcharth (2006) for a 1:2 sea dike. A semi-analytical model was derived to relate spatial distribution of wave overtopping water behind coastal structures to landward ground level, velocity and layer thickness on the crest. This semi-analytical model agrees reasonably well with both numerical model results and measurements close to coastal structures. Our numerical model results suggest that the proportion of wave overtopping water passing a landward location increases with a seaward slope when it is less than 1:3 and decreases with a seaward slope when it gets steeper. The proportion of wave overtopping water passing a landward location increases with landward ground level and overtopping discharge. It also increases with the product of incident wave height and wavelength, but decreases with increasing relative structure freeboard and crest width. We also found that the extent of hazard area due to wave overtopping is significantly reduced by using a permeable structure crown. Findings in this study will enable engineers to establish the extent of hazard zones due to wave overtopping behind coastal structures.