Exceedance probability for wave overtopping on a fixed deck

Detailed laboratory measurements were made of the instantaneous free surface elevation in front of a fixed deck and the instantaneous free surface elevation, velocity, and overtopping rate at the leading edge of the deck. The study showed that the exceedance probabilities for the normalized maximum instantaneous overtopping rate and the normalized overtopping volume were predicted by a simple exponential curve. The measured exceedance probability seaward of the deck compared well with the nonlinear theory of Kriebel and Dawson (Kriebel D.L., Dawson T.H., 1993. Nonlinearity in wave crest statistics. In: Proceedings Ocean Wave Measurement and Analysis. American Society of Civil Engineers, pp. 61–75). Conditional sampling of the crest heights seaward of the deck gave a normalized probability distribution similar to that of the maximum water level measured on the deck for each overtopping event. However, the values used to normalize each distribution were not the same.     

An application of Boussinesq modeling to Hurricane wave overtopping and inundation

Wave and combined wave-and-surge overtopping was significant across a large portion of the hurricane protection system of New Orleans during Hurricane Katrina. In particular, along the east-facing levees of the Mississippi River-Gulf Outlet (MRGO), the overtopping caused numerous levee breaches. This paper will focus on the MRGO levees, and will attempt to recreate the hydrodynamic conditions during Katrina to provide an estimate of the experienced overtopping rates. Due to the irregular beach profiles leading up to the levees and the general hydrodynamic complexity of the overtopping in this area, a Boussinesq wave model is employed. This model is shown to be accurate for the prediction of waves shoaling and breaking over irregular beach profiles, as well as for the overtopping of levees. With surge levels provided by ADCIRC and nearshore wave heights by STWAVE, the Boussinesq model is used to predict conditions at the MRGO levees for 10 h near the peak of Katrina. The peak simulated overtopping rates correlate well with expected levee damage thresholds and observations of damage in the levee system. Finally, the predicted overtopping rates are utilized to estimate a volumetric flooding rate as a function of time for the entire 20 km stretch of east-facing MRGO levees.     

Simulation of wave overtopping by an incompressible SPH model

The paper presents an incompressible Smoothed Particle Hydrodynamics (SPH) model to investigate the wave overtopping of coastal structures. The SPH method is a grid-less Lagrangian approach which is capable of tracking the large deformations of the free surface with good accuracy. The incompressible algorithm of the model is implemented by enforcing the constant particle density in the pressure projection. The SPH model is employed to reproduce a transient wave overtopping over a fixed horizontal deck and the regular/irregular waves overtopping of a sloping seawall. The computations are validated against the experimental and numerical data and a good agreement is observed. The SPH modelling is shown to provide a promising tool to predict the overtopping characteristics of different waves. The present model is expected to be of practical purpose if further improvement in the spatial resolution and CPU time can be adequately made.     

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.     

The role of offshore boundary conditions in the uncertainty of numerical prediction of wave overtopping using non-linear shallow water equations

The paper examines the variability of wave overtopping parameters predicted by numerical models based on non-linear shallow water equations, due to the boundary conditions obtained from wave energy density spectra. Free surface elevation time series at the boundary are generated using the principle of linear superposition of the spectral components. The components' phases are assumed to be random, making it possible to generate an infinite number of offshore boundary conditions from only one spectrum.A reference case was provided by carrying out overtopping tests on a simple concrete structure in a wave flume. Numerical tests using the measured free surface elevation at the toe of the structure were carried out. Three parameters were analysed throughout the paper: the overtopping discharge, the probability of overtopping and the maximum overtopping volume. These showed very good agreement between the numerical solver prediction and the overtopping measurements. Subsequently, the measured spectra at the toe were used to generate a population of reconstructed offshore boundary time series for each test, following a Monte Carlo approach. A sensitivity analysis determined that 500 tests were suitable to perform a statistical analysis on the predicted overtopping parameters. Results of these tests show that the variability in the predicted parameters is higher for the smaller number of overtopping waves in the modelled range and decreases significantly as overtopping becomes more frequent. The characteristics of the distributions of the predictions have been studied. The average value of the three parameters has been compared with the measurements. Although the accuracy is lower than that achieved by the model when the measured time series are used at the boundary, the prediction is still fairly accurate above all for the highest overtopping discharges. The distribution of the modelled probability of overtopping was found to follow a normal distribution, while the maximum value follows a GEV one. The overtopping discharge shows a more complex behaviour, values in the middle of the tested range follow a Weibull distribution, while a normal distribution describes the top end of the range better.Results indicate that when the probability of overtopping is smaller than 5%, a sensitivity analysis on the seeding of the offshore boundary conditions is recommended.     

A numerical model of wave overtopping on seadikes

This paper describes the development of a numerical model for wave overtopping on seadikes. The model is based on the flux-conservative form of the nonlinear shallow water equations (NLSW) solved with a high order total variation diminishing (TVD), Roe-type scheme. The goal is to reliably predict the hydrodynamics of wave overtopping on the dike crest and along the inner slope, necessary for the breach modelling of seadikes. Besides the mean overtopping rate, the capability of simulating individual overtopping events is also required. It is shown theoretically that the effect of wave breaking through the drastic motion of surface rollers in the surfzone is not sufficiently described by the conventional nonlinear shallow water equations, neglecting wave setup from the mean water level and thus markedly reducing the model predictive capacity for wave overtopping. This is significantly improved by including an additional source term associated with the roller energy dissipation in the depth-averaged momentum equation. The developed model has been validated against four existing laboratory datasets of wave overtopping on dikes. The first two sets are to validate the roller term performance in improving the model prediction of wave overtopping of breaking waves. The last two sets are to test the model performance under more complex but realistic hydraulic and slope geometric conditions. The results confirm the merit of the supplemented roller term and also demonstrate that the model is robust and reliable for the prediction of wave overtopping on seadikes.     

Wave run-up and overtopping on smooth and rough slopes of coastal structures

A series of hydraulic model tests has been carried out in a glass wave flume to investigate the influences of wave height, wave period, wave steepness, surf similarity parameter, roughness, layer thickness and porosity on wave run-up and overtopping of 1:2 sloped impermeable and permeable breakwaters fronted by a 1:10 gentle, smooth beach slope. The analysis of results involves the correlation between the overtopping energy transfer with the relative wall height and the relationship between wave run-up and overtopping rate. Further, measured wave run-up and overtopping rates are compared with the results given in the Shore Protection Manual (1984), Automated Coastal Engineering System (1992)and results of other investigators.     

Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations

A one-dimensional high-resolution finite volume model capable of simulating storm waves propagating in the coastal surf zone and overtopping a sea wall is presented. The model (AMAZON) is based on solving the non-linear shallow water (NLSW) equations. A modern upwind scheme of the Godunov-type using an HLL approximate Riemann solver is described which captures bore waves in both transcritical and supercritical flows. By employing a finite volume formulation, the method can be implemented on an irregular, structured, boundary-fitted computational mesh. The use of the NLSW equations to model wave overtopping is computationally efficient and practically flexible, though the detailed structure of wave breaking is of course ignored. It is shown that wave overtopping at a vertical wall may also be approximately modelled by representing the wall as a steep bed slope. The AMAZON model solutions have been compared with analytical solutions and laboratory data for wave overtopping at sloping and vertical seawalls and good agreement has been found. The model requires more verification tests for irregular waves before its application as a generic design tool.     

The applicability of the shallow water equations for modelling violent wave overtopping

The shallow water equations (SWE) have been used to model a series of experiments examining violent wave overtopping of a near-vertical sloping structure with impacting wave conditions. A finite volume scheme was used to solve the shallow water equations. A monotonic reconstruction method was applied to eliminate spurious oscillations and ensure proper treatment of bed slope terms. Both the numerical results and physical observations of the water surface closely followed the relevant Rayleigh probability distributions. However, the numerical model overestimated the wave heights and suffered from the lack of dispersion within the shallow water equations. Comparisons made on dimensionless parameters for the overtopping discharge and percentage of waves overtopping between the numerical model and the experimental observations indicated that for the lesser impacting waves, the shallow water equations perform satisfactorily and provide a good alternative to computationally more expensive methods.     

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.     

Laboratory observations of green water overtopping a fixed deck

A small-scale laboratory experiment was conducted to quantify a transient wave overtopping a horizontal, deck fixed above the free surface. Detailed free surface and velocity measurements were made for two cases with and without the deck structure to quantify the effect of the deck on the wave kinematics. The study showed that the structure increased the free surface above the leading edge of the deck by 20%. The velocity profile at the leading edge was fairly uniform, and the maximum horizontal velocity was similar to the maximum crest velocity measured without the deck. Immediately below the deck, the maximum velocity was 2.5 times greater than the corresponding velocity without the deck and 2.1 times greater than the maximum crest velocity without the deck. On the deck, the wave collapsed into a thin bore with velocities that exceeded 2.4 times the maximum crest velocity measured without the deck.     

Computation of Long-Term Statistical Properties of Wave Agitation in Harbors

In this paper,the long-term statistical properties of wave height in an idealized square harborwith a partial opening are studied.The incident waves are propagated into the harbor numerically by the fi-nite/infinite element method using three different wave models:(1)monochromatic wave train,(2)long-crested random wave train,and(3)short-crested random wave train.This study shows that for a giv-en incident wave,the wave height in the harbor is affected by the wave model used.For long-term estima-tion of wave height exceedance probability,it is recommended that the waves be propagated into the har-bor using the random wave model,and that wave heights be computed by use of the Rayleigh probabilitydistribution.     

黄河三角洲沿岸海浪风暴潮耦合作用漫堤风险评估研究

海浪、风暴潮是重要的海洋灾害因子,过去人们主要对这些灾害因子本身进行研究,而对它们作用的承灾体研究甚少。实际上,只有它们作用的承灾体遭到破坏,才产生海洋灾害。本研究的目的就是要针对海浪风暴潮漫堤灾害,提出漫堤灾害的风险评估标准及风险评估方法和程式,为沿海防灾减灾提供科学依据。针对黄河三角洲示范区,根据漫堤程度,提出了漫堤灾害风险等级标准,并基于建立的海浪和风暴潮潮汐数值模式及长期预测结果,提出了风险评估方法和程式步骤。对黄河三角洲近岸海域主要堤段进行了多年一遇和典型台风过程漫堤灾害的风险评估。得到的结果是:该区沿岸海堤在风暴潮水位下一般都不能发生水位漫堤现象,只有加上波浪作用时,才会出现海水漫堤;当发生五十年一遇的风暴潮、浪时,多数的海堤的风暴潮、浪漫堤灾害风险在3—4级,即有效波高的浪已爬上或接近爬到堤顶;9216和9711号台风所产生的风暴潮、浪灾害约为150—200年一遇的情况。从实际情况看,本研究中提出的漫堤风险评估标准、评估方法是可行的,评估结果为有效防减海浪风暴潮漫堤灾害造成的损失提供了参考。     

斜向和多向不规则波在斜坡堤上的单波越浪量的实验研究

通过三维物理模型实验对斜坡堤上斜向和多向不规则波的单波越浪量进行了研究.实验考察了入射方向为0°~45°的斜向波和方向分布宽度为0°~25°的多向波以及混凝土和扭工字块体两种护面形式.在混凝土护面堤上用Weibull分布函数拟合了单波越浪量的累积频率分布,在影响因素不同的条件下确定了分布函数中的系数和越浪比例,给出了计算单波越浪量的公式,同时对扭工字块体护面堤上大约100个波中最大的单波越浪量进行了估算.     

Green water overtopping analyzed with a SPH model

Wave overtopping on the decks of offshore platforms and ships can cause severe damage due to the high forces generated by the water. This phenomenon is analyzed within the framework of the Smoothed Particle Hydrodynamics (SPH) method. The presence of a fixed horizontal deck above the mean water level modifies strongly the wave kinematics. In particular, the flow in the wave crest is split into two, showing a different behavior above and below the deck. Numerical results generated by the SPH method are compared to laboratory experiments. The formation of a jet in the rear of the deck after overtopping is observed under extreme conditions.     

斜向和多向不规则波对直立堤平均越浪量研究

通过三维波浪模型试验研究了斜向和多向不规则波对直立堤的越浪量。分别按平均越浪量和单波最大越浪量进行研究,探讨了平均越浪量随相对堤高、波浪方向、波浪方向分布宽度、波陡和相对水深等影响因素的变化规律,导得了斜向和多向不规则波作用于直立堤上的平均越浪量的计算公式。     

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.     

Quantification of changes in current intensities induced by wave overtopping around low-crested structures

The phenomenon of overtopping is traditionally studied for well-emerged harbour structures and often focuses on safety and stability. In this paper laboratory tests are presented and analysed to sharpen the hypothesis that overtopping is capable of changing the horizontal circulation pattern around low-crested structures. A unique data set from laboratory experiments was acquired in the wave basin at Delft University of Technology. The experiments were performed using an emerged impermeable low-crested structure (three freeboards and three different wave conditions for each freeboard) and yielded nine different combinations of set-up and overtopping driving forces. Using this information it was possible to quantify the changes in cross-shore and longshore velocity induced by the overtopping and the set-up changes under the different freeboard and wave conditions described. It is found that overtopping enhances the outgoing flows (longshore velocities parallel to the structure) away from the lee side of the structure and dampens the water level gradient driven flow towards the structure.     

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.