Wave reflection in 3D conditions

Based on recent experiments carried out in wave basin on breakwaters with armour layer of rocks and cubes, this paper examines the dependence of the reflection coefficient on wave directional spreading and obliquity. Results suggest that long-crested and short-crested waves give similar reflection. The reflection coefficient is markedly dependent on the wave angle of incidence. The performance of formulae available in the literature is checked against the new dataset and a significant improvement is proposed by including the wave obliquity factor that appears in the traditional expression for the overtopping discharge.     

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.     

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.     

斜向和多向不规则波在斜坡堤上的平均越浪量的试验研究

通过三维物理模型试验研究了在斜坡堤上斜向和多向不规则波在非破碎条件下的平均越浪量与波浪参数及堤参数的关系.着重考察了波浪以小角度(0°~30°)斜向入射时平均越浪量的变化情况,肯定了多向波的越浪量在这一范围内有所谓“小角度斜向增加”的现象,但否定了单向波也具有这一现象.在考察波浪的方向分布影响时发现波浪斜向入射时多向波的越浪量往往要比单向波的大.比较了已有的相关研究成果,给出了适用于混凝土护面和扭工字块体护面斜坡堤上斜向和多向不规则波的平均越浪量的估算公式.     

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.     

An approximate solution for the wave energy shadow in the lee of an array of overtopping type wave energy converters

In this study we investigate how the wave energy deficit in the lee of an array of overtopping type wave energy converting devices (WECs), redistributes with distance from the array due to the natural variability of the wave climate and wave structure interactions. Wave directional spreading has previously been identified as the dominant mechanism that disperses the wave energy deficit, reducing the maximum wave height reduction with increasing distance from the array. In addition to this when waves pass by objects such as an overtopping type WEC device, diffracted waves re-distribute the incident wave energy and create a complex interference pattern. The effect of wave energy redistribution from diffraction on the wave energy shadow in the near and far field is less obvious. In this study, we present an approximate analytical solution that describes the diffracted and transmitted wave field about a single row array of overtopping type WECs, under random wave conditions. This is achieved with multiple superpositions of the analytical solutions for monochromatic unidirectional waves about a semi-infinite breakwater, extended to account for partial reflection and transmission. The solution is used to investigate the sensitivity of the far field wave energy shadow to the array configuration, level of energy extraction, incident wave climate, and diffraction. Our results suggest that diffraction spreads part of the wave energy passing through the array, away from the direct shadow region of the array. This, in part, counteracts the dispersion of the wave energy deficit from directional spreading.     

Effects of new variables on the overtopping discharge at steep rubble mound breakwaters — The Zeebrugge case

This paper describes on the one hand parametric tests on wave overtopping for a steep rubble mound breakwater in Zeebrugge, Belgium. On the other hand the comparison between prototype measurements at the breakwater and their scale reproductions in two laboratories is dealt with. The objective is to gain information on possible scale and model effects for wave overtopping from this comparison. The prototype measurements are described together with the resulting dataset of 11 storms where wave overtopping occurred. Scale models and the laboratory measurements are described into detail mentioning similarities and differences to the prototype. Several model effects are identified and special attention is given to wind effects and to the placement pattern of the armour units, respectively. Monte Carlo simulations have been performed to get an idea about the influence of selected model uncertainties. Finally, scale effects are discussed and the influence of model and scale effects for the performed tests is quantified. Recommendations on how to treat these effects are presented.     

Estimation of wave directional spreading in shallow water

This paper describes wave directional spreading in shallow water. Waves were measured for a period of 2 months using the Datawell directional waverider buoy at 15 m water depth on the east coast of India in the Bay of Bengal. The study also showed that in shallow water wave directional spreading was narrowest at peak frequency and widened towards lower and higher frequencies. The wind direction was found to deviate from the wave direction during most of the time. The unidirectional spectrum was found to be satisfactorily represented by Scott spectra.     

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.     

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.     

Analysis of overtopping flow on sea dikes in oblique and short-crested waves

Dike resilience against wave overtopping has gained more and more attention in recent years due to the effect of expected future climate changes. The overtopping flow velocities and flow depths on dikes have recently been studied in 2D small-scale experiments. This has led to semi-empirical formulae for the estimation of flow depths and flow velocities across a dike. The results have been coupled to the actual erosion of the landward dike slope determined by full-scale 2D tests using the so-called “Overtopping Simulator”. This paper describes the results from 96 small-scale tests carried out in a shallow water basin at Aalborg University to cover the so far unknown 3D effects from oblique long-crested and short-crested waves. Based on results from the laboratory tests, expansions are proposed to the existing 2D formulae so as to cover oblique and short-crested waves. The wave obliquity is seen to significantly reduce the overtopping flow velocities and flow depths on especially the landward slope of a sea dike. Moreover, the tests showed that the average flow directions on the dike crest from oblique long-crested and short-crested waves correspond approximately to the incident wave direction. Flow depths and the squared flow velocities on the dike are concluded to be Rayleigh-distributed in case of both long-crested and short-crested waves for all considered incident wave obliquities. Findings in the present paper are needed to obtain more realistic estimates of dike erosion caused by wave overtopping.     

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.     

Numerical investigations of wave overtopping at coastal structures

Under the numerical modelling work package of the EU funded CLASH project, the time accurate, free surface capturing, incompressible Navier–Stokes solver AMAZON-SC has been applied to study impulsive wave overtopping at Samphire Hoe, near Dover in the United Kingdom. The simulations show that the overtopping process on this vertical, sheet pile, seawall is dominated by impulsive, aerated, near vertical overtopping jets. In order to perform the simulations AMAZON-SC has been extended to incorporate an isotropic porosity model and for validation purposes the solver has been applied to study overtopping of a low crested sea dike and a 10:1 battered wall. The results obtained for the battered wall and Samphire Hoe tests are in good agreement both with predicted overtopping discharges calculated using the UK overtopping manual and with available experimental results.     

Some statistical characteristics of large deepwater waves around the Korean Peninsula

The relationship between significant wave height and period, the variability of significant wave period, the spectral peak enhancement factor, and the directional spreading parameter of large deepwater waves around the Korean Peninsula have been investigated using various sources of wave measurement and hindcasting data. For very large waves comparable to design waves, it is recommended to use the average value of the empirical formulas proposed by Shore Protection Manual in 1977 and by Goda in 2003 for the relationship between significant wave height and period. The standard deviation of significant wave periods non-dimensionalized with respect to the mean value for a certain significant wave height varies between 0.04 and 0.21 with a typical value of 0.1 depending upon different regions and different ranges of significant wave heights. The probability density function of the peak enhancement factor is expressed as a lognormal distribution, with its mean value of 2.14, which is somewhat smaller than the value in the North Sea. For relatively large waves, the probability density function of the directional spreading parameter at peak frequency is also expressed as a lognormal distribution.     

Comparison of new large and small scale overtopping tests for rubble mound breakwaters

Many breakwaters are, due to functional requirements, designed for small wave overtopping discharges. From the EC-research projects OPTICREST and CLASH it is known that overtopping discharges determined from conventional Froude scale models of rubble mound breakwaters are smaller than measured in corresponding prototypes. The present study examines this scale effect by comparing overtopping discharges in small scale and large scale tests. The length scale ratio between the models was 5.7.     

Field measurements of wave overtopping at the rubble mound breakwater of Rome–Ostia yacht harbour

This paper describes a new station for full-scale measurement of wave overtopping at the Rome yacht harbour rubble mound breakwater in Ostia (Italy) and the results of the successful first measurement campaign carried out during the winter season 2003–2004. The equipment and the research activities were supported by the EU project CLASH, focusing on scale effects for wave overtopping at coastal structures. The site is characterized by a very small tidal range, a long shallow foreshore and depth-limited breaking waves which interact with a shallow sloping porous rock structure. Overtopping water is collected by a steel tank installed on the crown slab behind the parapet wall. The measurement of water level variation inside the tank by means of two pressure transducers allows the calculation of individual overtopping volumes. Incident waves, sea levels and wind are also measured. During seven independent storms, more than 400 individual overtopping events were recorded and about 86 h of valid data are available. This extensive dataset is presented, discussed and then used for comparison with two commonly used overtopping prediction formulae based on small-scale model tests showing their tendency to underestimate the prototype results. A strong correlation between the hourly mean overtopping discharge and corresponding maximum volume is also presented. The paper generally confirms the validity of the approach used in Troch et al. (2004) [Troch, P., Geeraets, J., Van de Walle, B., De Rouck, J., Van Damme, L., Allsop, W., Franco, L., 2004. Full-scale wave overtopping measurements on the Zeebrugge rubble mound breakwater. Coastal Engineering 51, 609–628] for field measurement of wave overtopping.     

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。     

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.     

长江口横沙东滩典型海堤越浪量现场和试验研究

越浪量是允许越浪海堤设计的重要参数。在对以往相关研究成果进行回顾和分析基础上,结合长江口横沙东滩促淤圈围五期工程现场波浪和越浪量实测资料,通过对横沙东滩典型断面型式进行整体和断面物理模型试验,研究结构各参数对越浪量的影响,进而提出适合长江口海堤的越浪量计算公式。公式计算结果与试验数据吻合良好,与Van der Meer公式相比具有较好的一致性。     

Numerical implementation and sensitivity analysis of a wave energy converter in a time-dependent mild-slope equation model

Several Wave Energy Converters (abbreviated as WECs) have intensively been studied and developed during the last decade and currently small farms of WECs are getting installed. WECs in a farm are partly absorbing, partly redistributing the incident wave power. Consequently, the power absorption of each individual WEC in a farm is affected by its neighbouring WECs. The knowledge of the wave climate around the WEC is needed to predict its performance in the farm. In this paper a technique is developed to implement a single and multiple WECs based on the overtopping principle in a time-dependent mild-slope equation model. So far, the mild-slope equations have been widely used to study wave transformations around coastal and offshore structures, such as breakwaters, piles of windmills and offshore platforms. First the limitations of the WEC implementation are discussed through a sensitivity analysis. Next the developed approach is applied to study the wave height reduction behind a single WEC and a farm. The wake behind an isolated WEC is investigated for uni- and multidirectional waves; it is observed that an increase of the directional spread leads to a faster wave redistribution behind the WEC. Further the wake in the lee of multiple WECs is calculated for two different farm lay-outs, i.e. an aligned grid and a staggered grid, by adapting the performance of each WEC to its incident wave power. The evolved technique is a fast tool to find the optimal lay-out of WECs in a farm and to study the possible influence on surrounding activities in the sea.