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.     

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.     

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.     

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.     

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.     

Field and laboratory measurements of mean overtopping discharges and spatial distributions at vertical seawalls

Within the CLASH project, wave overtopping at the vertical seawall at Samphire Hoe was measured by HR Wallingford (HRW), and compared laboratory tests in 2 & 3 dimensions carried out at the University of Edinburgh and HRW. At Samphire Hoe, overtopping volumes were captured in three volumetric tanks capable of measuring wave-by-wave and total overtopping volumes. The three tanks were placed progressively farther back from the seawall edge so that the spatial distribution of the overtopping discharges could be determined. The field measurement equipment was successfully deployed on three occasions, and measured overtopping discharges ranged from that barely considered to be hazardous to the public to over q = 3.0 l/s/m. The 2d testing at Edinburgh was modelled at a scale of 1:40, and the 3d model at HRW was modelled at 1:20. For both sets of laboratory tests, a range of conditions, representative of the storm wave conditions and water levels, was reproduced in addition to a set of parametric conditions. The storm conditions allowed a direct comparison between the field and laboratory measurements, and the parametric conditions were used to test the generic overtopping behaviour of the structure. For both sets of laboratory tests, mean overtopping discharges and the spatial distribution were measured separately. Analysis of the distribution data relates the proportion of the discharge that has landed as a function of (x / L_o); where x is the distance behind the crest, and L_o is the offshore wavelength. Analysis of the field, 2d & 3d laboratory data, and empirical prediction methods have not identified any scale effects for overtopping discharges at vertical and near-vertical seawalls.     

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.     

Overtopping performance of different armour units for rubble mound breakwaters

This paper describes a major programme of small-scale physical model tests to establish better the influence of armour type and configuration on overtopping. Specifically, 179 tests determined the relative difference in overtopping behaviour for 13 types/configurations of armour. Roughness factors γ_f were determined for rock (two layers), cubes (single layer and two layers), Tetrapod, Antifer, Haro, Accropode, Core-Loc™ and Xbloc™. These roughness influence factors have been included in the CLASH database and are for use in the neural network prediction of overtopping. Individual wave-by-wave overtopping volumes were analysed and found to compare well with current prediction methods. Measured reflection coefficients for the different units are also presented and compared with recent formulae.     

Neural network modelling of wave overtopping at coastal structures

A method has been developed to estimate wave overtopping discharges for a wide range of coastal structures. The prediction method is based on Neural Network modelling. For this purpose use is made of a data set obtained from a large number of physical model tests (collected within the framework of the European project CLASH, see e.g. [Steendam, G.J., Van der Meer, J.W., Verhaeghe, H., Besley, P., Franco, L. and Van Gent, M.R.A. (2004). The international database on wave overtopping. World Scientific, Proc. 29th ICCE, vol. 4, pp. 4301–4313, Lisbon, Portugal.]). Moreover, a method was developed to obtain confidence intervals for the overtopping predictions of the neural network.     

Sand suction mechanism in artificial beach composed of rubble mound breakwater and reclaimed sand area

An artificial beach has been constructed compensating for losing of the natural one caused by the development of coastal area. In this paper, the hydraulic model tests are carried out to investigate the suction phenomenon on the artificial beach constituted of rubble mound breakwater with gravel and the reclaimed sand area. In addition, the numerical model for waves, structures and seabed interaction as well as the numerical method based on the u–p approximation of the Biot equations is developed for investigation of suction mechanism. After verification of the numerical models by comparing numerical results with experimental data, the numerical models are further used to clarify the detailed suction mechanism of the reclaimed sand. The factors that affect the suction phenomenon are examined experimentally and their critical values are presented. Also, it can be pointed out that the vertical discharge velocity as well as the volumetric strain around the still water level of the boundary between the breakwater and the beach gets up to the critical value, the reclaimed sand starts to flow out to the offshore, and it finally leads to caves and cave-ins in the reclaimed zone.     

中长周期波作用下的斜坡堤胸墙波浪力试验研究

在印度洋、大西洋沿岸,海岸工程设计波浪周期多在14 s以上,具有显著的中长周期波特征。通过以往工程项目的试验结果发现中长周期波下,规范计算的斜坡堤胸墙波浪力明显小于试验结果。因此,通过系列物理模型试验研究了中长周期波下的斜坡堤胸墙波浪力。分析斜坡坡度、肩台宽度和波浪条件对胸墙波浪力的影响。通过将试验结果与我国现有规范中的经验公式计算所得结果进行对比,发现规范更适用于胸墙底淹没的情况,而对于肩台出水情况,规范计算结果小于试验结果。由此提出了一种新的波浪力计算方法,计算准确度得到明显提高。     

斜坡堤天然块石护脚的稳定性计算

试验研究表明 ,不规则波对斜坡堤护脚棱体稳定性的威胁大于波高对应于Hs 的规则波 ,斜坡堤护面形式对护脚块石的稳定也有影响。Gerding公式虽然准确地描述了棱体在波浪作用下的稳定性规律 ,但由于护面糙率、透水率等因素的影响在工程上应用仍需进一步修正。文章指出在中低水位 ,Gerding公式计算的护脚棱体稳定重量有可能偏小 ,并给出了不同类型护面下护脚棱体稳定计算的修正系数     

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.     

A comparison of several wave spectra for the random wave diffraction by a semi-infinite breakwater

A comparison of the diffraction of multidirectional random waves using several selected wave spectrum models is presented in this paper. Six wave spectrum models, Bretschneider, Pierson–Moskowitz, ISSC, ITTC, Mitsuyasu, and JONSWAP spectrum, are considered. A discrete form for each of the given spectrum models is used to specify the incident wave conditions. Analytical solutions based on both the Fresnel integrals and polynomial approximations of the Fresnel integrals and numerical solutions of a boundary integral approach have been used to obtain the two-dimensional wave diffraction by a semi-infinite breakwater at uniform water depth. The diffraction of random waves is based on the cumulative superposition of linear diffraction solution. The results of predicted random wave diffraction for each of the given spectrum models are compared with those of the published physical model presented by Briggs et al. [1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal and Ocean Engineering—ASCE 121(1), 23–35]. Reasonable agreement is obtained in all cases. The effect of the directional spreading function is also examined from the results of the random wave diffraction. Based on these comparisons, the present model for the analysis of various wave spectra is found to be an accurate and efficient tool for predicting the random wave field around a semi-infinite breakwater or inside a harbor of arbitrary geometry in practical applications.     

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.     

On the role of shoreline boundary conditions in wave overtopping modelling with non-linear shallow water equations

The note extends and completes the analysis carried out by Briganti and Dodd [Briganti, R., Dodd, N., 2009. Shoreline motion in nonlinear shallow water coastal models. Coastal Eng. 56(5–6) (doi:101016/j.coastaleng.2008.10.008), 495–505.] on the performance of a state of the art Non-Linear Shallow Water Equations solver in common coastal engineering applications. The case of bore-generated overtopping of a truncated plane beach is considered and the performance of the model is assessed by comparing with the Peregrine and Williams [Peregrine, D., Williams, S.M., 2001. Swash overtopping a truncated beach. J. Fluid Mech. 440, 391–399.] analytical solution. In particular the influence of shoreline boundary conditions is investigated by considering the two best performing approaches discussed in Briganti and Dodd [Briganti, R., Dodd, N., 2009. Shoreline motion in nonlinear shallow water coastal models. Coastal Eng. 56(5–6) (doi:101016/j.coastaleng.2008.10.008), 495–505.]. Different distances of the edge of the beach from the bore collapse point are tested. For larger distances, the accuracy of the overtopping modelling decreases, as a consequence of the error in modelling the tip of the swash lens and, consequently, the run-up. A sensitivity analysis using the numerical resolution is carried out. This reveals that the approach in which cells shallower than a prescribed threshold are drained and wave propagation speeds for wet/dry Riemann problem are used at the interface between a wet and a dry cell (referred as Option 2ea in [Briganti, R., Dodd, N., 2009. Shoreline motion in nonlinear shallow water coastal models. Coastal Eng. 56(5–6) (doi:101016/j.coastaleng.2008.10.008), 495–505.]) performs consistently better than the other.     

Verification of a VOF-based two-phase flow model for wave breaking and wave–structure interactions

The objective of the present study is to develop a volume of fluid (VOF)-based two-phase flow model and to discuss the applicability of the model to the simulation of wave–structure interactions. First, an overview of the development of VOF-type models for applications in the field of coastal engineering is presented. The numerical VOF-based two-phase flow model has been developed and applied to the simulations of wave interactions with a submerged breakwater as well as of wave breaking on a slope. Numerical results are then compared with laboratory experimental data in order to verify the applicability of the numerical model to the simulations of complex interactions of waves and permeable coastal structures, including the effects of wave breaking. It is concluded that the two-phase flow model with the aid of the advanced VOF technique can provide with acceptably accurate numerical results on the route to practical purposes.     

An experimental investigation into the wave power extraction of a floating box-type breakwater with dual pneumatic chambers

The oscillating water column (OWC) device is in a leading position for wave power extraction but has not achieved fully commercial at the current stage. In addition to enhancing the OWC performance, installing OWCs on floating breakwaters, which owns the merits of both cost-sharing and offshore power supply, is a practicality with high economic viability. In this study, a series of wave-flume experiments were conducted in regular waves to examine the wave power extraction of a floating box-type breakwater with dual pneumatic chambers. The flow characteristics of the orifices used to simulate the PTOs was pre-calibrated through another series of experiments, so the power extraction in this study can be obtained with only the pressure measurement. The effects of wave period, chamber draft, water depth and arrangement of chambers on the power extraction were examined. Our experimental results showed that the power extraction was mainly due to the water column oscillation inside the chamber, and differentiation in the designed natural periods of dual chambers could widen the efficiency bandwidth of power extraction. The front chamber always played the main role in power extraction and its natural period should be designed against the dominating period of the wave spectrum; in contrast, the power extraction of the rear chamber was only a supplement and its natural period should be designed against longer waves which were more easily transmitted, thus a PTO of small power capacity maybe more realistic. It was also worth noting that the water column oscillation was more dependent on the wave period rather than controlled by the wave scattering under different water depths.     

Modelling the effect of wave overtopping on nearshore hydrodynamics and morphodynamics around shore-parallel breakwaters

Wave overtopping nearshore coastal structures, such as shore-parallel breakwaters, can significantly alter the current circulation and sediment transport patterns around the structures, which in turn affects the formation of tombolos and salients in the nearshore area. This paper describes the implementation of a wave overtopping module into an existing depth-averaged coastal morphological mode: COAST2D and model applications to investigate the effect of wave overtopping on the hydrodynamics and morphodynamics around a group of shore-parallel breakwaters. The hydrodynamic aspects of the model were validated against a series of laboratory conditions. The model was then applied to a study site at Sea Palling, Norfolk, UK, where 9 shore-parallel segmented breakwaters including 4 surface-piercing and 5 low-crested breakwaters are present, for the storm conditions in Nov 2006. The model results were compared with laboratory data and field measurements, showing a good agreement on both hydrodynamics and morphological changes. Further analysis of wave overtopping effect on the nearshore hydrodynamics and morphodynamics reveals that wave overtopping has significant impacts on the nearshore circulation, sediment transport and the resulting morphological changes within such a complex breakwater scheme under the storm and macro-tide conditions. The results indicate the importance of including the wave overtopping in modelling nearshore morphodynamics with the presence of coastal structures.     

Comparison of wind and wave measurements and models in the Western Mediterranean Sea

We have hindcast the wind and wave conditions in the Mediterranean Sea for two one month periods. Four different meteorological models and three different wave models have been used. The results have been compared with satellite and buoy wind and wave observations.Several conclusions concerning both the instruments and the models have been derived. The quality of both wind and wave results has been assessed. Close to the coasts high resolution, nested wave models are required for sufficient reliability.A wave threshold analysis suggests a sufficient reliability only off the coast, with a substantial decrease for low wave heights.