Modelling of waves and currents around submerged breakwaters

Recent experimental data collected during the DELOS project are used to validate two approaches for simulating waves and currents in the vicinity of submerged breakwaters.The first approach is a phase-averaged method in which a wave model is used to simulate wave transformation and calculate radiation stresses, while a flow model (2-dimensional depth averaged or quasi-3D) is used to calculate the resulting wave driven currents. The second approach is a phase resolving method in which a high order 2DH-Boussinesq-type model is used to calculate the waves and flow.The models predict wave heights that are comparable to measurements if the wave breaking sub-model is properly tuned for dissipation over the submerged breakwater. It is shown that the simulated flow pattern using both approaches is qualitatively similar to that observed in the experiments. Furthermore, the phase-resolving model shows good agreement between measured and simulated instantaneous surface elevations in wave flume tests.     

On rubble-mound breakwaters of composite slope

The geometrical properties of the armor layer of rubble mound breakwaters were investigated by observations made on two cases. The first case is a laboratory-scaled model of natural rock, designed with a composite slope. The second is a breakwater in the sea, constructed with a uniform slope of tetrapods. In both cases the cross-section underwent changes, resulting in an apparently stable profile of composite slope. This implied that for stability the optimal armour layer should be of composite slope. The general nature of this profile was implied by the geometrical similarity between the two cases which were basically so different.     

Analysis of far-field erosion induced by low-crested rubble-mound structures

This paper focuses on the analysis of the morphological response induced by low-crested structures on the adjacent seabed, with emphasis on the far-field erosion that is frequently observed close to roundheads and at the gaps between structures. The analysis is based on observations of far-field erosion, both at prototype scale and in laboratory experiments. Mechanisms responsible for the observed erosion are highlighted using coastal area numerical modelling tools to simulate the flow patterns induced by schemes involving low-crested structures. Finally, an example of the use of a coastal area morphological modelling system to investigate the dependence of the far-field erosion processes on the freeboard of the coastal protection structures is presented and discussed.     

Deformation of rubble-mound breakwaters under cyclic loads

Rubble-mound breakwaters usually consist of a core of small quarry-run rock protected by one or more intermediate layers or underlayers that separate the core from the cover layers, which are composed of large armor units. Failure of rubble-mound breakwaters may be due to effects such as removal or damage of the armor units, overtopping leading to scouring, toe erosion, loss of the core material, or foundation problems under waves. However, whether rubble mounds fail under seismic loads is unknown. High seismic activity can lead to large settlements and even to failure of the breakwaters. The design of coastal structures should take into account the most relevant factors in each case, including seismic loading. The objective of this study is to understanding the failure mechanisms of conventional breakwater structures under seismic loads on rigid foundations. Hence, an experimental study was carried out on conventional breakwater structures with and without toes, subjected to different dynamic loadings of variable frequencies and amplitudes, in a shaking tank. A shaking tank with a single degree of freedom was developed to study the simple responses of conventional rubble-mound breakwaters under cyclic loads. For each test, an automatic raining crane system was used to achieve the same relative density and porosity of the core material. The input motion induced horizontal accelerations of different magnitudes during the tests. The accelerations and the deformation phases of the model were measured by a data acquisition system and an image processing system. The experiments on the conventional rubble-mound type breakwater model were performed under rigid-bottom conditions. The model's scale was 1:50. Cyclic responses of breakwaters with toes and without toes were examined separately, and their behaviors were compared. The results were compared with a numerical study, and the material properties and failure modes were thus defined.     

A virtual laboratory for stability tests of rubble-mound breakwaters

The prediction of rubble-mound breakwater damage under wave action has usually relied on costly and time-consuming physical model tests. In this work, artificial neural networks (ANNs) are applied to estimate the outcome of a physical model throughout an experimental campaign comprising of 127 stability tests. In order to choose the network best suited to the problem data, five different activation function options and 38 network architectures are compared. The good agreement found between the physical model and the neural network shows that an ANN may well serve as a virtual laboratory, reducing the number of physical model tests necessary for a project.     

Wave height parameter for damage description of rubble-mound breakwaters

In this paper it will be shown that the wave height parameter H₅₀, defined as the average wave height of the 50 highest waves reaching a rubble-mound breakwater in its useful life, can describe the effect of the wave height on the history of the armor damage caused by the wave climate during the structure's usable life.Using Thompson and Shuttler (Thompson, D.M., Shuttler, R.M., 1975. Riprap design for wind wave attack: A laboratory study on random waves. HRS Wallingford, Report 61, UK) data it will be shown that H₅₀ is the wave parameter that best represents the damage evolution with the number of waves in a sea state. Using this H₅₀ parameter, formulae as van der Meer (van der Meer, J.W., 1988. Rock slopes and gravel beaches under wave attack. PhD Thesis. Technical University of Delft) and Losada and Giménez-Curto (Losada, M.A., Gimenez–Curto, L.A., 1979. The joint effect of the wave height and period on the stability of rubble mound breakwaters using Iribarren's number. Coastal Engineering, 3, 77–96) are transformed into sea-state damage evolution formulae. Using these H₅₀-transformed formulae for regular and irregular sea states it will be shown how damage predictions are independent of the sea state wave height distribution.To check the capability of these H₅₀-formulae to predict damage evolution of succession of sea states with different wave height distributions, some stability tests with regular and irregular waves have been carried out. After analysing the experimental results, it will be shown how H₅₀-formulae can predict the observed damage independently of the sea state wave height distribution or the succession of sea states.     

Analysis of wave transmission behind low-crested breakwaters using neural networks

This paper aims at improving the prediction of wave transmission behind low-crested breakwaters by means of a numerical model based on Artificial Neural Networks (ANNs). The data here used are those gathered within the European research project DELOS.Firstly, the motivations that lead to employ an ANN numerical model to forecast the wave transmission behind low-crested structures are discussed. Then, the ANN model is tested and its architecture is optimized with a test targeted on assessing both the accuracy and the robustness of the method. A study is devoted to investigate the ANN model capability in reproducing some physical relationships among the involved parameters. Finally, comparisons of ANN results with those from experimental formulations based on the classic regression approach demonstrate a considerable improvement in the forecast accuracy.The ANN forecasting tool is available as a user-friendly Internet applet at: http://w3.uniroma1.it/cmar/wave_transm_kt.htm.     

2-D numerical analysis of near-field flow at low-crested permeable breakwaters

This paper describes the capability of a numerical model named COrnell BReaking waves And Structures (COBRAS) [Lin, P., Liu, P.L.-F., 1998. A numerical study of breaking waves in the surf zone. Journal of Fluid Mechanics 359, 239–264; Liu, P.L.-F., Lin, P., Chang, K.A., Sakakiyama, T., 1999. Numerical modeling of wave interaction with porous structures. Journal of Waterway, Port, Coastal and Ocean Engineering 125, 322–330, Liu, P.L.-F., Lin, P., Hsu, T., Chang, K., Losada, I.J., Vidal, C., Sakakiyama, T., 2000. A Reynolds averaged Navier–Stokes equation model for nonlinear water wave and structure interactions. Proc. Coastal Structures '99, 169–174] based on the Reynolds Averaged Navier–Stokes (RANS) equations to simulate the most relevant hydrodynamic near-field processes that take place in the interaction between waves and low-crested breakwaters. The model considers wave reflection, transmission, overtopping and breaking due to transient nonlinear waves including turbulence in the fluid domain and in the permeable regions for any kind of geometry and number of layers. Small-scale laboratory tests were conducted in order to validate the model, with different wave conditions and breakwater configurations. In the present study, regular waves of different heights and periods impinging on a wide-crested structure are considered. Three different water depths were tested in order to examine the influence of the structure freeboard. The experimental set-up includes a flow recirculation system aimed at preventing water piling-up at the lee of the breakwater due to overtopping. The applicability and validity of the model are examined by comparing the results of the numerical computations with experimental data. The model is proved to simulate with a high degree of agreement all the studied magnitudes, free surface displacement, pressure inside the porous structure and velocity field. The results obtained show that this model represents a substantial improvement in the numerical modelling of low-crested structures (LCS) since it includes many processes neglected previously by existing models. The information provided by the model can be useful to analyse structure functionality, structure stability, scour and many other hydrodynamic processes of interest.     

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.     

Transmission of obliquely incident waves at low-crested breakwaters: Theoretical interpretations of experimental observations

The paper presents a series of analytical and numerical investigations of oblique wave transmission at low-crested breakwaters. For a smooth breakwater, two important features of wave height and direction are analyzed to establish the generic nature of the wave transmission process at oblique incidence. The proposed framework of research is validated against laboratory data from the EU-sponsored project, DELOS. The numerical simulations exhibit a significant decrease of the transmission coefficient with increasingly oblique incidence at a smooth breakwater. The roles of wave-breaking, nonlinearity, wave-induced currents and set-up in determining the characteristics of oblique wave transmission are demonstrated in the paper. It is found that both the amplitude-dependent phase velocity and the decrease of mean wave period contribute to the change of mean wave direction on the transmission side. An attempt has also been made to qualitatively explain the different behaviour of oblique wave transmission at a rubble-mound breakwater.     

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.     

透空式防波堤周围的非线性波浪传播的数值模拟

对非线形波浪在透空式防波堤周围的波浪变形进行了数值模拟,在Boussinesq波浪方程中加入与透空建筑物有关的新的耗散项,从而界定了透空建筑物引起的部分反射和透射,波浪折射衍射的传播过程通过控制方程求解。波浪控制方程通过有限差分方法求解。模型应用于模拟波浪经过具有部分反射的群桩式透空结构,结果表明透空式防波堤可以有效地衰减波浪,是重力式结构的一种替代形式。     

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.     

Using RANS to simulate vortex generation and dissipation around impermeable submerged double breakwaters

In this paper, a Reynolds Averaged Navier–Stokes (RANS) model was developed to simulate the vortex generation and dissipation caused by progressive waves passing over impermeable submerged double breakwaters. The dynamics of the turbulence are described by introducing a k–ɛ model with Boussinesq closure. The Height Function (HF) is implemented to define the free-surface configuration. The governing equations are discretized by means of a finite volume method based on a staggered grid system with variable width and height. The feasibility of the numerical model was verified through a series of comparisons of numerical results with the existing analytical solutions and the experimental data. The good agreements demonstrate the satisfactory performance of the developed numerical model. The flow separation mechanism both near the upstream and the downstream edges of the obstacles demonstrates the physical and expected nature of development of the flow. The present model provides an accurate and efficient tool for the simulation of flow field and wave transformation near coastal structures without breaking.     

Breaking wave forces and velocity fields

A new technique for measuring velocities under breaking wave crests using laser-doppler anemometry has been developed. Results may be obtained at positions up to 4 millimeters from the crest.A wave field is presented for a vertically fronted wave and comparison is made with an appropriate numerical study. The velocities obtained are far in excess of the predictions of linear theory.Measurements have also been made of the forces produced by this wave on a horizontal cylinder. Comparisons with large regular waves indicate that forces due to breaking waves can be up to five times greater for similar wave heights.