Porosity effects on non-breaking surface waves over permeable submerged breakwaters

This study investigated how the porosity of submerged breakwaters affects non-breaking wave transformations. Eight model geometries each with six different porosities, from 0.421 to 0.912, were also considered. Experimental results reveal that the model width has little effect on wave reflection and transmission when the model heights are fixed. The transmission coefficient is maximum at a kh in the range from 1.3 to 2.0 and minimum at a kh around 0.7. The wave reflection maximum is at kh of near 0.5. The energy loss of the primary waves is maximum near kh=0.81 and minimum when the porosity of the model is large. Porosity does affect wave transformation and its influence becomes significant as the heights of the models increase. For the range of porosities tested, wave energy loss from the primary harmonic was found to be almost constant at around 0.4 when kh >1.3, decreasing slowly when kh <1.3; wave energy loss decreases for porosities above 0.75.     

Long wave reflection from submerged trapezoidal breakwaters

This study addresses the reflection and transmission of long waves from a trapezoidal breakwater and a series of trapezoidal breakwaters, using the matching method. A systematic shape transfer is derived to determine wave reflection and transmission. The peak Bragg reflection of long waves from a series of trapezoidal breakwaters is shifted toward low frequency. In spite of the spacing between any pair of breakwaters, the top plane width and the arrangement of the series of breakwaters are found to be the two major parameters in designing multiply composite Bragg breakwaters.     

The interaction of surface water waves with submerged breakwaters

This paper concerns the behaviour of nonlinear regular waves interacting with rectangular submerged breakwaters. A new series of experimental results is presented and compared with numerical calculations based upon a Boundary Element Method (BEM) that utilises multiple fluxes to deal with the discontinuities encountered at the corners of the domain. Specifically, comparisons concern both the spatial water surface profiles at various times and the spatial evolution of the harmonics generated by the breakwaters, the latter being an important focus for the paper. The BEM is shown to accurately model both the water surface profile and the harmonic generation, provided the breakwater width is sufficient to ensure that flow separation is not a controlling influence. Furthermore, evidence is provided to confirm that reflection from rectangular submerged breakwaters is fundamentally a linear phenomenon.     

Dynamic response and sliding distance of composite breakwaters under breaking and non-breaking wave attack

Over the last 15 years improved awareness of wave impact induced failures has focused attention on the need to account for the dynamic response of maritime structures to wave impact load. In this work a non-linear model is introduced that allows evaluating the effective design load and the potential sliding of caisson breakwater subject to both pulsating and impulsive wave loads. The caisson dynamics is modelled using a time-step numerical method to solve numerically the equations of motion for a rigid body founded on multiple non-linear springs having both horizontal and vertical stiffness. The model is first shown to correctly describe the dynamics of caisson breakwaters subject to wave attack, including nonlinear features of wave–structure–soil interaction. Predictions of sliding distances by the new method are then compared with measurements from physical model tests, showing very good agreement with observations. The model succeeds in describing the physics that stands behind the process and is fast, accurate and flexible enough to be suitable for performance design of caisson breakwaters.     

T型防波堤与波浪相互作用数值研究

针对T型透空式防波堤,通过浪高仪采集防波堤前后不同位置波面变化曲线,使用声学多普勒流速仪(NDV)测量不同位置流速随时间的变化,并分析了其相位平均流速的分布。基于VOF法的二维波浪数值水槽,对规则波作用下T型防波堤附近的动力特性进行了计算,水槽模型试验结果和数值模拟结果对比表明,数值计算结果与实验值吻合较好。采用该模型进一步对T型防波堤附近波浪场、流线、紊动动能、紊动动能耗散率变化以及不同尺寸的防波堤消浪效果进行模拟计算,重点分析了入射波高、防波堤入水深度和防波堤宽度变化的影响。     

Simplified analytical solutions for wave interaction with absorbing-type caisson breakwaters

Simplified analytical solutions are presented to model the interaction of linear waves with absorbing-type caisson breakwaters, which possess one, or two, perforated or slotted front faces which result in one, or two, interior fluid regions (chambers). The perforated/slotted surfaces are idealized as thin porous plates. Energy dissipation in the interior fluid region(s) inside the breakwater is modelled through a damping function. Under the assumption of potential flow and linear wave theory a boundary-value problem may then be formulated to describe wave interaction with the idealized structure. A solution to this simplified problem may be obtained by an eigenfunction expansion technique and an explicit analytical expression may be obtained for the reflected wave height. Using the experimental work of previous authors, damping coefficients are determined for both single and double chamber absorbing-type caisson breakwaters. Based on the damping for a single perforated-wall breakwater, a methodology is proposed to enable the estimation of the damping coefficients for a breakwater with two chambers. The theoretical predictions of the reflection coefficients for the two-chamber structures using the present model are compared with those obtained from laboratory experiments by other authors. It is found that the inclusion of the damping in the interior fluid region gives rise to improved agreement between theory and experiment.     

Experimental study of strong reflection of regular water waves over submerged breakwaters in tandem

A series of laboratory experiments was carried out to investigate the strong reflection of regular water waves over a train of submerged breakwaters. Rectangular and trapezoidal shapes of submerged breakwaters are employed and compared for reflecting capability of incident waves. Measured reflection coefficients of regular waves over impermeable submerged breakwaters are verified by comparing with those of the eigenfunction expansion method. A very good agreement is observed. Reflection coefficients of permeable submerged breakwaters are less than those of impermeable breakwaters. The trapezoidal shape is recommended for a submerged breakwater in terms of reflecting capability and practical application.     

Wave interaction with T-type breakwaters

The wave transmission, reflection and energy dissipation characteristics of partially submerged ‘T'-type breakwaters (Fig. 1) were studied using physical models. Regular and random waves, with wide ranges of wave heights and periods and a constant water depth were used. Five different depths of immersions of the ‘T'-type breakwater were selected. The coefficient of transmission, K_t, coefficient reflection, K_r, were obtained from the measurements and the coefficient of energy loss, K_l is calculated using the law of conservation of energy. It is found that the coefficient of transmission generally reduces with increased wave steepness and increased relative water depth, d/L. This breakwater is found to be effective closer to deep-water conditions. K_t values less than 0.35 is obtained for both normal and high input wave energy levels, when the horizontal barrier of the T type breakwater is immersed to about 7% of the water depth. This breakwater is also found to be very efficient in dissipating the incident wave energy to an extent of about 65% (i.e. K_l>0.8), especially for high input wave energy levels. The wave climate in front of the breakwater is also measured and studied.

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Fig. 1. Schematic view of the T-type breakwater.     

Wave diffraction through submerged flexible breakwaters

This paper presents an analytical, computationally efficient method for the wave reflection and dynamic displacement of a submerged flexible breakwater. The solution of the two-dimensional linearized hydrodynamic problem introduced is based on the eigenfunction expansion technique. The breakwater is assumed to be thin, impermeable, flexible, moored to the bed through tethers and kept in tension by means of a floating buoy at its tip. The beam structure is considered to be either clamped or hinged at the sea bed, situated in an arbitrary water depth and subjected to normal linear waves. Numerical examples presented by this method are compared with those obtained by the Boundary Integral Equation Method, presented by Williams et al. Comparisons show an excellent agreement over a wide range of parameters for the wave reflection and the dynamic displacement. Numerical results are presented, mainly to show the effect of the breakwater rigidity and the method of fixation on the wave reflection and the structural displacement over a wide range of wave frequencies.     

RANS modelling applied to random wave interaction with submerged permeable structures

This paper is the second part of the work presented by Garcia et al. [Garcia, N., Lara, J.L., Losada, I.J., 2004. 2-D numerical analysis of near-field flow at low-crested breakwaters. Coastal Engineering 51 (10), 991–1020]. In the mentioned paper, flow conditions at low-crested rubble-mound breakwaters under regular wave attack were examined, using a combination of measured data of free surface, bottom pressure and fluid velocities from small-scale experiments and numerical results provided by a VOF-type model (COBRAS) based on the Reynolds-Averaged Navier–Stokes (RANS) equations. This paper demonstrates the capability of the COBRAS model to reproduce irregular wave interaction with submerged permeable breakwaters. Data provided by the numerical model are compared to experimental data of laboratory tests, and the main processes of wave–structure interaction are examined using both experimental and numerical results. The numerical model validation is carried out in two steps. First, the procedure of irregular wave generation is verified to work properly, comparing experimental and numerical data of different cases of irregular wave trains propagating over a flat bottom. Next, the validation of the numerical model for wave interaction with submerged rubble-mound breakwaters is performed through the simulation of small-scale laboratory tests on different incident wave spectra. Results show that the numerical model adequately reproduces the main aspects of the interaction of random waves with submerged porous breakwaters, especially the spectral energy decay at the structure and the spectrum broadening past the structure. The simulations give good results in terms of height envelopes, mean level, spectral shape, root-mean-square height for both free surface displacement and dynamic pressure inside the breakwater. Moreover, large-scale simulations have been conducted, on both regular and irregular incident wave conditions. The overall pattern of the wave interaction with a large-scale submerged breakwater is adequately reproduced by the numerical model. The processes of wave reflection, shoaling and breaking are correctly captured. The good results achieved at a near prototype scale are promising regarding the use of the numerical model for design purposes.     

2D Wave setup behind submerged breakwaters

In addition to reducing the incoming wave energy, submerged breakwaters also cause a setup of the sea level in the protected area, which is relevant to the whole shadow zone circulation, including alongshore currents and seaward flows through the gaps. This study examines such a leading hydraulic parameter under the simplified hypothesis of 2D motion and presents a prediction model that has been validated by a wide ensemble of experimental data. Starting from an approach originally proposed by Dalrymple and Dean [(1971). Piling-up behind low and submerged permeable breakwaters. Discussion note on Diskin et al. (1970). Journal of Waterways and Harbors Division WW2, 423–427], the model splits the rise of the mean water level into two contributions: one is due to the momentum flux release forced by wave breaking on the structure, and the other is associated with the mass transport process. For the first time, the case of random wave trains has been explicitly considered.     

Numerical prediction of performance of submerged breakwaters

The results of a numerical model study on the transmission characteristics of a submerged breakwater are presented. Study aimed to determine the effect of depth of submergence, crest width, initial wave conditions and material properties on the transmission characteristics of the submerged breakwater. The results highlight the optimum crest width of the breakwater and optimum clear spacing between two breakwaters. A submerged permeable breakwater with d_s/d=0.5, p=0.3 and f=1.0, reduces the transmission coefficient by about 10% than the impermeable breakwater. The results indicates an optimum width ratio of B/d=0.75 for achieving minimum transmission. By restricting the effective width ratio of the series of breakwaters to 0.75, studies were conducted to determine the effect of clear spacing between breakwaters on transmission coefficient, suggesting an optimum clear spacing of w/b=2.00 to obtain K_t below 0.6.     

Performance of hemi-cylindrical and rectangular submerged breakwaters

A parametric experimental study is conducted to compare the reflection and transmission characteristics of submerged hemi-cylindrical and rectangular rigid and water-filled flexible breakwater models. The results show that, for the rigid breakwaters, rectangular models are more effective than hemi-cylindrical ones in terms of reduction of transmitted waves. As for the flexible breakwaters, the hemi-cylindrical models may give better wave reflection than rectangular ones. However, the energy loss induced by the rectangular breakwaters is much larger and more significant to result in an overall better efficiency in terms of reduction in wave transmission. The effects of internal pressure show that the lowest pressurized flexible models considered in this work are the most effective in the reduction of the transmitted wave height. Higher wave reflection, lower wave transmission and higher energy loss are obtained consistently at the lower submergence depth ratio.     

Prediction of scour depth at breakwaters due to non-breaking waves using machine learning approaches

Coastal structures may cease to function properly due to seabed scouring. Hence, prediction of the maximum scour depth is of great importance for the protection of these structures. Since scour is the result of a complicated interaction between structure, sediment, and incoming waves, empirical equations are not as accurate as machine learning schemes, which are being widely employed for the coastal engineering modeling. In this paper, which can be regarded as an extension of Pourzangbar et al. (2016), two soft computing methods, a support vector regression (SVR), and a model tree algorithm (M5′), have been implemented to predict the maximum scour depth due to non-breaking waves. The models predict the relative scour depth (S_max/H₀) on the basis of the following variables: relative water depth at the toe of the breakwater (h_toe/L₀), Shields parameter (θ), non-breaking wave steepness (H₀/L₀), and reflection coefficient (Cr). 95 laboratory data points, extracted from dedicated experimental studies, have been used for developing the models, whose performances have been assessed on the basis of statistical parameters. The results suggest that all of the developed models predict the maximum scour depth with high precision, the M5′ model performed marginally better than the SVR model and also allowed to define a set of transparent and physically sound relationships. Such relationships, which are in good agreement with the existing empirical findings, show that the relative scour depth is mainly affected by wave reflection.     

淹没矩形防波堤透反射系数特性研究

采用解析方法研究了斜向入射波作用下淹没矩形防波堤的透反射系数特性.首先利用特征函数展开法导出了绕射势函数的分析解和透反射系数的计算公式,然后利用边界元方法验证了解析解,在此基础上利用解析解分析了若干工况下的防波堤透反射特性.计算结果表明,淹没矩形防波堤截面的宽度、高度和相对位置以及入射角的改变都不同程度影响反射系数和透射系数.在中等深度条件下,对于一定频率的波浪,位置和尺寸适当的淹没矩形堤可以反射大部分斜向入射波.研究结果对设计淹没的矩形防波堤具有重要的参考价值.     

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.     

Interaction of non-breaking regular waves with a periodic array of artificial porous bars

A computational model is developed to investigate the wave damping characteristics of a periodic array of porous bars. The transmission and reflection coefficients as well as the wave energy dissipation are evaluated relating to the physical properties and geometric factors of bars. It is shown that the porosity, number, width and height of bars all play important roles in the wave damping characteristics, compared to other factors such as the intrinsic permeability. It is observed that like impermeable bars, permeable bars display Bragg phenomenon. However, Bragg reflection produced by permeable bars is smaller than that by impermeable bars. Permeable bars reflect smaller waves, transmit smaller waves and dissipate more wave energy. It is indicated that if the porosity increases, both the reflection and transmission coefficients decrease and more wave energy is dissipated. Further, it is found that the porosity controls the magnitude, but not the oscillation frequency of the reflection coefficient, which depends only on the number of bars.     

Wave modelling in the vicinity of submerged breakwaters

This paper describes a simple method for modelling wave breaking over submerged structures, with the view of using such modelling approach in a coastal area morphodynamic modelling system.A dominant mechanism for dissipating wave energy over a submerged breakwater is depth-limited wave breaking. Available models for energy dissipation due to wave breaking are developed for beaches (gentle slopes) and require further modifications to model wave breaking over submerged breakwaters.In this paper, wave breaking is split into two parts, namely: 1) depth-limited breaking modelled using Battjes and Janssen's (1978) theory [Battjes, J.A. and Jannsen, J.P.F.M. (1978). Energy loss and setup due to breaking of random waves. Proceedings of the 16th Int. Conf. Coast. Eng., Hamburg, Germany, pp. 569-587.] and 2) steepness limited breaking modelled using an integrated form of the Hasselmann's whitecapping dissipation term, commonly used in fully spectral wind–wave models. The parameter γ₂, governing the maximum wave height at incipient breaking (H_max = γ₂d) is used as calibration factor to tune numerical model results to selected laboratory measurements. It is found that γ₂ varies mainly with the relative submergence depth (ratio of submergence depth at breakwater crest to significant wave height), and a simple relationship is proposed. It is shown that the transmission coefficients obtained using this approach compare favourably with those calculated using published empirical expressions.     

Multidirectional wave transformation around detached breakwaters

The performance of the new wave diffraction feature of the shallow-water spectral model SWAN, particularly its ability to predict the multidirectional wave transformation around shore-parallel emerged breakwaters is examined using laboratory and field data. Comparison between model predictions and field measurements of directional spectra was used to identify the importance of various wave transformation processes in the evolution of the directional wave field. First, the model was evaluated against laboratory measurements of diffracted multidirectional waves around a breakwater shoulder. Excellent agreement between the model predictions and measurements was found for broad frequency and directional spectra. The performance of the model worsened with decreasing frequency and directional spread. Next, the performance of the model with regard to diffraction–refraction was assessed for directional wave spectra around detached breakwaters. Seven different field cases were considered: three wind–sea spectra with broad frequency and directional distributions, each coming from a different direction; two swell–sea bimodal spectra; and two swell spectra with narrow frequency and directional distributions. The new diffraction functionality in SWAN improved the prediction of wave heights around shore-parallel breakwaters. Processes such as beach reflection and wave transmission through breakwaters seem to have a significant role on transformation of swell waves behind the breakwaters. Bottom friction and wave–current interactions were less important, while the difference in frequency and directional distribution might be associated with seiching.