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.     

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.     

圆弧板透空式防波堤消波性能试验研究

提出了一种由多层圆弧板组成的新型透空式防波堤结构,并对其在二维规则波浪作用下的消波性能进行了物理模型试验研究。在不同入射波高条件下,对圆弧板和水平板透空结构的消波性能进行了比较分析,探讨了圆弧板间距和层数对圆弧板透空式结构消波性能的影响。研究结果表明,圆弧板透空式结构的消波效果优于水平板式透空结构,在相对宽度为0.2时,可以使透射系数达0.5以下。随着圆弧板间距从0.15 m减小到0.05 m时,消波效果逐步提升,而圆弧板的层数对结构的消波性能也有一定影响。     

Nonlinear time–domain analysis of motion-restrained pneumatic floating breakwater

A pneumatic-type floating breakwater is simulated in the time–domain to evaluate wave blocking and wave energy absorption. For accurate nonlinear time–domain simulation, a fully nonlinear numerical wave tank (NWT) technique has been used. In the present study, the NWT for the pneumatic breakwater is extended to the case of restrained body motion using the mode-decomposition method in the acceleration potential field. In particular, the effect of individual body motion coupled with pneumatic damping in the chamber is investigated for the case in which the breakwater is only allowed to move one degree-of-freedom: for instance, using a heave-only allowable body. The present results are compared with various motion cases as well as a box-shaped breakwater.     

Numerical investigation on the dynamics of a vertical wall defenced by an offshore breakwater

The numerical and experimental investigations on the performance of an offshore-submerged breakwater in reducing the wave forces and wave run-up on vertical wall are presented. A two-dimensional finite-element model is employed to study the hydrodynamic performance of the submerged breakwater under the action of regular and random waves. The numerical prediction has been supported with experimental measurements. The wave forces and wave run-up on the vertical wall were measured for different breakwater configurations. The applicability of linear theoretical model in the prediction of wave forces on the wall by a submerged breakwater has been discussed.     

Wave Forces on Submerged Semi-Circular Breakwater and Similar Structures

—The results of design and experiment of a submerged semi-circular breakwater at the Yangtzeestuary show that the submerged structure will be unsafe when the general empirical wave force formulafor semi-circular breakwater is used in design.Therefore,a new calculation method for the wave forces act-ing on a submerged semi-circular structure is given in this paper,in which the wave force acting on the in-side circumference of semi-circular arch is included,and the phase modification coefficient in the generalempirical formula is adjusted as well.The new wave force calculation method has been verified by the re-sults of seven related physical model tests and adopted in the design of the south esturary jetty of the firststage project of Deep Channel Improvement Project of the Yangtze River Estuary,the total jetty length be-ing 17.5km.     

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.     

Curved and Stepped Breakwater Wall

This paper introduces the main points of design and operation features of a curved combinative breakwater wall which can not only resist storm surge but also roll wave back and which has the functions of seawall, tide protection, anti-wave, land development, traffic and tourism. The new kind of breakwater optimized by wave model test has been utilized in the seawall in the coast regulation project in Zhanjiang City, and good results have been achieved.     

动力输出系统(PTO)对集成波能转换装置式防波堤消波性能及波能捕获率影响研究

针对波浪能转换装置(WEC)研究重点主要集中在能量捕获效率方面,而忽略其附带的消波功能的问题。基于Open FOAM程序,建立垂荡浮子式波浪能发电装置与桩式约束的浮式防波堤的集成系统(OBC-FB)。主要研究WEC中的重要组件动力输出系统(PTO)对集成系统波能捕获效率及消波性能的影响。分析流体黏性影响下线性PTO系统的最优PTO阻尼特性。开发非线性电磁阻尼模型与线性PTO系统性能进行比较。结果显示,考虑黏性影响下线性的最优PTO阻尼系数略大于无黏的理论值;适当增大PTO阻尼系数可以获得更大的波能捕获宽度比(CWR),从而可以保证装置单位特征尺寸的波能转换效率更高,同时可以在更宽波况范围保证消波性能;相较于线性PTO阻尼系统,非线性电磁PTO阻尼系统可以更好地兼顾波能捕获效率和消波性能。因此,在OBC-FB集成系统的优化设计中,PTO阻尼系统是一个重要的优化参数。     

Experimental study on the performance of the multiple-layer breakwater

Based on the idea of disturbing the water motion in the upright direction, a new kind of multiple-layer breakwater is proposed in this article, which mainly consists of several horizontal plates. The breakwater's performance of dissipating waves has been investigated in detail in the regular wave tests. The factors identified with the characteristics of the breakwater are discussed, such as the relative width, the wave steepness and the models geometrical parameters (the width and the gap). The comparison and analysis of the transmission and reflection coefficients with respect to different factors are presented. The model test results indicate that the multiple-layer breakwater has the good characteristic of dissipating waves. Further more, only in a little extent can it reflect the waves. The multiple-layer breakwater proposed in the paper is very significative to promote the open type breakwater to be the permanent wave attenuator in the application.     

Numerical study on the interaction among a nonlinear wave,composite breakwater and sandy seabed

Most previous investigations related to composite breakwaters have focused on the wave forces acting on the structure itself from a hydrodynamic aspect. The foundational aspects of a composite breakwater under wave-induced cyclic loading are also important in studying the stability of a composite breakwater. In this study, numerical simulations were performed to investigate the wave-induced pore water pressure and flow changes inside the rubble mound of the composite breakwater and seabed foundation. The validity and applicability of the numerical model were demonstrated by comparing numerical results with existing experimental data. Moreover, the present model clearly has shown that the instantaneous directions of pore water flow motion inside the seabed induced by surface waves are in good agreement with the general wave-induced pore water flow inside the seabed. The model is further used to discuss the stability of a composite breakwater, i.e., the interaction among nonlinear waves, composite breakwater and seabed. Numerical results suggest that the stability of a composite breakwater is affected by not only downward shear flow generating on the seaward slope face of the rubble mound but, also, a high and dense pore water pressure gradient inside the rubble mound and seabed foundation.     

Hydrodynamic performance of a T-shaped floating breakwater

The comprehensive utilization of floating breakwaters, specially acting as a supporting structure for offshore marine renewable energy explorations, has received more and more attention recently. Based on linear water-wave theory, the hydrodynamic performance of a T-shaped floating breakwater is semi-analytically investigated through the matched eigenfunction expansion method (MEEM). Auxiliary functions, to speed up the convergence and improve the accuracy in the numerical computations, are introduced to represent the singular behavior of fluid field near the lower salient corners of the structure. The effects of the height and installation position of the vertical screen on the reflection and transmission coefficients, dynamic response and wave forces are examined. It is found that the presence of the screen shifts the resonance frequency of RAO for both surge and pitch modes to the low-frequency area, while has no effect on heave mode. The identical added masses, damping and transmission coefficients can be obtained in the cases where the screen holds the same distance away from the longitudinal central axis of the upper box-type structure. Moreover, a relatively small pitch response can be achieved in a wide wave–frequency range, when the breakwater is Γ-shaped.     

Interaction Between Waves and A Comb-Type Breakwater

The characteristics of wave transmission, reflection and energy dissipation of comb-type caisson breakwaters are studied through laboratory physical model tests. Regular and irregular waves, with a wide range of wave heights and periods and a constant water depth, are considered. Different dimensions of each portion of the comb-type caisson breakwater are tested. Empirical formulae for calculating the reduction coefficient k, which is the ratio of horizontal wave force on unit length of the comb-type breakwater to that on unit length of the vertical wall breakwater, and for calculating the reflection coefficient of waves k, are obtained from the measurements. The comb-type caisson breakwater has been found to be very efficient in dissipating incident wave energy and in reducing wave reflection, and has already been used for the construction of an island breakwater in the Dayao Bay of Dalian Port, Liaoning Province, China. Compared with the cost of a common caisson breakwater, about 24. 5% of the investm     

Incompressible SPH flow model for wave interactions with porous media

The paper presents an Incompressible Smoothed Particle Hydrodynamics (ISPH) method to simulate wave interactions with a porous medium. The SPH method is a mesh free particle modeling approach that is capable of tracking the large deformation of free surfaces in an easy and accurate manner. The ISPH method employs a strict incompressible hydrodynamic formulation to solve the fluid pressure and the numerical solution is obtained by using a two-step semi-implicit scheme. The ISPH flow model solves the unsteady 2D Navier–Stokes (NS) equations for the flows outside the porous media and the NS type model equations for the flows inside the porous media. The presence of porous media is considered by including additional friction forces into the equations. The developed ISPH model is first validated by the solitary and regular waves damping over a porous bed and the solitary wave interacting with a submerged porous breakwater. The convergence of the method and the sensitivity of relevant model parameters are discussed. Then the model is applied to the breaking wave interacting with a breakwater covered with a layer of porous materials. The computational results demonstrate that the ISPH flow model could provide a promising simulation tool in coastal hydrodynamic applications.     

Hydrodynamic performance of a pile-supported OWC breakwater: An analytical study

A pile-supported OWC breakwater is a novel marine structure in which an oscillating water column (OWC) is integrated into a pile-supported breakwater, with a dual function: generating carbon-free energy and providing shelter for port activities by limiting wave transmission. In this work we investigate the hydrodynamics of this novel structure by means of an analytical model based on linear wave theory and matched eigenfunction expansion method. A local increase in the back-wall draft is adopted as an effective strategy to enhance wave power extraction and reduce wave transmission. The effects of chamber breadth, wall draft and air chamber volume on the hydrodynamic performance are examined in detail. We find that optimizing power take-off (PTO) damping for maximum power leads to both satisfactory power extraction and wave transmission, whereas optimizing for minimum wave transmission penalizes power extraction excessively; the former is, therefore, preferable. An appropriate large enough air chamber volume can enhance the bandwidth of high extraction efficiency through the air compressibility effect, with minimum repercussions for wave transmission. Meanwhile, the air chamber volume is found to be not large enough for the air compressibility effect to be relevant at engineering scales. Finally, a two-level practical optimization strategy on PTO damping is adopted. We prove that this strategy yields similar wave power extraction and wave transmission as the ideal optimization approach.     

双消浪室局部开孔沉箱防波堤反射特性的理论与试验研究

双消浪室局部开孔沉箱防波堤具有低反射、结构受力小、适宜较大水深和工程造价低等优点。为明确双消浪室局部开孔沉箱水动力特性的主要影响因素,采用理论分析和物理模型试验相结合的方法,对规则波和不规则波作用下双消浪室局部开孔沉箱防波堤的反射特性进行研究。基于势流理论,建立规则波和不规则波对局部开孔沉箱防波堤作用的三维解析解,采用二次压力损失边界条件考虑沉箱开孔墙对波浪运动的影响,利用周期性边界条件考虑防波堤结构沿长度方向的周期性变化。开展相应规则波和不规则波物理模型试验,验证理论模型的合理性。通过算例分析,研究不同波浪要素和结构参数对防波堤反射特性的影响。研究表明:双消浪室局部开孔沉箱相对消浪室宽度取值为0.08~0.20,沉箱前墙开孔率大于后墙开孔率时,防波堤在较大波浪频率范围内消波效果显著;当前后墙的开孔率相等时,防波堤反射系数的最小值随着开孔率增大而减小。     

Moored floating breakwater response to regular and irregular waves

The simple, yet versatile numerical technique particularly suitable for investigating the problem of the wave attenuation by moored floating breakwater was recently developed by the author. In order to verift the theory, nearly full scale model tests were conducted in a large wave tank ($\text{3.6}\text{m wide}\text{× 4.5}\text{m high}\text{× 106}\text{m long}$). Both random waves and monochromatic waves were used to compare the results. A breakwater with a rectangular cross-section and a hydrodynamically shaped «three-cycle cylinderå breakwater were tested. Incident wave spectra were successfully decomposed from the multi-reflected sea spectra. Frequency response functions of transmitted wave, sway, heave and roll motions of the breakwater as well as mooring forces were all experimentally determined and compared with the theory. Generally, excellent agreements between the theory, the random wave tests and the monochromatic wave tests were obtained for the hydrodynamically shaped breakwater. Except near the modal frequencies of body motion generally good agreement between theory and experiment was obtained for the rectangular breakwater. Near the modal frequencies, the body motion was damped by the flow separation at the sharp corners of the rectangular breakwater. Generation of higher harmonics in wave, body motion and mooring forces was observed and measured, but was generally small. The slow drift oscillation and its effects on the performance of the spring moored breakwaters were also small. From the comaprisons of the small scale test and the large scale tests, it was found that the scale effects were negligibly small on the performance of the spring-moored breakwaters.     

Computation of wave transmission over a shore protecting submerged breakwater

Among the offshore breakwaters which are increasingly used in shore protection projects, a bevelled block submerged breakwater with 1 on 1.67 seaward slope and a vertical shoreward face is most advantageous, especially from the point of view of optimum wave damping, minimum wave reflection and maximum sand trapping effects. Different computational methods of wave transmission coefficient of this breakwater are examined with laboratory tests. The Goda's method is found to be the simplest and most suitable in the case of the shore protecting submerged breakwater. However, the consideration of wave steepness also, in selecting the constants may yield better results with this method.     

Performance characteristics of a conceptual ring-shaped spar-type VLFS with double-layered perforated-wall breakwater

A ring-shaped spar-type Very Large Floating Structure (VLFS) is proposed as an intermediate base for supporting deepwater resource exploitation far away from the coast line. The proposed VLFS is composed of eight rigidly connected deep-draft spar-type modules and an inside harbor. A double-layered perforated-wall breakwater is vertically attached to the VLFS and pierces through the water surface to attenuate the wave energy in the inside harbor. The hydrodynamic performance characteristics of the ring-shaped VLFS was experimentally evaluated in the present study, focusing on the motion responses, wave elevations, and wave run-ups. The natural periods of the motions in vertical plane were determined to be larger than 40 s, which is much larger than common wave periods. This enhanced the motion performance in vertical plane and afforded favorable habitation and operation condition on the VLFS. A large surge damping was induced by the vertical breakwater, which tended to significantly affect the surge and pitch motions, but had a negligible effect on the heave motion. The component frequencies of the wave elevations in the inside harbor and the wave run-ups were identical with those of the incident waves. The wave attenuation was frequency-dependent and effective for the common wave frequencies, with a smaller loss coefficient observed in higher sea state. The wave attenuation and wave run-ups tended to improve in the absence of the leeward walls.