Analytical Research on Wave Diffraction on Arc-Shaped Bottom-Mounted Perforated Breakwaters

An analytical method is developed to study wave diffraction on arc-shaped and bottom-mounted perforated breakwaters.The breakwater is assumed to be rigid,thin,vertical,immovable and located in water of constant depth.The fluid domain is divided into two regions by imaginary interface.The velocity potential in each region is expanded by eigenfunctions.By satisfying the continuity of pressure and normal velocity across the imaginary fluid interface,a set of linear algebraic equations can be obtained to determine the unknown coefficients of eigenfunctions.Numerical results,in the form of contour maps of the relative wave amplitude around the breakwater,are presented for a range of wave and breakwater parameters.Results show that the wave diffraction on the arc-shaped and bottom-mounted perforated breakwater is related to the incident wavelength and the porosity of the breakwater.The porosity of the perforated breakwater may have great effect on the diffracted field.     

多消浪室局部开孔沉箱防波堤反射特性的迭代解析研究

基于势流理论,对多消浪室局部开孔沉箱防波堤的反射特性进行解析研究。研究中采用开孔墙处的二次压力损失边界条件,可以直接考虑波高对于开孔墙处能量损失的影响。利用匹配特征函数展开法和迭代方法得到当前问题的解析解。收敛性验证表明,迭代计算和级数解均具有良好的收敛性。该解析解的计算结果与分区边界元的数值计算结果一致,并且与已有的试验结果符合良好。通过算例分析,研究开孔沉箱防波堤反射系数的主要影响因素。结果表明：与单消浪室开孔沉箱防波堤相比,多消浪室开孔沉箱防波堤可以在更宽的波浪频率范围内保持低反射;增大开孔墙的开孔率,有利于降低多消浪室开孔沉箱防波堤的反射系数;当开孔墙的开孔率沿着入射波方向依次递减时,多消浪室开孔沉箱防波堤的反射系数较小。本文所建立的解析模型简单可靠,可用于工程初步设计中分析开孔沉箱防波堤的水动力性能。     

Reflection of irregular waves from perforated-wall caisson breakwaters

An analytical model has been developed that predicts the reflection of irregular waves normally incident upon a perforated-wall caisson breakwater. To examine the predictability of the developed model, laboratory experiments have been conducted for the reflection of irregular waves of various significant wave heights and periods impinging upon breakwaters having various wave chamber widths. For frequency-averaged reflection coefficients, though the overall agreement is fairly good between measurement and calculation, the model somewhat over-predicts the reflection coefficients at larger values, and under-predicts at smaller values. The model also underestimates the energy loss coefficients as wave reflection becomes larger. These differences occur because the model neglects the evanescent waves near the breakwater, which increase the energy loss at the perforated wall. The frequency-averaged reflection coefficient shows a minimum when the wave chamber width is approximately 0.2 times the significant wavelength, and it decreases with increasing wave steepness. Finally, it is shown that the reflection of irregular waves from a perforated-wall caisson breakwater depends on the wave frequency, so that the reflected wave spectrum shows a frequency dependent oscillatory behavior.     

Impedance analysis of hydrodynamic behaviors for a perforated-wall caisson breakwater under regular wave orthogonal attack

An impedance analytical method (IAM) is developed to study the interaction between regular waves and a perforated-wall caisson breakwater that consists of a front perforated-wall and a chamber with a rigid impermeable back wall. The boundary conditions at the perforated-wall are established in terms of the flow resistances of the fluid passing through the holes. As a result, explicit algebraic expressions are obtained for reflection coefficients and wave loads. In the formulae, all of the parameters are known a priori. The predicted reflection coefficients and the wave forces are compared with the experimental data of other authors.     

Wave diffraction on arc-shaped floating perforated breakwaters

An analytical method is developed to study the sheltering effects on arc-shaped floating perforated breakwaters. In the process of analysis, the floating breakwater is assumed to be rigid, thin, vertical, and immovable and located in water with constant depth. The fluid domain is divided into two regions by imaginary interface. The velocity potential in each region is expanded by eigenfunction in the context of linear theory. By satisfying continuity of pressure and normal velocity across the imaginary fluid interface, a set of linear algebraic equations can be obtained to determine the unknown coefficients for eigenfunction expansions. The accuracy of the present model was verified by a comparison with existing results for the case of arc-shaped floating breakwater. Numerical results, in the form of contour maps of the non-dimensional wave amplitude around the breakwater and diffracted wave amplitude at typical sections, are presented for a range of wave and breakwater parameters. Results show that the sheltering effects on the arc-shaped floating perforated breakwater are closely related to the incident wavelength, the draft and the porosity of the breakwater.     

Hydraulic performance and wave loadings of perforated/slotted coastal structures: A review

This paper reviews recent progress in the study of perforated/slotted breakwaters, with an emphasis on two main groups of such breakwaters: (1) perforated/slotted breakwaters with impermeable back walls, and (2) perforated/slotted breakwaters without a back-wall. The methods commonly used to simulate the interactions between such structures and various linear/nonlinear waves are summarized. The transmission and reflection characteristics of perforated/slotted breakwaters in these two groups are reviewed extensively. Several methods for calculating wave forces on perforated caissons are also reviewed. Some recent works published in Chinese journals, which are generally not well-known to non-Chinese researchers, are reviewed with a hope that these works can be beneficial to other researchers working in this area.     

Floating pontoon breakwaters

The hydrodynamic properties of a pair of long floating pontoon breakwaters of rectangular section are investigated theoretically. The structures are partially restrained by linear symmetric moorings fore and aft. The fluid motion is idealized as linearized, two-dimensional potential flow. The breakwater motions are assumed to be two-dimensional, in surge, heave and pitch. The solution for the fluid motion is obtained by the boundary integral equation method using an appropriate Green's function. Numerical results are presented that illustrate the effects of the various wave and structural parameters on the efficiency of the breakwaters as barriers to wave action. It is found that the wave reflection properties of the structures depend strongly on their width, draft and spacing and the mooring line stiffnesses, while their excess buoyancy is of lesser importance.     

Analytical and Experimental Studies on Hydrodynamic Performance of Semi-Immersed Jarlan-Type Perforated Breakwaters

The present study proposes a new semi-immersed Jarlan-type perforated breakwater including a perforated front wall, a solid rear wall, and a horizontal perforated plate connecting the lower tips of the two walls. An analytical solution is developed to estimate the hydrodynamic performance of the new breakwater. The analytical solution is confirmed by solutions for special cases, an independently developed multi-domain boundary element method solution and experimental data. Numerical examples based on the analytical solution indicate that compared with previous semi-immersed breakwaters, the new breakwater may have better wave-absorbing performance and smaller wave forces. Some useful results are presented for practical designs of semi-immersed Jarlan-type perforated breakwaters.     

Investigation of Π-type breakwaters performance under regular and irregular waves

In this paper, performance of solid and perforated Π-type breakwaters was investigated experimentally. Both regular and irregular waves were used during testing. Four depths of immersions were selected for each breakwater and wave type. Different wave groups were generated over these breakwaters, and the transmission, reflection and energy-dissipation characteristics were determined. The results of the experimental study were evaluated and some empirical expressions based on the results were suggested to define the transmission, reflection and energy-dissipation coefficients for different immersion depths of solid and perforated breakwaters under regular and irregular waves. Moreover, performance of solid and perforated Π-type breakwaters were compared with that of solid and perforated U-type breakwaters investigated by Günaydın and Kabdaşlı [2006. Performance of solid and perforated U-type breakwaters under regular and irregular waves. Ocean Engineering 31, 1377–1405]. These comparisons showed that the most reasonable model and wave type are selected to determine requiring performance parameters.     

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。     

Numerical Simulation of Wave Interaction with Perforated Caisson Breakwaters

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深水工况下弧面胸墙沉箱堤的反射形态分析

为推广应用新型弧面胸墙沉箱堤,结合模型试验和数值模拟对比分析了深水工况下弧面胸墙沉箱堤和削角胸墙沉箱堤的反射形态。波面和波压的数值结果与试验数据吻合良好,验证了数值方法的有效性。反射系数表明,入射波浪在与弧面胸墙沉箱堤相互作用过程中的能量损耗最小,其反射强于削角胸墙沉箱堤。波面和流速包络图显示,两种堤型均在堤前形成了部分立波系统,腹点和节点以四分之一波长的距离增量交替出现,胸墙和直立部分产生的反射波存在相位差,导致初始腹点的位置向海侧偏移。弧面胸墙沉箱堤前叠合波的相位差影响最小,腹点包络高度最大,节点包络高度最小,反射效应最明显。两种堤型前中下层水流的周期平均速度均较小且对称,表明底床泥沙不会产生趋势性输移,但迎浪基床上方的环流系统可能引起局部冲刷。相对而言,弧面胸墙沉箱堤前的环流强度最弱,更有利于冲刷防护。     

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.     

Wave interactions with multiple-row curtainwall-pile breakwaters

In this study, a mathematical model has been developed that can compute various hydrodynamic characteristics of a multiple-row curtainwall-pile breakwater. To examine the validity of the developed model, laboratory experiments have been conducted for double- and triple-row breakwaters with various combinations of drafts of curtain walls, porosities between piles, and distances between rows. Comparisons between measurement and prediction show that the mathematical model adequately reproduces most of the important features of the experimental results. As a whole, the transmission coefficient decreases with an increase in relative water depth, whereas the reflection coefficient, normalized run-up and force exhibit an opposite trend in their variations. With fixed values of the draft of the curtain wall and the porosity of lower perforated part of the first row of a double-row breakwater, as these values of the second row increase and decrease, respectively, the transmission coefficient decreases, as expected. On the other hand, their effects on wave reflection, run-up, and wave force change with the relative depth. As for the distance between the rows, the transmission coefficient becomes a maximum when it is about one half of the wave length, suggesting that this condition should be avoided to achieve the advantage of the breakwater in reducing wave transmission. It is shown that for prototype breakwaters, on an average, the transmission coefficient would be smaller than 0.3 for wave periods less than 6.0 s, and it would be about 0.45 even for the wave period of 9.0 s, although there would be a variation depending on the geometry of the breakwater. It is also shown that wave transmission is significantly reduced by multiple-row breakwaters compared with a single-row breakwater, while the difference between double-row and triple-row breakwaters is marginal. Finally, engineering monograms are provided for double-row breakwaters to be used in practical engineering applications of the breakwaters.     

Hydrodynamic efficiency of partially immersed caissons supported on piles

The efficiency of the breakwater, which consists of caissons supported on two or three rows of piles, was studied using physical models. The efficiency of the breakwater is presented as a function of the transmission, reflection and the wave energy dissipation coefficients. Regular waves with wide ranges of wave heights and periods and constant water depth were used. Different characteristics of the caisson structure and the supporting pile system were also tested. It was found that, the transmission coefficient (k_t) decreases with increasing the relative breakwater draft D/L, increasing the relative breakwater width B/h, and decreasing the piles gap-diameter ratio G/d. It is possible to achieve k_t values less than 0.25 when D/L≥0.1. The reflection coefficient takes the opposite trend especially when D/L≤0.15. The proposed breakwater dissipates about 10-25% of the incident wave energy. Also, simple empirical equations are developed for estimating the wave transmission and reflection. In addition, the proposed breakwater model is efficient compared with other floating breakwaters.     

The reffection of regular and irregular waves by a partially perforated caisson breakwater on a step bed

This study examines the reffection of regular and irregular waves from a partially perforated caisson breakwater located on a step bed. The step bed is treated as an idealized rubble mound foundation. Based on the linear potential theory, an analytical solution is developed to calculate the reffection coefficient of the structure subjected to regular waves. The matched eigenfunction expansion method is used for the solution. The regular wave method is also extended to irregular waves using a linear transfer...     

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.     

Vibrating-Rocking Motion of Caisson Breakwater Under Breaking Wave Impact

The possible motions of a caisson breakwater under dynamic load excitation include vibrating, vibrating-sliding and vibrating-rocking motions. The models of vibrating motion and vibrating-sliding motion have been proposed in an early paper. In this paper, a model of vibrating-rocking motion of caisson breakwaters under breaking wave impact is presented, which can be used to simulate the histories of vibrating-rocking motion of caisson breakwaters. The effect of rocking motion on the displacement, rotation, sliding force and overturning moment of breakwaters is investigated. In case the overturning moment exceeds the stability moment of a caisson, the caisson may only rock. The caisson overturns only in case the rocking angle exceeds the critical angle. It is shown that the sliding force and overturning moment of breakwaters can be reduced effectively due to the rocking motion. It is proposed that some rocking motion should be allowed in breakwater design.     

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     

Wave interaction with a wave absorbing double curtain-wall breakwater

This study examines the hydrodynamic performance of a wave absorbing double curtain-wall breakwater. The breakwater consists of a seaward perforated wall and a shoreward impermeable wall. Both walls extend from above the seawater to some distance above the seabed. Then the below gap allows the seawater exchange, the sediment transport and the fish passage. By means of the eigenfunction expansion method and a least square approach, a linear analytical solution is developed for the interaction of water waves with the breakwater. Then the reflection coefficient, the transmission coefficient and the wave forces acting on the walls are calculated. The numerical results obtained for limiting cases agree very well with previous predictions for a single partially immersed impermeable wall, the double partially immersed impermeable walls and the bottom-standing Jarlan-type breakwater. The predicted reflection coefficients for the present breakwater also agree reasonable with previous experimental results. Numerical results show that with appropriate structure parameters, the reflection and transmission coefficients of the breakwater may be both below 0.5 at a wide range of the relative water depth. At the same time, the magnitude of wave force acting on each wall is small. This is significant for practical engineering.