Wave interaction with a perforated wall breakwater with a submerged horizontal porous plate

This study examines the hydrodynamic performance of a new perforated-wall breakwater. The breakwater consists of a perforated front wall, a solid back wall and a submerged horizontal porous plate installed between them. The horizontal porous plate enhances the stability and wave-absorbing capacity of the structure. An analytical solution based on linear potential theory is developed for the interaction of water waves with the new proposed breakwater. According to the division of the structure, the whole fluid domain is divided into three sub-domains, and the velocity potential in each domain is obtained using the matched eigenfunction method. Then the reflection coefficient and the wave forces and moments on the perforated front wall and the submerged horizontal porous plate are calculated. The numerical results obtained for limiting cases are exactly the same as previous predictions for a perforated-wall breakwater with a submerged horizontal solid plate [Yip, T.L., Chwang, A.T., 2000. Perforated wall breakwater with internal horiontal plate. Journal of Engineering Mechanics ASCE 126 (5), 533–538] and a vertical wall with a submerged horizontal porous plate [Wu, J.H., Wan, Z.P., Fang, Y., 1998. Wave reflection by a vertical wall with a horizontal submerged porous plate. Ocean Engineering 25 (9), 767–779]. Numerical results show that with suitable geometric porosity of the front wall and horizontal plate, the reflection coefficient will be always rather small if the relative wave absorbing chamber width (distance between the front and back walls versus incident wavelength) exceeds a certain small value. In addition, the wave force and moment on the horizontal plate decrease significantly with the increase of the plate porosity.     

A highly wave dissipation offshore breakwater

The aim of this paper is to develop an offshore breakwater, for which coefficients of both the wave reflection and transmission have low values. The breakwater is suggested to compose of n layers of porous materials with different porosities. A complex eigen function method is used in the theoretical analysis. Continuities of both mass flux and fluid pressure are assumed at interfaces between every two adjoining porous materials and at the interface between end materials and water region. Following a series of mathematical processes, the coefficients of the wave transmission and reflection along with the wave energy loss are calculated. The porosity of materials is varied in computations; and results are compared among structures composing of different layers of porous materials. A single layer offshore breakwater is shown to reduce simultaneously the coefficients of transmission and reflection only when the structure is very wide in the direction of wave propagation, and the structure material has a high porosity. A multilayer breakwater, however, can function well in reducing both coefficients at a much narrower width; structure having more layers can be more effective at narrower width. Finally, several experiments are conducted; theoretical computations and experimental results agree well.     

Hydrodynamic characteristics of a single-row pile breakwater

The present paper extends the impedance analytical method to the study of the interaction of regular plane waves with a row of rectangular piles. The dissipative energy is estimated from the flow resistance for the row of piles. Formulas of wave reflection and transmission coefficients and the wave force for the row of piles are derived. Predictions obtained using the present model agree with experimental data in the literature.     

Scattering of water wave by a submerged horizontal plate and a submerged permeable breakwater

Based on a two-dimensional linear water wave theory, this study develops the boundary element method (BEM) to examine normally incident wave scattering by a fixed, submerged, horizontal, impermeable plate and a submerged permeable breakwater in water of finite depth. Numerical results for the transmission coefficients are also presented. In addition, the numerical technique's accuracy is demonstrated by comparing the numerical results with previously published numerical and experimental ones. According to that comparison, the transmission coefficient relies not only on the submergence of the horizontal impermeable plate and the height of the permeable breakwater, but also on the distance between horizontal plate and permeable breakwater. Results presented herein confirm that the transmission coefficient is minimum for the distance approximately equal to four times the water depth.     

Wave damping characteristics of vertically stratified porous structures under oblique wave action

The characteristics of wave damping for the vertically stratified porous breakwaters are investigated under oblique wave action. It is found that for common angles of incidence, the wave damping efficiency of a vertically stratified porous structure behaves very similar to a simple structure. The reflection coefficient decreases with increasing angle of incidence while the transmission coefficient only slightly increases as the angle of incidence increases. It is shown that the wave energy loss is in direct proportional to the structure thickness and its porosity regardless of the angle of incidence. Considering small transmission coefficient as a basic requirement and if a moderate reflection coefficient is accepted, a structure thickness of b/h=1 is proposed. In this situation, since the structure does not have a very large thickness, adopting a vertically stratified structure is not an effective way to improve its wave damping efficiency.     

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 motion over a submerged breakwater with an upper horizontal porous plate and a lower horizontal solid plate

This study examines the hydrodynamic performance of a modified two-layer horizontal-plate breakwater. The breakwater consists of an upper submerged horizontal porous plate and a lower submerged horizontal solid plate. By means of the matched eigenfunction expansion method, a linear analytical solution is developed for the interaction of water waves with the structure. Then the reflection coefficient, the transmission coefficient, the energy-loss coefficient and the wave forces acting on the plates are calculated. The numerical results obtained for limiting cases are exactly the same as previous predictions for a single submerged horizontal solid plate and a single submerged horizontal porous plate. Numerical results show that with a suitable geometrical porosity of the upper plate, the uplift wave forces on both plates can be controlled at a low level. Numerical results also show that the transmission coefficient will be always small if the dimensionless plate length (plate length versus incident wavelength) exceeds a certain moderate value. This is rather significant for practical engineering, as the incident wavelength varies over a wide range in practice. Moreover, it is found that the hydrodynamic performance of the present structure may be further enhanced if the lower plate is also perforated.     

Hydrodynamic performance of a dual cylindrical caisson breakwater

The hydrodynamic performance of a dual cylindrical caisson breakwater (DCBW) formed by a row of caissons each of which consisting of a porous outer cylinder circumscribing an impermeable inner cylinder has been theoretically investigated. The theoretical formulation is based on the eigenfunction expansion method proposed by Spring and Monkmeyer (1974) which was further modified by Linton and Evans [Linton, C.M., Evans, D.V., 1990. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics 215, 549–569] for an array of impermeable cylinders. The present formulation is an extension of the work of Wang and Ren [Wang, K.H., Ren, X., 1994. Wave interaction with a concentric porous cylinder system. Ocean Engineering 21(4), 343–360], wherein; the interaction of linear waves with a single concentric porous cylinder system was studied. In the present study, the formulation has been extended to the case of a group of porous dual cylinder system. Parametric studies are carried out to study the influence of porosity (G₀) on the outer caisson, width of the doughnut chamber (a/b) and the angle of wave incidence on the variation in the hydrodynamic loading, wave run-up, free-surface elevation in its vicinity as well as the transmission on its lee-side. The importance of the presence of the inner cylinder in achieving the required hydrodynamic performance in terms of either protection or providing tranquility on its lee side keeping higher stability for the breakwater system is highlighted.     

Wave interaction with partially immersed twin vertical barriers

The wave transmission, reflection and energy dissipation characteristics of partially immersed twin vertical barriers and the water surface fluctuations in between the barriers were studied using physical models. Regular and random waves of wide ranges of wave heights and periods, nine different immersions of the barriers and a constant water depth were used for the investigation. The coefficient of transmission, and the coefficient of reflection were obtained from the measurements and coefficient of energy dissipation is estimated using the law of conservation of energy. It is found in general that the twin barrier is better in reducing the coefficient of transmission and increasing the coefficient of dissipation in random waves than with the regular waves, especially for increasing incident wave energy levels. The coefficient of transmission reduces significantly with the increased relative water depth. Increase of relative water depth from 0.09 to 0.45 resulted in reduction of transmission coefficient from 0.65 to 0.05. It is possible to achieve a transmission coefficient less than 0.20 for six immersion configurations with relative depth of immersions of the barrier less than (0.28, 0.43), especially in the region closer to deep water conditions. Coefficient of dissipation ranging from 0.65 to 0.85 can be obtained due to random wave interaction.     

Wave interaction with twin plate wave barrier

The wave transmission and reflection characteristics and wave induced pressures on single surface plate and twin plate barriers were investigated experimentally for a wide range of wave heights and periods in regular and random waves. Seven different spacing between the plates were tested. It is found in general, hydrodynamically the twin plate is better than the single surface plate to reduce the wave transmission and increase the wave reflection. It is found that the transmission coefficient of twin plate reduced from 0.8 to 0.3 when the relative plate width is increased from 0.18 to 0.84. Transmission coefficient of twin plate barrier shows oscillating behavior, when relative plate width is increased due to blocking and pumping effect. The reflection coefficient increased from 0.25 to 0.65, when the relative width of the plate is increased from 0.18 to 0.84. The increase in spacing between the plates was also found to increase the reflection coefficient. The transmission coefficient, K_t for 98% probability of non-exceedence was found to be minimum and is about 0.60 when the relative spacing between the plate is about 0.12, compared to K_t=0.76 for single surface plate. The reflection coefficient for 98% probability of non-exceedence was found to exceed 0.66 for single surface plate, whereas it is 0.73 for twin plate with relative spacing of about 0.40. From the investigation with wide range of input parameters, it is found that the twin plate barrier needs to be designed for highest 98% pressure ratio of 2.0, which is equal to the static pressure induced by the design incident wave height.     

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.     

The theoretical study on diagonal wave interaction with perforated-wall breakwater with rock fill

The interaction of diagonal waves with perforated-wall breakwater partially filled with rock fill is studied using the linear potential theory. By means of the matched eigenfunction expansion method, an analytical method is presented to calculate the reflection coefficient and the wave force coefficient of the breakwater. The calculated results of the reflection coefficient for limiting cases are the same to the existing results. The main effect factors of the reflection coefficient and the wave force coefficient are analyzed by numerical examples. With the increasing of thickness of rock fill, the wave force coefficient on the perforated wall generally decreases, while the reflection coefficient increases. With the increasing of the incident angle of the wave, the reflection coefficient of the breakwater first decreases, reaches its minimum, and then increases monotonously.     

Wave motion over a breakwater system of a horizontal plate and a vertical porous wall

A two-dimensional analytical solution is presented to study the reflection and transmission of linear water waves propagating past a submerged horizontal plate and through a vertical porous wall. The velocity potential in each fluid domain is formulated using three sets of orthogonal eigenfunctions and the unknown coefficients are determined from the matching conditions. Wave elevations and hydrodynamic forces acting on the porous wall are computed. Reflection and transmission coefficients are presented to examine the performance of the breakwater system. The present analytical solutions are found in fairly good agreement with the available laboratory data. The results indicate that the plate length, the porous-effect, the gap between plate and porous wall, and the submerged depth of the plate all show a significant influence on the reflected and transmitted wave fields. It is also interesting to note that the submerged plate plays an important role in reducing the transmitted wave height, especially for long incident waves.     

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.     

波浪与起伏水平板防波堤相互作用数值模拟

利用自主研发的基于紧致插值曲线CIP(constrained interpolation profile)方法的数学模型,开展规则波与起伏水平板防波堤相互作用的数值模拟研究。模型在笛卡尔直角坐标下建立,以CIP方法为流场基本求解器,分步求解Navier-Stokes方程,利用高精度的流体体积类型的THINC/SW (tangent of hyperbola for interface capturing with slope weighting)方法重构自由液面,采用浸入边界IBM(immersed boundary method)方法处理波浪与起伏板防波堤的耦合作用问题,通过动量源项造波方法模拟波浪的产生。重点关注波浪的浅水变形和板两端涡旋脱落的非线性现象,分析不同潜深、波要素下的板周围流场分布、板的运动响应和波浪的反透射系数。结果表明:起伏水平板主要通过能量反射、板上浅水变形和板两端的涡脱落消能,能有效减小板后波高,具有作为防波堤的可行性。     

Application of smoothed particle hydrodynamics for modeling the wave-moored floating breakwater interaction

The application of a Smoothed Particle Hydrodynamics (SPH) model to simulate the nonlinear interaction between waves and a moored floating breakwater is presented. The main aim is to predict and validate the response of the moored floating structure under the action of periodic waves. The Euler equations together with an artificial viscosity are used as the governing equations to describe the flow field. The motion of the moored floating body is described using the Newton’s second law of motion. The interactions between the waves and structures are modeled by setting a series of SPH particles on the boundary of the structure. The hydrodynamic forces acting on the floating body are evaluated by summing up the interacting forces on the boundary particles from the neighboring fluid particles. The water surface elevations, the movements of the floating body and the moored forces are all calculated and compared with the available experimental data. Good agreements are obtained for the dynamic response and hydrodynamic performance of the floating body. The numerical results of different immersion depths of the floating body are compared with that of the corresponding fixed body. The effects of the relative length and the density of the structure on the performance of the floating body are analyzed.     

Wave reflection from vertical breakwater with porous structure

This paper presents numerical solutions for the wave reflection from submerged porous structures in front of the impermeable vertical breakwater. A new time-dependent mild-slope equation involves the parameters of the porous medium including the porosity, the friction factor and the inertia coefficient, etc. is derived for solving the boundary value problem. A comprehensive comparison between the present model and the existing analytical solution for the case of simple rectangular geometries of the submerged structure is performed first. Then, more complicated cases such as the inclined and trapezoidal submerged porous structures in front of the vertical breakwater with sloping bottom are considered. This study also examines the effects of the permeable properties and the geometric configurations of the porous structure to the wave reflection. It is found that the submerged porous structure with trapezoidal shape has more efficiency to reduce the wave reflection than that of triangular shape. The numerical results show that the minimum wave reflection is occurred when the breakwater is located at the intermediate water depth.     

V形防波堤与圆弧型防波堤之浅水波绕射作用的比较

应用椭圆余弦波的绕射理论,推导了V形防波堤的浅水波浪绕射解析解,从而对现有的Airy微幅波理论进行了有效拓展。据此理论对V形防波堤的浅水波绕射作用进行了解析计算,并与几何形状相近的圆弧型防波堤结果加以了对比。结果表明：椭圆余弦波理论计算的V形防波堤最大波浪力和最大绕射波面明显大于微幅波理论的对应值。本方法适用于张角180°的有限长直立薄壁防波堤的浅水波绕射作用计算,从而将无限长直立薄壁堤的反射波理论加以有效拓展。张角同为120°的V形堤与圆弧堤的堤后防浪效果相近,而180°圆弧堤的堤后防浪效果优于张角90°的V形堤。     

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.     

弧形防波堤波浪力试验研究

在圆筒形防波堤和V形防波堤的基础上,结合离岸堤后形成V形和半圆形连续出现的韵律海岸的地貌平面形态特点,提出一种前墙为连续的半圆筒形防波堤形式。通过在波浪水槽内进行规则波物理模型试验,探究这一新型防波堤的波压力分布规律及波高、周期、水深等因素对波压力的影响。将试验结果与海港水文公式和合田良实公式计算的理论值对比分析,给出了以合田良实公式的折减系数来拟合新型弧形防波堤波浪总水平力的计算公式。结果表明:新型弧形防波堤上的波压力随波高、周期的增大而增大,其水平波浪总力比同等尺度直墙少10%左右。