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.     

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.     

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.     

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.     

Hydrodynamic characteristics of semi-immersed breakwater with an attached porous plate

In the present study, wave interaction with a fixed, partially immersed breakwater of box type with a plate attached (impermeable-permeable) at the front part of the structure is investigated numerically and experimentally. The large scale laboratory experiments on the interaction of regular waves with the special breakwater were conducted in the wave flume of Laboratori d’Enginyeria Marνtima (LIM) at Universitat Politecnica de Catalunya (UPC) in Barcelona. Experimental results are compared with numerical results obtained with the use of the Cornell breaking Wave and Structures (COBRAS) wave model. The effects of an impermeable as well as a permeable plate attached to the bottom of the breakwater on its hydrodynamic characteristics (wave transmission, reflection, dissipation, velocity and turbulence kinetic energy) are investigated. Computed velocities and turbulence kinetic energy in the vicinity of the structure indicate the effects of the breakwater with the attached (impermeable/permeable) plate on the flow pattern and the turbulence structure. The attached impermeable plate at the front part of the breakwater enhances significantly the efficiency of the structure in attenuating the incident waves. The permeable plate reduces the efficiency of the structure since wave energy is transmitted through the porous body of the plate. Based on the hydrodynamic characteristics it is inferred that the breakwater with an impermeable plate attached to its bottom is more efficient. The comparison of horizontal and vertical forces acting on the breakwater for all cases examined reveals that plate porosity influences slightly vertical force and severely horizontal force acting on the structure, reducing maximum values in both cases.     

Wave transmission and reflection characteristics of a rigid surface and submerged horizontal plate

The wave transmission and reflection characteristics of a rigidly fixed surface and submerged horizontal plate were investigated experimentally in detail for a wide range of incident wave steepnesses and for different depths of submerge of the plate in deep water conditions in regular water wave fields. The experiments were conducted at the Ocean Engineering Centre, Indian Institute of Technology, Madras, India, in a wave flume 10 m long, 0.3 m wide and in a constant water depth of 0.8 m. The horizontal plate is 0.22 m thick and 1.2 m in length, covering the enrire width of the flume. From the present investigation, it is found that for a rigid surface plate, the coefficient of transmission is a minimum and the coefficient of reflection is a maximum, but the maximum value of the coefficient of energy loss occurs for plates submerged closer to the still-water level (SWL) and not for the surface plate. It is also found that the value of the coefficient of reflection increases with the increase in the value of the Reddy-Neelamani (RN) number, the ratio of horizontal water particle excursion at the bottom of the plate in its absence to the length of the plate. The coefficient of transmission is found to decrease rapidly with increase in the value of RN number up to 0.1. The wave transmission is only 5% for RN from 0.1 to 0.2. It is also found that for RN number greater than 0.04, the minimum energy dissipation is consistently about 60% of the incident wave energy.     

Transmitted and reflected coefficients for horizontal or vertical plate type breakwater

Surface or submerged horizontal or vertical plate can be considered as a new concept breakwater.This paper investigates the wave-plate interaction of this type of breakwater by use of the boundary element method.The relationships of wave transmitted and reflected among plate thickness,submergence and length are carefully studied by numerical simulation.It is shown that:(1) The transmitted coefficients of submerged horizontal plate or vertical plate will become larger with the increase of plate thickness and reduce rapidly with the decrease of plate submergence.(2) Both surface horizontal and vertical plate are efficient for intermediate and short wave elimination,but vertical plate is more effective.(3) Submerged horizontal plate can act more effectively than submerged vertical plate does.With all wave frequencies,the vertical plate almost has no wave elimination effect.     

波浪作用下方箱-水平板浮式防波堤时域水动力分析

在线性化势流理论范围内求解方箱-水平板浮式防波堤的波浪绕射和辐射问题,从时域角度分析了浮式防波堤的水动力特性.采用格林函数法将速度势定解问题的控制微分方程变换成边界上的积分方程进行数值求解,浮式防波堤的运动方程采用四阶Runge-Kutta方法求解.对不同层数水平板的浮式防波堤的波浪透射系数、运动响应和锚链受力进行了计算分析,结果表明方箱相对宽度对方箱-水平板浮式防波堤的波浪透射作用有重要的影响,透射系数随着方箱相对宽度的增加而减小.对于方箱加二层水平板的浮式防波堤,在本研究的计算条件下,当方箱相对宽度从0.110增加至0.295时,透射系数从0.88减小至0.30.水平板有利于增加浮式防波堤对波浪的衰减作用,但随着水平板层数从0增加至2,这种波浪衰减作用增加的程度趋弱.方箱-水平板的浮式防波堤的运动量小于单一方箱防波堤的运动量.与此对应,方箱-水平板防波堤的锚链受力小于单一方箱防波堤的锚链受力.     

Forces and moment on a horizontal plate due to wave scattering

Wave reflection and transmission from a fixed horizontal plate have been widely studied but theoretical solutions are only available for certain limiting conditions. A general solution for this wave scattering problem is presented using the finite-element method, covering the whole range of relative depth ratio from shallow to deep water limits and submergence depth ratio from the water surface to the bed. Existing long-wave solutions for the surface plate and the submerged plate have been extended to obtain the hydrodynamic forces and overturning moment exerted on the plate. Results from the finite-element program compare well with these solutions. Variations of the reflection coefficient, wave forces and moment, with the plate width to wave length ratio, relative depth ratio and submergence depth ratio are discussed.     

Experimental studies on a perforated horizontal floating plate breakwater

In recent years floating breakwaters are considered for creating calm basin under open sea conditions for short period of time. In this paper, experimental studies on the performance characteristics of a horizontal floating plate breakwater are presented. The results of this two-dimensional model study are for regular waves of shallow and intermediate water depths. Analysis of the results shows that the transmission coefficient is strongly influenced by wave steepness and relative length of breakwater. It is also found to be dependent, to a lesser extent, on the relative depth of draft. Mooring forces are found to increase with increasing wave steepness and relative depth of draft. The performance of this breakwater is compared with other types of breakwater reported by earlier workers.     

波浪在Jarlan型开孔潜堤上的运动

The wave motion over a submerged Jarlan-type breakwater consisting of a perforated front wall and a solid rear wall was investigated analytically and experimentally. An analytical solution was developed using matched eigenfunction expansions. The analytical solution was confirmed by previously known solutions for single and double submerged solid vertical plates, a multidomain boundary element method solution, and experimental data. The calculated results by the analytical solution showed that compared with double submerged vertical plates, the submerged Jarlan-type perforated breakwater had better wave-absorbing performance and lower wave forces. For engineering designs, the optimum values of the front wall porosity, relative submerged depth of the breakwater, and relative chamber width between front and rear walls were 0.1–0.2, 0.1–0.2, and 0.3–0.4, respectively. Interchanging the perforated front wall and solid rear wall may have no effect on the transmission coefficient. However, the present breakwater with a seaside perforated wall had a lower reflection coefficient.     

基于OpenFOAM的潜堤—双弧板组合结构水动力特性数值研究

鉴于双弧板式透空堤的消浪性能仍不理想,提出了一种潜堤—双弧板组合结构,并基于OpenFOAM软件建立了波浪与该结构相互作用的数值模型,采用试验结果对所建数值模型进行验证。在此基础上,讨论了该新型结构的消浪特性、波压力分布特征以及所受波浪力的影响因素。结果表明,透射系数随相对板宽的增大而减小,反射系数则相反。透射与反射系数随相对潜深的变化较为显著。当结构位于静水位上方（即相对潜深为-0.05）时,透射系数最小而反射系数最大;当结构位于静水位下方（即相对潜深为0.05）时,透射系数最大而反射系数最小。该组合结构两块弧板上下表面的正负压力变化关于横轴近似对称,不同测点处的压力值差异显著。水平波浪力与垂直波浪力的变化趋势大致相似,但垂直波浪力远大于水平波浪力。研究结果可为其工程应用提供理论指导与技术支撑。     

Wave reflection by a vertical wall with a horizontal submerged porous plate

By applying the linear water wave theory and the eigenfunction expansion method, the wave reflection by a vertical wall with a horizontal submerged porous plate is investigated in this paper. The numerical results, concerning the effects of the dimensionless plate length, the relative water depth, and the porous effect parameter of the plate on the wave loads on the plate and the wave height near the wall as well as the reflection coefficient, are discussed. It is found that the submerged plate increases the complexity of the phenomenon related to the wave reflection and refraction in the close region of the wall, and leads to the occurrence of the phenomenon of wave trapping. The results indicate that there may exist a process of focusing wave energy near the wall for small dimensionless porous effect parameters, whereas the increase of the dimensionless porous effect parameter decreases gradually the wave height until setdown occurs. The behavior of a larger plate with proper porosity is similar to that of a wave absorber which can significantly suppress not only the wave height above the plate but also the reflection waves. The ability of the porous plate to reduce the wave height on the wall surface is, in general, directly proportional to the dimensionless plate length and may be strongest for a proper value of the dimensionless porous effect parameter. It is also demonstrated that the wave loads on a porous plate are smaller than those on an impermeable plate.     

Study on scattering wave force of horizontal and vertical plate type breakwaters

The interaction between wave and horizontal and vertical plates is investigated by the boundary element method,and the relations of wave exciting force with plate thickness,submergence and length are obtained.It is found that:1) The efficient wave exciting force exists while plate submergence is less than 0.5 m,and the plate is very thin with order O(0.005 m).2) The maximum heave wave exciting force exists,and it is the main factor for surface and submerged horizontal plate while the roll force can be ignored.3) The maximum sway wave exciting force exists,it is the main factor for surface or submerged vertical plate,and the roll force is about 20 times of horizontal plate.     

水下平板与波浪相互作用完全非线性数值模拟(英文)

利用完全非线性数值波浪水槽技术研究水下平板与波浪的相互作用。假定水下平板厚度极薄、刚性,位于有限水深并且非常接近自由水面。应用四阶龙格库塔方法追踪每一时刻的波面形状,采用阻尼层来吸收反射波以保证算法的稳定性,同时引入平滑和重组的方法抑制自由表面控制点的较高梯度。通过对波浪与浮动圆柱相互作用的数值模拟证实了数值波浪水槽方法的有效性,计算结果与线性理论吻合良好。在波浪数值水槽方法中引入造波板模拟波浪产生并与水下平板发生相互作用,应用傅立叶解析方法对波面变形、波浪力作了分析。结果表明在板非常接近自由水面的情况下会表现出现很强的非线性,揭示了线性理论的局限性。     

Hydroelastic Response of VLFS with An Attached Submerged Horizontal Solid/Porous Plate Under Wave Action

The hydroelastic responses of a submerged horizontal solid/porous plate attached at the front of a very large rectangular floating structure(VLFS) under wave action has been investigated in the context of linear water wave theory. Darcy's law is adopted to represent energy dissipation in pores. It is assumed that the porous plates are made of material with very fine pores so that the normal velocity across the perforated porous is linearly associated with the pressure drop. In the analytic method, the eigenfunction expansion-matching method(EEMM) for multiple domains is applied to solve the hydrodynamic problem and the elastic equation of motion is solved by the modal expansion method. The performance of the proposed submerged horizontal solid/porous plate can be significantly enhanced by selecting optimal design parameters, such as plate length, horizontal position, submerged depth and porosity. It is concluded that good damping effect can be achieved through installation of solid and porous plate.Porous plate has better damping effect at low frequencies, while solid plate has better damping effect at high frequencies. The optimal ratio of plate length to water depth is 0.25-0.375, and the optimal ratio of submerged depth to water depth is 0.09-0.181.     

Interaction mechanisms among waves,currents and a submerged plate

Wave-induced loads on a submerged plate, representative of submerged breakwater, coastal-bridge deck and a certain type of wave energy converter, in a uniform current are investigated in this study using fully nonlinear numerical wave tanks (NWTs) based on potential flow theory. The coupling effect of wave and current is explored, and the underlying interaction mechanisms of the hydrodynamic forces are described. The presence of a background current modifies the frequency dispersion. It produces changes of the water-surface elevation, and also has an effect on wave-induced loads. Depending on the nonlinearity, higher harmonic wave components are generated above the submerged plate. These contribute to the wave forces. It is found that the horizontal and the vertical force, hence the moment, are affected in the opposite way by the currents. The Doppler shifted effect dominates the vertical force and the moment on the plate. Whereas, the Doppler shifted effect and the generation of higher wave harmonics play opposite roles on the horizontal forces. The contribution of 2^nd order harmonics is found to be up to 30% of the linear component. The current-induced drag force, represented by the advection term ρU∂φ/∂x in the pressure equation, is found to lead to a decrease in the moment for the most range of wavelengths considered, and an increase in the moment for a small range of longer waves.     

Experimental study on the performance of twin plate breakwater

The wave transmission characteristics and wave induced pressures on twin plate breakwater are investigated experimentally in regular and random waves.A total of twenty pressure transducers are fixed on four surfaces of twin plate to measure the wave induced dynamic pressures.The spatial distribution of dynamic wave pressure is given along the surface of the twin plate.The uplift wave force obtained by integrating the hydrodynamic pressure along the structure is presented.Discussed are the influence of different incident wave parameters including the relative plate width B /L,relative wave height /i H a and relative submergence depth s /a on the non-dimensional dynamic wave pressures and total wave forces.From the investigation,it is found that the optimum transmission coefficient,t K occurs around B /L 0.41 ~ 0.43,and the twin plate breakwater is more effective in different water depths.The maximum of pressure ratio decreases from 1.8 to 1.1 when the relative submergence depth of top plate is increased from 0.8to +0.8.     

Higher harmonics induced by a submerged horizontal plate and a submerged rectangular step in a wave flume

The decomposition of a monochromatic wave over a submerged plate is investigated experimentally in a wave flume. Bound and free higher harmonic modes propagating upstream and downstream the structure are discriminated by means of moving resistive probes. The first-order analysis shows a resonant behaviour linked to the ratio of the plate's width and the fundamental mode wavelength over the plate. The second-order analysis shows an energy transfer from the fundamental mode towards free harmonics propagating downstream the structure. This transfer is linked to the ratio of the width of the plate and the bound harmonic wavelength over the plate. We also performed experiments with a submerged step to compare the efficiency of both structures. The submerged plate is shown to be a more efficient breakwater than the step, at the first as well as the second-order.     

没水倾斜板式防波堤消波性能分析

提出了一种将波浪中倾斜板问题等效化简为波浪中水平板单元组的方法,该方法建立在使用分离变量法求解水工结构边值问题的基础上,并使用伽辽金法精确求解连续边界条件,确定考虑衰减波态的速度势函数,从而求解没水倾斜板结构的消波性能。等效化简法计算精度于边界元法相当,且计算单元数量少、开销低。基于二维线性势波理论,对没水倾斜板式防波堤消波性能分析显示,没水板的倾斜角度、没水深度与板长是结构消波性能的控制因素:没水倾斜板防波堤的消波性能优于没水水平板防波堤的消波性能,随着没水板结构的倾斜角度增大,没水倾斜板结构的波浪透射系数显著减小,且长板优于短板,浅板优于深板;与前人的水槽实验对比显示,相对没水深度与波陡影响结构的消波性能,且波陡造成的波浪破碎贡献了显著的波能消耗。该结论对板式防波堤的结构配置、优化设计有重要意义。