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.     

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.     

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.     

基于类海啸波型的岛礁水动力特性数值模拟研究

基于非静压单相流模型NHWAVE建立了高精度二维数值波浪水槽,采用日本2011年实测真实海啸波型系统研究了海啸波在岛礁上传播变形的规律,并且分析了波高、礁坪淹没水深和礁前斜坡坡度等因素对孤立波和真实海啸传播变形的影响。结果表明,相比孤立波,类海啸波的波长明显大于孤立波波长,在测点处引起的水面变化持续时间更长,同等波高情况下真实海啸波型比孤立波能够携带更多的能量,与岛礁的相互作用也更为复杂,在礁坪上形成的淹没水深约为孤立波的两倍。礁前斜坡坡度和礁坪淹没水深均对类海啸波的反射和透射系数有显著影响。随着礁前斜坡坡度的增加,反射系数和透射系数均逐渐增加。随着礁坪淹没水深的增加,反射系数逐渐减小,而透射系数逐渐增大。但是,反射系数和透射系数均随着入射波高的增加而逐渐减小。     

Numerical Wave Flume Study on Wave Motion Around Submerged Plates

1 .IntroductionApile supportedplatesubmergedatacertaindepthunderseasurfacewasdevelopedasanewtypeofunderwaterbreakwaterfortheprotectionofcoastlinesandharbors .Thisisbecauseitdoesnothinderthewaterexchangebetweentheopenseaandtheprotectedareanordoesithindertheviewovertheopensea .Besides,itislessdependentonthegeotechnicalconditionsoftheseabottomwherethestructureistobeinstalled ;however,itscostishigh ,particularlyinrelativelydeepwaters .Formanyapplicationsitispossibletoreducethewavemotionintheprotec…     

Experimental investigation of the harmonic generation by waves over a submerged plate

Experiments in a wave flume have been performed to analyse the nonlinear interaction between regular gravity waves and a submerged horizontal plate used as breakwater. A new method, based on the Doppler shift generated by a moving probes, has been used to discriminate the incident fundamental mode and the reflected fundamental mode. The relationships of the reflection and transmission coefficients to the wave number at different submergence depth ratios are presented. The accurate discrimination, by this method, of the phase-locked and free modes allows the quantification of the higher harmonics generated by the breakwater and the analysis of the nonlinear interaction between the waves and the submerged plate. The transfer of energy from the fundamental mode to higher harmonics is very large in the cases of small submergence depth ratios. The vortices produced at the edges take part in the production of higher harmonics by interaction with the free surface but involve, at the same time, a dissipation process that increases the efficiency of the breakwater.     

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 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.     

Estimation of incident and reflected waves in regular wave experiments

This paper presents a laboratory technique for measurement of reflected waves by a submerged horizontal plate. A simple method is proposed to decompose the composite wave record obtained from the wave reflection experiments in the wave flume. The data collected were used to compute the reflected wave height by means of two and three probe methods proposed by other investigators and compared with the directly computed reflected wave using the measured incident wave. The experiment was carried out for a horizontal plate of 1 m length spanning the full width of the flume with wave periods ranging from 0.8 to 1.8 sec with 0.1 sec increments and wave heights of 5, 10 and 15 cm. The methods using two and three probes with phase measurement yield better results than the three probe method without phase measurement, and in general they have a wider range of application. The method using three probes without the phase measurement generally fails due to numerical instability of the scheme. The results obtained by the proposed method are compared with the two and three probe methods and a comparative analysis of the four methods is presented and discussed.     

Physical model studies on wave transmission of a submerged inclined plate breakwater

This paper examines the results of physical model studies conducted in a monochromatic wave flume, to evaluate the wave transmission characteristics of a submerged plate breakwater consisting of a fixed plate of 0.50 m length and 0.003 m thickness. The model was oriented at varying inclinations and submergence. The influence of wave steepness, relative depth, relative submergence and angle of inclination on wave transmission was analysed. It was found that the horizontal plate is effective for short waves with steepness parameter higher than 5×10^?3 in relative depth grater than 0.21. The plate oriented at an angle of inclination of 60° is found to be effective for the entire ranges of wave parameters considered for the study and it reduces the wave height by about 40%.     

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.     

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.     

Modelling of Random Waves over Submerged Breakwaters and Its Application to Reflection Estimation

1.IntroductionGreat efforts have been devoted to the protection of coastal areas over many years by erectingdikes,seawalls,groin systems,and detached breakwaters.The sea walls,jetties,detached breakwa-ters,etc.are traditionally adopted as absorbingfacilit…     

Wave interaction with ‘’-type breakwaters

The wave transmission, reflection and energy dissipation characteristics of ‘’-type breakwaters were studied using physical models. Regular and random waves in a wide range of wave heights and periods and a constant water depth were used. Five different depths of immersion (two emerged, one surface flushing and two submerged conditions) of this breakwater were selected. The coefficient of transmission, K_t, and coefficient of reflection, K_r, were obtained from the measurements, and the coefficient of energy loss, K_l was calculated using the law of balance of energy. It was found that the wave transmission is significantly reduced with increased relative water depth, d/L, whether the vertical barrier of the breakwater is surface piercing or submerged, where ‘d’ is the water depth and ‘L’ is the wave length. The wave reflection decreases and energy loss increases with increased wave steepness, especially when the top tip of the vertical barrier of this breakwater is kept at still water level (SWL). For any incident wave climate (moderate or storm waves), the wave transmission consistently decreases and the reflection increases with increased relative depth of immersion, Δ/d from −0.142 to 0.142. K_t values less than 0.3 can be easily obtained for the case of Δ/d=+0.071 and 0.142, where Δ is the height of exposure (+ve) or depth of immersion (−ve) of the top tip of the vertical barrier. This breakwater is capable of dissipating wave energy to an extent of 50–80%. The overall performance of this breakwater was found to be better in the random wave fields than in the regular waves. A comparison of the hydrodynamic performance of ‘’-type and ‘T’-type shows that ‘T’-type breakwater is better than ‘’-type by about 20–30% under identical conditions.     

The effect of relative crest submergence on wave breaking over submerged slopes

Experiments were performed in a wave flume to measure the intensity, transmission and reflection of waves breaking over a submerged reef with an offshore gradient of 1:10. The results demonstrate that the relative water depth over the reef crest (h_c/H_o) is a dominant factor affecting the breaking characteristics. In particular it is found that as the relative crest submergence is reduced, there is a considerable increase in the intensity of wave breaking over the reef that can be quantified through measurements of the air cavity enclosed beneath the plunging jet. It is also shown that there is a corresponding decrease in wave transmission and reflection as the submergence is reduced.     

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。     

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     

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.