Effect of a submerged plate on the near-bed dynamics underincoming waves in deep water conditions

It is well known that wave induced bottom oscillations become more and more negligible when the water depth exceeds half the wavelength of the surface gravity wave. However, it was experimentally demonstrated for regular waves that the bottom pressure oscillations at both first and second wave harmonic frequencies could be significant even for incoming waves propagating in deep water condition in the presence of a submerged plate [16]. For a water depth h of about the wavelength of the wave, measurements under the plate (depth immersion of top of plate h/6, length h/2) have shown bottom pressure variations at the wave frequency, up to thirty times larger than the pressure expected in the absence of the plate. In this paper, not only regular but also irregular wave are studied together with wave following current conditions. This behavior is numerically verified by use of a classical linear theory of waves. The wave bottom effect is explained through the role of evanescent modes and horizontally oscillating water column under the plate which still exist whatever the water depth. Such a model, which allows the calculation of the velocity fields, has shown that not only the bottom pressure but also the near bed fluid velocity are enhanced. Two maxima are observed on both sides of the location of the plate, at a distance of the plate increasing with the water depth. The possible impact of such near bed dynamics is then discussed for field conditions thanks to a scaling based on a Froude similarity. It is demonstrated that these structures may have a significant impact at the sea bed even in very deep water conditions, possibly enhanced in the presence of current.     

一种起伏板防波堤最优支撑刚度计算方法

带有弹簧支撑的水平板结构,可在波浪作用下起伏运动进行消浪,作为防波堤具有广泛的应用前景,但如何设计支撑刚度仍是当前研究的重点课题。基于黏性流理论建立数值波浪水槽,开展规则波与起伏板防波堤相互作用的模拟,得到起伏板透反射系数随支撑刚度的变化曲线,并分析最小透射系数对应刚度下起伏板运动相位对消浪的影响。为快速得到最小透射系数对应的支撑刚度,根据弹簧—阻尼—质量模型,建立一种以运动相位为输入反推起伏板最优支撑刚度的计算方法,并将推导结果与数值结果进行比较。结果表明,该方法推导的最优支撑刚度值与数值最优值接近,且可省去遍历取最优值的步骤,可为起伏板防波堤的支撑刚度设计提供参考。     

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.     

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.     

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.     

Laboratory Study on the Interaction Between Regular Obliquely Incident Waves and Vertical Walls

The characteristics of wave forces are studied based on physical model tests with regular waves. The ratio of obliquely incident wave forces to normally incident wave forces on unit length of a vertical wall is related with various factors. A linear reduction of the mean force of obliquely incident waves is confirmed with an increase in the relative caisson length. Also the characteristics of reflection coefficient of diagonal waves 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.     

珊瑚岸礁破碎带附近波浪演化实验研究

通过波浪水槽实验对珊瑚岸礁破碎带附近波浪演变规律开展研究,实验采用了概化的岸礁模型,测试了4种礁坪水深、4种礁前斜坡坡度和一系列入射波高的组合工况。对破碎带宽度和破碎带附近波浪的入射、反射、透射以及能量耗散进行了测量分析,透射波的计算考虑了礁坪上高次谐波的影响。结果表明:礁坪水深和入射深水波高的比值(即礁坪相对水深)是影响岸礁破碎带附近波浪演化的关键参数,而礁前斜坡坡度的影响在本文测量的范围内可以忽略不计。破碎带宽度与礁坪上浅水波波长为同一数量级,并与礁坪相对水深成反比;透射系数随礁坪相对水深的增大呈线性增长,而反射系数的变化却无类似规律;岸礁能够削弱超过50%入射波能,礁坪相对水深越小,波浪破碎造成的能量耗散越大。     

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

This study examines the reflection 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 reflection 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 function. The calculated results obtained for limiting cases are exactly the same as corresponding results given by the previous researchers. The present predictions also agree well with experimental data in the published literatures. Numerical experiments are conducted to examine the variations of the reflection coefficient versus its main effect factors, and some interesting results are presented.     

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。     

Investigations on the reflection behaviour of a slotted seawall

Based on the linear wave theory and the eigenfunction expansion method, the interaction between waves and a slotted seawall is studied analytically as well as experimentally. The analytical investigations show that the reflection characteristics of a slotted seawall depend mainly on the porosity of the slotted plate and the incident wave height. It is found that the reflection coefficient reaches its minimum value as the chamber width is about a quarter of the incident wavelength. The reflection behaviour becomes optimal when the porosity is moderate (about 0.2 in the present study). The immersed depth has some effect on the reflection coefficient of the seawall structure, but the improvement is small when the immersed depth is larger than the half of the water depth. A series of physical model experiments are carried out to examine the analytical results. Comparisons between the analytical and experimental results of reflection coefficients are made for some comparable cases and show good agreement provided certain parameters of this model are suitably chosen. This demonstrates that the analytical model is able to account adequately for energy dissipation by the slotted plate and can provide instruction for the design of such seawalls.     

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。     

斜向波与带填料开孔板式防波堤相互作用的研究

基于线性势流理论,对斜向波与消浪室内带部分填料的开孔板式防波堤结构的相互作用进行了理论研究.利用匹配特征函数展开法给出了开孔防波堤结构反射系数和波浪力系数的理论计算方法,在极限情况下的计算结果与已有结果一致.利用数值算例分析了开孔结构反射系数和波浪力系数的主要影响因素.增加消浪室内填料厚度通常可以降低开孔墙结构的波浪力系数,加大结构的反射系数.随着波浪入射角度的增加,带填料防波堤结构的反射系数值先减小,达到最小值后又单调增加.     

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 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.     

Experimental investigating on the reflected waves from the caisson-type vertical porous seawalls

The hydrodynamic efficiencies of caisson-type vertical porous seawalls used for protecting coastal areas were calculated in this study. Physical models were developed to compare the wave reflection from vertical plane, semi-porous, and porous seawalls caused by both regular and random waves. Tests were carried out for a wide range of wave heights, wave periods, and different water depths (d=0.165, 0.270 and 0.375 m). The performance regarding the reflected waves from porous and semi-porous seawalls showed improvement when compared with those from the plane seawall. The reflection coefficients of the porous and semi-porous seawalls were calculated as 0.6 and 0.75, respectively, while the coefficient for the fully reflecting plane vertical wall was significantly higher (0.9). It was also observed that the reflection coefficient decreases with increase in wave steepness and relative water depth. In addition, the reduction in the reflection coefficient of porous and semi-porous seawalls, as compared to that of a plane seawall, was observed for both regular and random waves. New equations were also proposed to calculate the reflection coefficient of different types of seawalls with the aid of laboratory experiments. By verifying the developed equations using some other experimental data, it was validated that the equations could be used for practical situations. The results of the present study can be applied to optimize the design of vertical seawalls and for coastal protecting schemes.     

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 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.     

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.     

Experimental determination of wavelengths in the presence of a mean current

This paper describes a simple method for determining the wavelength of small amplitude waves under laboratory conditions where reflected wave components are present both with and without a mean current flow superimposed. It assumes a locally horizontal bed but requires no a priori assumption concerning the form of the dispersion relation with a coexisting current. Synchronous measurements of the water surface recorded along any straight line are analysed to yield Fourier coefficients at each location. It is then shown that for all practical conditions excluding a perfect standing wave, the average rate of change of wave phase in the chosen direction can be related directly to the component of incident wave number in that direction, irrespective of reflection coefficient or relative current strength. The technique has been applied to regular and bichromatic waves in a flume with an absorbing wave generator, and can also be applied in 3-D wave basins where waves and currents intersect at arbitrary angles. In combined wave–current experiments, by assuming the linear dispersion relation, it is also possible to estimate the effective current velocity.