斜向波对台阶地形上有限吃水半无限长弹性板的散射作用

基于线性势流理论和欧拉-伯努利梁理论,采用匹配特征函数展开法建立斜向波对台阶地形上有限吃水半无限长弹性板散射的解析解。与以往研究不同,本文同时考虑波浪入射角度、弹性板吃水、三种不同板端条件（自由板端、简支板端、固定板端）以及海底地形的影响。本文还直接将板端条件引入匹配边界条件,建立线性方程组求解速度势中的展开系数,计算过程简单、高效。计算结果表明：本文方法收敛性好,并满足能量守恒方程。将本文计算结果与文献中的特例结果进行对比,吻合良好。分析了波浪入射角度、弹性板吃水、不同板端条件以及海底地形对弹性板水动力参数的影响,研究结果可以为工程设计提供参考。     

Modified eigenfunction expansion methods for interaction of water waves with a semi-infinite elastic plate

The eigenfunction expansion method (will be referred to as error function method in this paper) of analysing reflection and transmission of ocean waves at a semi-infinite thin elastic plate [J Geophys Res 95 (1990) 11629; Phil Trans R Soc Lond A 347 (1994) 185] is modified and extended to cases with simply supported and built-in edges. The form of the error function in the eigenfunction expansion method of Fox and Squire [J Geophys Res 95 (1990) 11629] has been modified based on a dimensional analysis and also extended to plates with either a simply supported or a built-in edge. The modified error function does not include the so-called Lagrange multipliers used in the original method and therefore the modified solution is independent of the selection of the Lagrange multipliers. It is demonstrated that the modified error function method satisfies the relation of energy conservation very well for the three edge conditions examined. The relation of energy conservation for plates is derived for elastic plates with simply supported and built-in edges and it is found that the relation of energy conservation for a free edge is also held for simply supported and built-in edges.In addition, a minor modification has also been made to the eigenfunction method (will be called inner product method in this study) of Sahoo et al. [Proceedings of 10th International Offshore and Polar Engineering Conference 3 (2000) 594]. It will be shown that the modified inner product method becomes mathematically well defined. The modified coefficient matrixes for different edge conditions are diagonal and thus the linear simultaneous equations can be solved very easily. It is also demonstrated with examples that the extended error function method and the modified inner product method give identical results.     

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.     

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.     

Hydroelastic response of a circular plate in waves on a two-layer fluid of finite depth

The hydroelastic response of a circular, very large floating structure （VLFS）, idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the plate-covered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presentedto investigate the effects of different physical quantities, such as the thickness of the plate, Young＇s modulus, the ratios ofthe densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid.Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.     

波浪作用下沙坝不稳定性实验研究

对波群、规则波和不规则波作用下沙质海岸上沙坝运动进行了实验研究。研究沙坝产生的机理和不稳定性,以及不同波浪下所产生的海岸平衡剖面形状。实验中发现,波浪作用下沙坝处于向岸和离岸运动的不稳定状态,其原因可由地形不稳定性分析。探讨了波群调制系数对沙坝运动的影响,讨论了不同波况对海岸剖面形态的影响。     

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。     

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.     

有限长正弦地形上的波浪传播问题研究

应用基于势流理论的频域边界元方法,研究了波浪在有限长正弦周期地形上的传播问题.开展了网格收敛性分析,并与物理模型试验结果做了对比,验证了数值方法的准确性.研究了正弦地形长度和幅度对水波反射率的影响,以及波浪在周期性地形上传播时的沿程波幅变化.研究发现,波浪反射系数随波数的变化及波浪幅值沿程的变化均呈包络状;当频率处于布拉格共振区域边缘且反射率为零时,周期地形上会出现极大的波幅;随海床波幅增大,第一布拉格共振带变宽且向低频移动.     

透空式水平板波浪上托力分布

通过系列模型试验，对波浪上托力沿板宽分布进行了详细分析，提出对于透空式平板结构，发生较大冲击压强或上托力的分布主要分为均布型和局部冲击型两类，由此得到压强分布的计算公式。大量试验资料表明，该公式与实验值有着较好的一致性。     

Hydroelastic interaction between obliquely incident waves and a semi-infinite elastic plate on a two-layer fluid

The hydroelastic response of a semi-infinite thin elastic plate floating on a two-layer fluid of finite depth due to obliquely incident waves is investigated. The upper and lower fluids with different densities separated by a sharp and stable interface are assumed to be inviscid and incompressible and the motion to be irrotational. Simply time-harmonic incident waves of the surface and interfacial wave modes with a given angular frequency are considered within the framework of linear potential flow theory. With the aid of the methods of matched eigenfunction expansion and the inner product of the two-layer fluid, a closed system of simultaneous linear equations is derived for the reflection and transmission coefficients of the series solutions. Based on the dispersion relations for the gravity waves and the flexural–gravity waves in a two-layer fluid and Snell’s law for refraction, we obtain a critical angle for the incident waves of the surface wave mode and three critical angles for the incident waves of the interfacial wave mode, which are related to the existence of the propagating waves. Graphical representations of the series solutions show the interaction between the water waves and the plate. The effects of several physical parameters, including the density and depth ratios of the fluid and the thickness of the plate, on the wave scattering and the hydroelastic response of the plate are studied. It is found that the variation of the thickness of the plate may change the wave numbers and the critical angles. The density ratio is the main factor to influence the wave numbers of the interfacial wave modes. Finally, the stress state is considered.     

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.     

Analytical Study on Transmission and Reflection of Non-Linear Shallow Water Waves

The analytical study is made by using the method of matched asymptotic expansions on the transmission and reflection of solitary waves and cnoidal waves on two-dimensional floating bodies. The solutions give explicitly the variation pattern of the transmitted waves and the characteristics of the reflected waves, including the wave profile, amplitude, phase shift and evolution. The effects of the gap between the body and the sea bottom on the transmission and reflection of those waves are also discussed.     

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.     

Numerical study on the effect of submerged depth on the horizontal plate wave energy converter

The growing search for clean and renewable energy sources has given rise to the studies of exploring sea wave energy. This paper is concerned with the numerical evaluation of the main operational principle of a submerged plate employed for the conversion of wave energy into electrical one. The numerical model used to solve the conservation equations of mass, momentum and transport of volume fraction is based on the finite volume method （FVM）. In order to tackle with the flow of mixture of air-water and its interaction with the device, the multiphase model volume of fluid （VOF） is employed. The purpose of this study is the evaluation of a numerical model for improvement of the knowledge about the submerged plate wave energy converter, as well as the investigation of the effect of the distance from the plate to the bottom of the sea （HP） on the performance of the converter. The simulations for several distances of the plate from the seabed show that the optimal efficiency is 64%, which is obtained for HP=0.53 m （88% of the depth）. This efficiency is 17% larger than that found in the worst case （HP=0.46 m, 77% of the depth）.     

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.     

Surface gravity wave interaction with elastic bottom

In the present paper, a hydroelastic model is developed to deal with surface gravity wave interaction with an elastic bed based on the small amplitude water wave theory and plate deflection in finite water depth. The elastic bottom bed is modelled as a thin elastic plate and is based on the Euler-Bernoulli beam equation. The wave characteristics in the presence of the elastic bed is analyzed in both the cases of deep and shallow water waves. Further, the linearized long wave equation is generalized to include bottom flexibility. A generalized expansion formula for the velocity potential is derived to deal with the boundary value problems associated with surface gravity waves having an elastic bed. The utility of the expansion formula is illustrated by demonstrating specific physical problems which will play significant role in the analysis of wave structure interaction problems. Behavior of the wave spectra are discussed in the case of closed basin having a free surface and an elastic bottom topography.     

Multidirectional wave transformation around detached breakwaters

The performance of the new wave diffraction feature of the shallow-water spectral model SWAN, particularly its ability to predict the multidirectional wave transformation around shore-parallel emerged breakwaters is examined using laboratory and field data. Comparison between model predictions and field measurements of directional spectra was used to identify the importance of various wave transformation processes in the evolution of the directional wave field. First, the model was evaluated against laboratory measurements of diffracted multidirectional waves around a breakwater shoulder. Excellent agreement between the model predictions and measurements was found for broad frequency and directional spectra. The performance of the model worsened with decreasing frequency and directional spread. Next, the performance of the model with regard to diffraction–refraction was assessed for directional wave spectra around detached breakwaters. Seven different field cases were considered: three wind–sea spectra with broad frequency and directional distributions, each coming from a different direction; two swell–sea bimodal spectra; and two swell spectra with narrow frequency and directional distributions. The new diffraction functionality in SWAN improved the prediction of wave heights around shore-parallel breakwaters. Processes such as beach reflection and wave transmission through breakwaters seem to have a significant role on transformation of swell waves behind the breakwaters. Bottom friction and wave–current interactions were less important, while the difference in frequency and directional distribution might be associated with seiching.     

恒定流对潜堤波浪反射系数影响研究

为研究恒定均匀流对直立潜堤波浪反射系数的影响,采用了高阶边界元方法和混合欧拉-拉格朗日时间步进方法更新瞬时自由水面,运用基于二次形状函数的网格重分方案结合四阶龙格库塔方法更新时间积分,并运用两点法得到淹没潜体前的反射系数。将数值模拟得到的波面数据与物理模型试验结果进行对比,两者吻合良好。通过数值模拟研究给出了入射波周期、水流流速、潜堤相对宽度和相对淹没深度对反射系数的影响。结果表明,水流流速和潜堤相对淹没深度对反射系数影响较大,潜堤相对宽度的影响相对较小;水流的存在会使入射波周期等参数对反射系数的影响程度发生改变,在实际工程设计时应考虑水流对潜堤防浪效果的影响。     

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.