Forces and moment on a horizontal plate due to regular and irregular waves in the presence of current

This work presents an experimental study of a submerged plate used as a breakwater for coastal areas protection. Questions addressed concern the influence of current on the reflective power of the plate, and its influence on the hydrodynamic loads exerted on it. Results concern both monochromatic and irregular waves. Generally speaking, an influence of the current is found, changing the reflecting power of the structure up to 50%. A homogenized behavior of the loads and moments is found in the presence of currents, meaning that the load values become less sensitive to the frequency. Furthermore, the influence of waves reflected by the wave absorber, representing partially reflective conditions at the shore, is found to be of same order in the absence of current. In any case, the linear behavior of the breakwater is emphasized through the irregular waves approach.     

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.     

随机波对水平板冲击作用实验研究

波浪对透空式海上建筑物的冲击作用已经成为此类建筑物安全的重要影响因素。进行了单向随机波对水平板冲击作用水槽实验研究。总共进行了4个方向(0°、15°3、0°、45°),相对入射波波高H1/3/d=0.093 75~0.25,周期Tp=1.0~2.0 s,水平板距离静水面的高度s与入射波高H1/3的比值s/H1/3=0.0~0.5的实验研究。采用小波分析方法去除了由于测压传感器振荡引起的测量数据的振荡和漂移,在此基础上统计分析给出了不同方向水平板下的压力峰值分布情况。采用无因次方法,讨论了无因次冲击力与相对入射波高H1/3/d、相对板宽B/L、相对净空s/H1/3及波向角β的关系。     

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.     

立管-水平板结构消浪特性试验研究

在现有的矩形方箱和透空结构的基础上,提出一种由立管和水平板组合而成的消浪结构。利用波浪水槽物理模型试验,测试该结构在单向规则波作用下的消浪性能。分别探讨了其单排布置和双排布置时的透射系数随结构宽度、相对吃水深 度、相对间距等因素的变化规律。结果表明：单排布置时,透射系数随结构宽度的增大而减小,总体上随吃水深度的增大而减小;双排布置时,透射系数相对总宽度相同的单体结构减少 10 %,透射系数随吃水深度的增大而减小,前后间距对透射系数的影响不明显。对试验结果数据进行曲线拟合,得到了透射系数关于各影响因素的函数表达式。     

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。     

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.     

A new approximate analytic solution for water wave scattering by a submerged horizontal porous disk

This study gives a new approximate analytic solution for water wave scattering by a submerged horizontal porous disk in the context of the linear potential theory. The solution is based on the domain decomposition method. The velocity potentials are determined by two different approaches. One approach is to adopt decompositions for velocity potentials, and the other is to expand the vertical derivative of the velocity potential on the porous disk along the radial direction. Hence the velocity potentials are determined by the matched eigenfunction expansions. Differing from previous solutions with respect to the porous disk, the present solution needs no complex dispersion relations. Thus the new solution is easier for numerical implementation. According to numerical examples, the convergence of the present solution is satisfactory. In addition, the present predictions of the wave surface elevation and the vertical wave force on the disk agree very well with previous results by different approaches. The present solution can also be extended to other structures involving disks, such as a fish cage, a porous disk with finite thickness, and a submerged elastic disk.     

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。     

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.     

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）.     

Forces on a pitching plate: An experimental and numerical study

A flat plate in pitching motion is considered as a fundamental source of locomotion in the general context of marine propulsion. The experimental as well as numerical investigation is carried out at a relatively small Reynold number of 2000 based on the plate length c and the inflow velocity U_∞. The plate oscillates sinusoidally in pitch about its 1/3 − c axis and the peak to peak amplitude of motion is 20°. The reduced frequency of oscillation k = πfc/U_∞ is considered as a key parameter and it may vary between 1 and 5. The underlying fluid-structure problem is numerically solved using a compact finite-differences Navier–Stokes solution procedure and the numerical solution is compared with Particle Image Velocimetry (PIV) measurements of the flow field around the pitching foil experimental device mounted in a water-channel. A good agreement is found between the numerical and experimental results and the threshold oscillation frequency beyond which the wake exhibits a reverse von Kármán street pattern is determined. Above threshold, the mean velocity in the wake exhibits jet-like profiles with velocity excess, which is generally considered as the footprint of thrust production. The forces exerted on the plate are extracted from the numerical simulation results and it is shown, that reliable predictions for possible thrust production can be inferred from a conventional experimental control volume analysis, only when besides the wake's mean flow the contributions from the velocity fluctuation and the pressure term are taken into account.     

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.     

Dynamic pressure distribution on a cylinder due to wave diffraction

The experimental investigations on the dynamic pressure distribution around a large vertical cylinder resting on a flume bed and piercing the free surface subjected to regular waves have been carried out in a 4-m wide wave flume in a constant water depth of 2.5 m at Ocean Engineering Centre, Indian Institute of Technology, Madras, India. The cylinder of diameter 400 mm was fixed with diaphragm type pressure transducers at eight different locations below the still water level along with one at the still water level. In addition to this, to study the effect of nonlinearity, one pressure transducer was located above the still water level. The experimental results pertaining to mostly deep water conditions are compared with MacCamy and Fuchs theory and the agreement is found to be good. In order to account for the effects of nonlinearities the above said theory has been modified the results of which are found to be in better agreement.     

Second-order vertical and horizontal wave forces on a circular dock

A second-order potential solution is presented for the diffraction of a nonlinear progressive wave in finite-depth water, incident on a fixed circular dock. The usual perturbation analysis is used to produce first- and second-order subproblems. The mathematical method is based on the assumption that inner and outer solutions exist and these are matched by the requirements of continuity for mass flux and pressure between adjacent regions. It is shown that the solutions for the second-order problem can be derived in the same manner as in the first-order theory.     

On the wave damping due to a permeable seabed

Laboratory experiments were performed to study the wave damping induced by a porous bed. During the propagation of waves over a porous medium the wave characteristics change: a significant wave height attenuation of about 20–30% is observed and, in almost all cases, an increase in wavelength. The wave decay is found to depend on the wave characteristics like the wave height, the wavelength and the wave shape. We have also studied the influence of the geometric properties of the porous bed (i.e. thickness and length) on the wave dissipation. It is found that the attenuation of the wave height increases with the permeable bed thickness and that there is a maximum wave dissipation for a length of the porous seabed equal to 2.0–2.5 times the wavelength. A comparison is also made of our findings with available literature results. A parametric study of the wave damping has been performed by varying the values of the resistance coefficients derived by both literature and experiments. Literature analytical models have been applied by using the resistance coefficients that better describe our flow conditions. All models in use underpredict the observed wave attenuation for any sensible values of the resistance coefficients.     

Standing wave pressures due to regular and random waves on a vertical wall

The standing wave pressures due to laboratory-generated regular and random waves exerted on a vertical wall were measured in a wave flume. The standing wave pressures were measured at four relative depths of submergence on the test model. The regular wave test conditions ranged from intermediate to deep water conditions. The measured pressures due to regular waves were compared with results obtained using linear theory and third-order solution. In the case of random wave tests, the dynamic pressures due to the time histories of water surface elevation following the spectral characteristics of Pierson-Moskowitz and Bretschneider spectra were measured. These pressures are compared with simulated pressures obtained through the linear filter technique of Reid. The variation of pressure spectra along the depth are presented. In addition, comparison of spectral parameters, i.e. zeroth moment, spectral width parameter and narrowness parameter of measured and simulated pressure spectra, are reported and discussed. The behaviour of the coherence function between the wave elevation on the wall and the corresponding pressures is also discussed.     

Hydrodynamic Forces on Inclined Cylinder due to Waves with Crossing Current

Based on Morison's Equation and linear wave theory, hydrodynamic forces acting on inclined cylinders due to waves and crossing current at an angle of a, are analyzed. A method for calculating exciting forces is proposed. Experimental results show that the proposed method in this paper is feasible and can be used in engineering practice.