Wave Scattering by Double Slotted Barriers in A Steady Current： Experiments

The adoption of slotted breakwaters can be an ideal option in the protection of very large near-shore floating struc-trees that may extend offshore to a considerable water depth. In this paper, we experimently investigated the behaviour of wave transmission and reflection coefficients of double slotted barriers in the presence of a steady opposing current. The experimental results show that opposing currents have only minor effects on wave reflection, but can significantly reduce the wave transmission through double slotted barriers. The experimental results suggest that coastal currents should be taken into consideration for an economical design of slotted breakwaters.     

An experimental study of wave scattering by a vertical slotted barrier in the presence of a current

In coastal waters, tidal currents and surface waves co-exist. In this study, the influence of a steady current on the scattering of waves by a vertical slotted barrier is investigated experimentally in a wave flume. The separation of the incident and reflected waves is carried out by a two-point method that takes into account the effects of the current. Results show that currents significantly increase the wave-energy loss by the barrier and remarkably reduce the wave transmission through the barrier. It is suggested that the tidal currents should be taken into consideration in an economical design of slotted breakwaters.     

Simplified analytical solutions for wave interaction with absorbing-type caisson breakwaters

Simplified analytical solutions are presented to model the interaction of linear waves with absorbing-type caisson breakwaters, which possess one, or two, perforated or slotted front faces which result in one, or two, interior fluid regions (chambers). The perforated/slotted surfaces are idealized as thin porous plates. Energy dissipation in the interior fluid region(s) inside the breakwater is modelled through a damping function. Under the assumption of potential flow and linear wave theory a boundary-value problem may then be formulated to describe wave interaction with the idealized structure. A solution to this simplified problem may be obtained by an eigenfunction expansion technique and an explicit analytical expression may be obtained for the reflected wave height. Using the experimental work of previous authors, damping coefficients are determined for both single and double chamber absorbing-type caisson breakwaters. Based on the damping for a single perforated-wall breakwater, a methodology is proposed to enable the estimation of the damping coefficients for a breakwater with two chambers. The theoretical predictions of the reflection coefficients for the two-chamber structures using the present model are compared with those obtained from laboratory experiments by other authors. It is found that the inclusion of the damping in the interior fluid region gives rise to improved agreement between theory and experiment.     

Wave interaction with one or two rows of closely spaced rectangular cylinders

Experimental results are reported on the wave reflection from and transmission through one row or two rows of closely spaced rectangular cylinders. An empirical expression is proposed for the friction factor which models the head loss due to closely spaced rectangular cylinders. Algebraic expressions are presented to calculate the reflection and transmission coefficients of regular waves for a single slotted wall or double slotted walls. The model is validated by the published and present experimental results. The proposed method can be used for the preliminary design of slotted-wall breakwaters.     

A study of spar buoy floating breakwater

A floating breakwater produces less environmental impact, but is easily destroyed by large waves. In this paper, the spar buoy floating breakwater is introduced with a study on the wave reflection and transmission characteristics and mooring line tension induced by the waves. Mei (The Applied Dynamics of Ocean Surface Waves, Wiley, New York (1983) 740 p) proposed a theoretical solution for the reflection and transmission coefficients as the wave propagates through a one-layer slotted barrier. For a multiple-layer fence system, the analytical solution is proposed linearly. The results show that the theoretical computations agree well with the experimental trends. For a multiple-layer fence system, the transmission coefficients become maximal as the layer spacing to wavelength ratio moves to 1/2. Conversely, the coefficients become minimal, as the ratio moves to 0.3. To estimate the maximum tension of the mooring line, both numerical calculations and laboratory experiments were executed. The numerical calculation results were similar to the experimental results.     

双挡板透空堤透浪与反射系数实验研究

设有挡浪板结构的透空式防波堤适用于水深较大的海域,且具有较好的消浪效果。采用物理模型试验,探究具有双侧挡浪板结构的透空式防波堤透浪系数与反射系数的影响因素与规律,研究包括外侧与内侧挡浪板入水深度,水平板板宽,结构上部挡浪墙的高度与位置,水平板超高与波浪要素等因素。通过比较各家透浪系数的理论计算公式与实验结果,进行透浪系数的计算方法研究,给出修正Wiegel公式拟合双侧挡浪板透空式防波堤的透浪系数计算公式,供工程设计参考与进一步研究。     

Laboratory investigation of single floating booms a and series of booms in the prevention of oil slick and jellyfish movement

Laboratory experiments were carried out to test the effectiveness of single floating booms, and series of barriers in preventing oil slick and jellyfish movement under various current, wind, and wave conditions. Samples of Kuwait light crude, Kuwait heavy crude, and emulsified Kuwait heavy crude oil were selected for the test program. It was found that the single floating booms were only effective in preventing the oil slick movement at current speeds less than 0.15 m/s for emulsified oil and 0.25 nits for non-emulsified oil. Double floating booms (with a distance of 16 times the boom's draught between them) prevented both non-emulsified and emulsified oil movement when current speed was less than 0.25 nits. The double floating boom system had the best performance in containing oil slick movement.In the combined air-bubble barrier and floating boom system, the air-bubble plume lifted the jellyfish to the water's surface, and thus most jellyfish accumulated in front of the floating boom. With the help of a proper collection device (such as a suction pump), the accumulated jellyfish could be removed to a desired location. Therefore, the quantity of jellyfish moving into the intake channel was reduced.Based on the test results, three different arrangements were recommended for the protection Kuwait's water intakes and harbors from oil slick and jellyfish movement.     

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.     

Hydrodynamic characteristics of pile supported skirt breakwater models

Facilities for handling large draft vessels, modern container ships and tankers have become essential due to the rapid growth in marine traffic. A pile supported skirt breakwater (PSSB) is one of the most promising concepts that could fulfill this requirement as PSSBs are environment friendly and economical for locations where tidal fluctuations are large and soil conditions are poor compared to other types of conventional breakwaters. The structure consists of an impermeable barrier piercing the free surface and extending up to a certain depth of submergence. The barrier which is responsible for attenuating the incident waves through partial reflection is supported on closely spaced concrete or steel piles. The barrier would consist of pre-cast elements that are connected to the piles on site. A numerical model based on the Eigen function expansion theory for linear waves to investigate the reflection and transmission characteristics of a PSSB consisting of single and double rows has been developed. The wave run-up on the skirt of the front row as well as the oscillation of the water surface in between the two rows was also computed. The results on the above stated parameters are reported as a function of wave and structural parameters in a dimensionless form. The numerical results are compared with experimental results and the agreement in general is found to be good.     

Examination of Extraordinary Transmission of Waves Propagation through Gaps of Vertical Thin Barriers in Channels by A Hypersingular Boundary Element Method

The extraordinary transmission(ET) phenomenon is examined for waves propagating through gaps of vertical thin barriers in channels with a hypersingular boundary element method model on the linear potential theory, and an estimate formula based on small gap approximation for predicting the number of ET frequencies is proposed.Numerical computations are carried out to examine the influences of barrier number, barrier interval, gap size, gap position and barrier arrangement on extraordinary transmission and wave height in the channel. It shows that all of those factors evidently affect the extraordinary transmission frequencies. The contours of wave amplitude show that very high waves can be excited in the basins between barriers at the extraordinary transmission frequencies. Proper arrangement of barriers in a channel can avoid the occurrence of ET phenomenon and reduce wave height in the channel.     

分层流体中内孤立波在潜浮式竖直薄板上透射和反射

采用边缘层理论研究了两层流体系统中内孤立波在潜浮式竖直薄板上的透射和反射问题,提出了非线性演化方程的“初值”条件,分析了内孤立波与薄板非线性相互作用的效应。研究表明:流体层的密度比以及薄板伸入上下层的深度对于反射和透射波结构具有显著的影响,薄板伸入下层越深、密度差越小,则薄板阻碍孤立波透射的效率越高;透射波通常演化为单峰孤立波和迅速衰减的尾波,反射波演化为缓慢衰减的尾波列;对于具有小密度差的跃层结构,内孤立波在潜浮式竖直薄板上的透射及其演化近乎是无障碍的。     

On the Fifth-Order Stokes Solution for Steady Water Waves

This paper presents a universal fifth-order Stokes solution for steady water waves on the basis of potential theory. It uses a global perturbation parameter, considers a depth uniform current, and thus admits the flexibilities on the definition of the perturbation parameter and on the determination of the wave celerity. The universal solution can be extended to that of Chappelear (1961), confirming the correctness for the universal theory. Furthermore, a particular fifth-order solution is obtained where the wave steepness is used as the perturbation parameter. The applicable range of this solution in shallow depth is analyzed. Comparisons with the Fourier approximated results and with the experimental measurements show that the solution is fairly suited to waves with the Ursell number not exceeding 46.7.     

基于波高和周期双指标的福建海域海浪危险性分析

现行的海浪危险性评估方法仅以波高作为指标,没有考虑波浪周期对海上建筑物和船舶航行安全的影响。基于1979-2016年福建外海海浪数值后报结果,建立了基于周期的海浪强度和危险性等级划分标准,提出了基于波高和周期双指标的福建海域海浪危险性分析方法。结果表明,双指标下海浪危险等级分布结合了波高单指标下环状分布和周期单指标下带状分布的特点,以台湾海峡中南部海域海浪危险等级最高,闽南近岸海域海浪危险等级高于闽东和闽中海域,总体危险等级分布呈现南高北低的特征;双指标下的福建外海海浪危险等级分布比单指标考虑更为全面,不仅包含波高对结构物的影响还考虑了周期对浮式结构物和防波堤的作用,更加贴近真实情况下的海浪危险性特征。     

Scattering of oblique waves by permeable vertical flexible membrane wave barriers

The interaction of obliquely incident surface gravity waves with a vertical flexible permeable submerged membrane wave barrier is investigated in the context of three-dimensional linear water wave theory. From the general formulation of the submerged membrane barrier, the performance of bottom-standing, surface-piercing and fully extended membrane wave barriers are analyzed for various values of wave and structural parameters. The analytic solution of the physical problem is obtained using eigenfunction expansion method and a coupled boundary element-finite difference method has been used to get the numerical solution. In the boundary element method, since the boundary condition on the membrane barrier is not known a priori, the membrane response and velocity potentials are solved simultaneously using appropriate discretization with the help of finite difference scheme. The convergence of the analytic and numerical solution techniques is discussed. The study reveals that for suitable combination of wave and structural parameters, approximately (45–50)% incident wave energy can be dissipated irrespective of membrane barrier configurations. Further, in certain situations, nearly full wave reflection and zero transmission occur for all barrier configurations. The study will be useful in the design of flexible permeable membrane to act as an effective wave barrier for creation of tranquility zone in the marine environment.     

Wave Run-up on A Vertical Seawall Protected by An Offshore Submerged Barrier

Submerged barriers are constructed in coastal zones for shoreline or harbor protection or to prevent the beach erosion. In the present study, the wave run-up on a vertical seawall protected by a submerged barrier is analyzed. The physical configurations include a rigid barrier and a long channel of finite depth. For linear water waves, by matching the velocity along the barrier and along the gap, the systems of linear equations about the velocity potentials are obtained. The wave run-up is further analyzed for various settings of barrier height and distance between the barrier and the wall, i.e. the chamber length. For nonlinear waves and random sea waves, a numerical model is extended to investigate the effect parameters of the barrier on the wave run-up against the seawall. Not only the numerical simulations, but also the analytical results illustrate that the wave run-up on the seawall depends very much on the distance between the barrier and the vertical seawall.     

Steady drift force on vertical cylinder - viscous vs. potential

The contribution of the steady drift force on a floating structure may arise from waves, wind and current. The component of the wave drift force may be due to the second-order diffraction theory or potential effect and may be due to the velocity squared force or viscous effect. The presence of current in waves increases the effect of the viscous force. The expressions for these terms for a vertical cylinder are derived and their relative importance is investigated. Plots are presented showing the regions where the viscous or potential drift force predominates. Experiments were conducted with both small and large diameter cylinders. The mean drift forces obtained in these tests are compared with the theory.     

Numerical study of wave and longshore current interaction

Wave and longshore current interaction was examined based on the numerical models.In these models,water waves in the presence of longshore currents were modeled by parabolic mild slope equation,and wave breaking induced longshore currents were modeled by shallow water equation.Water wave provided the radiation stress gradients to drive current.Wave and longshore current interactions were considered by cycling the wave and longshore current models to a steady state.The experiments for regular and irregular breaking wave induced longshore currents by Hamilton and Ebersole（2001） and Reniers and Battjes（1997） were simulated.The numerical results indicate that the present models are effective for simulating the interaction of wave and breaking wave induced longshore currents,and the numerically simulated longshore current at wave breaking point considering wave and longshore current interaction show some disagreement with those neglecting the wave-current interaction,and the breaking wave induced longshore current effect on wave transformation is not obvious.     

Scattering of gravity waves by multiple surface-piercing floating membrane

Interaction of surface gravity waves with multiple vertically moored surface-piercing membrane breakwaters in finite water depth is analyzed based on the linearized theory of water waves. The study is carried out using least square approximation method to understand the effect of the vertical membrane as effective breakwater. Initially the problem is studied for a single membrane wave barrier but for the case of multiple membrane breakwaters the study is carried out using the method of wide-spacing approximation. In the present study, it is observed that the deflection of the membrane is reduced with the increase in the stiffness parameter of the mooring lines attached to the membrane. In the case of single surface-piercing membrane with moored and fixed edge conditions, the reflection and transmission coefficients are compared and analyzed in detail. The resonating pattern in the reflection coefficients are also observed for multiple floating membrane which can also be referred as Bragg's resonance. In the presence of the porosity constant the wave reflection is also observed to be decreasing and the change in the distance between the vertical floating breakwaters also helps in the attenuation of wave height. It is observed that the presence of multiple floating breakwater helps in the reduction of wave height in the transmitted region.     

Investigation on the Local Scour Beneath Piggyback Pipelines Under Clear-Water Conditions

A piggyback pipeline consists of two pipes such that the secondary line rides on the main pipe with a fixed distance between two pipes in length. The novel strategy is utilized in offshore areas instead of a single flow line. In this regard, there are only a handful of experimental and numerical studies investigating the effect of scour below a piggyback pipeline under steady current. Hence, this study focuses on examining the influential factors on scouring due to steady current including the pipe diameter and the gap between pipes through numerical simulations and experimental tests. Accordingly, at the first phase of the research, a single pipe was established and tested in laboratory to compare the results with those of an empirical equation. After finishing experimental verifications,piggyback pipelines were also assembled to study the scouring under steady current conditions. It was concluded that by increasing the gap distance between the pipes, the maximum scour depth decreases; however, an increase in the small pipe's diameter results in a larger maximum scour depth. Secondly, numerical simulations were carried out using the FLOW-3D software which was found to be a suitable tool for the numerical investigation of this study.Finally, the numerical results have been compared with the corresponding experimental data and a relatively good agreement was achieved between them.     

波流共同作用下珊瑚礁冠层附近平均流分布及阻力特性试验

本文通过物理模型试验研究了波流共同作用下珊瑚礁冠层附近平均流的分布特征以及阻力特性,分析了典型波浪工况下无潮流、正向潮流和反向潮流分别作用下平均流速、摩阻流速、阻力系数的沿礁变化规律。结果表明：无潮流时礁前斜坡及外礁坪上存在海底回流且在礁缘附近回流最强,在礁坪上冠层附近平均流表现为向岸流,且该流沿礁向海岸方向持续增大。相较于无潮流时,正向潮流作用下冠层内外均为向岸流,在礁坪上冠层内外的向岸流显著增大;反向潮流作用下冠层内外均为离岸流且在礁缘处达到最大,该离岸流在礁坪上逐渐减小然后趋于稳定。无潮流时礁坪上摩阻流速呈小幅波动;相较于无潮流时,正向潮流、反向潮流影响下礁坪上摩阻流速显著增大,其中正向潮流影响下增幅更大;无潮流时礁坪上水力粗糙度沿礁减小,正向潮流和反向潮流影响下水力粗糙度普遍有幅度不等的增加。三种工况下礁坪上的阻力系数均沿礁整体呈下降趋势,相较于无潮流时,正向潮流和反向潮流影响下礁坪上的阻力系数显著增大,且正向潮流作用时增幅更大。