Revisiting the complete wave transmission and reflection due to an array of 2-D surface-piercing truncated vertical plates fixed in regular incident waves

When two 2-D vertical surface-piercing plates are fixed with a certain distance in incident regular waves, it is known that complete wave transmission and reflection could take place, at least in a linear wave theory, depending on the wave period of the incident waves. This paper revisits the same subject from the viewpoint of the hydrodynamic interaction between the two plates induced by the waves transmitted and reflected due to the plates, which is enabled by accounting for the hydrodynamic interactions between the two plates while decomposing the waves into component waves. In doing so, some new insight into the mechanism of the complete transmission and the complete reflection has been obtained.     

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.     

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.     

On the radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas

The radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas of finite depth is investigated. The analytical expressions for the radiated and diffracted potentials are derived as infinite series by use of the method of separation of variables. The unknown coefficients in the series are determined by the eigenfunction expansion matching method. The expressions for wave forces, hydrodynamic coefficients and reflection and transmission coefficients are given and verified by the boundary element method. Using the present analytical solution, the hydrodynamic influences of the angle of incidence, the submergence, the width and the thickness of the structure on the wave forces, hydrodynamic coefficients, and reflection and transmission coefficients are discussed in detail.     

台阶型海脊俘获波的实验研究

基于物理模型实验研究瞬态冲击波在台阶地形上传播过程,揭示由于反射而在海脊上出现的波浪俘获现象。结果表明:在瞬态波产生区域附近,海脊上所测到的先导波即为最大波,其由泄漏至海脊外的深水波绕射至海脊所致。随着传播距离的增加,由于频散效应的影响,先导波逐渐减小,沿台阶近似直线传播的海脊俘获波和在台阶上曲折传播的海脊俘获波逐渐显现。在距离波浪产生较远区域所测的最大波晚于先导波出现,且这些由俘获波所叠加而成的最大波随着传播距离的增加而呈现出更加复杂的波面过程。     

Coupled modeling of currents and wind waves in the Kerch Strait

We present a numerical model of the dynamics of the Kerch Strait allowing one to perform the coordinated analysis of the fields of currents and wind waves. The model includes the spectral wave module and the hydrodynamic block of currents. The influence of waves on the currents is taken into account in the hydrodynamic block both via the surface and bottom tangential stresses and via the radiation stresses. In order to take into account the inverse influence of currents upon the waves, we use the fields of currents and sea level from the hydrodynamic block in the wave module. The specific features of the structure of currents and wind waves in the strait are studied for the typical wave situations. The results of the coupled and separate simulation are compared and the importance of taking into account the mechanisms of interaction between waves and currents in the analysis of the dynamic processes in the strait is demonstrated. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 3–20, September–October, 2007.     

An Efficient Model for Transient Surface Waves in Both Finite and Infinite Water Depth

A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Eulerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunction with an image Green function is used for the fluid domain. The boundary values on the free surface are updated at each time step by a fourth-order Runga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropriate wave theory. At the downstream boundary, an artificial damping zone is used to prevent wave reflection back into the computational domain. Using the image Green function in the whole fluid domain, the integrations on the two lateral walls and bottom are excluded. The simulation results on extreme wave elevations in finite and infinite water-depths are compared with experimental results and second-order analytical solutions respectively. The wave kinematics is also discussed in the present study.     

An Extended Mild-Slope Equation

On the assumption that the vortex and the vertical velocity component of the current aresmall,a mild-slope equation for wave propagation on non-uniform flows is deduced from the basichydrodynamic equations,with the terms of (V_hh)~2 and (V_h~2)h included in the equation.The terms of bot-tom friction,wind energy input and wave nonlinearity are also introduced into the equation.The wind en-ergy input functions for wind waves and swells are separately considered by adopting Wen′s(1989)empiri-cal formula for wind waves and Snyder′s observation results for swells.Thus,an extended mild-slope equa-tion is obtained,in which the effects of refraction,diffraction,reflection,current,bottom friction,wind en-ergy input and wave nonlinearity are considered synthetically.     

Water wave interaction with a floating porous cylinder

The interaction of water waves with a freely floating circular cylinder possessing a side-wall that is porous over a portion of its draft is investigated theoretically. The porous side-wall region is bounded top and bottom by impermeable end caps thereby resulting in an enclosed fluid region within the structure. The problem is formulated based on potential flow and linear wave theory and assuming small-amplitude structural oscillations. An eigenfunction expansion approach is then used to obtain semi-analytical expressions for the hydrodynamic excitation and reaction loads on the structure. Numerical results are presented which illustrate the effects of the various wave and structural parameters on these quantities. It is found that the permeability, size and location of the porous region may have a significant influence on the horizontal components of the hydrodynamic excitation and reaction loads, while its influence on the vertical components in most cases is relatively minor.     

NWF: Propagation of Tsunami and its Interaction with Continental Shelf and Vertical Wall

In this article, tsunamis represented as solitary waves was simulated using the fully nonlinear free surface waves based on Finite Element method developed by Sriram et al. (2006). The split up of solitary wave while it propagates over the uneven bottom topography is successfully established. Wave transmission and reflection over a vertical step introduced in the bottom topography is in good agreement with the experimental results from Seabra-Santos et al. (1987). The wave transformation over a continental shelf with different smooth slopes reveals that the solitary wave reflection increases while the continental slope varies from flat to steep. The interaction of the solitary wave with a vertical wall for different wave steepness has been analysed. The reflected shape of the profile is in good agreement with the observation made by Fenton and Rienecker (1982) and an increase in wave celerity is observed.     

Draft effect on wave action with a semi-infinite elastic plate

1Introduction Wave action on coastal and offshore structuresis investigated by many researches. In the recent pa-pers we can seen that Li et al. (2006) developed athree-dimesional(3D) numerical model for obliquewave action on vertical walls, Li et al. (20…     

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.     

Wave characteristics past a flexible fishnet

The scattering of surface waves by a flexible fishnet is studied analytically. The fishnet is modelled as a porous flexible barrier displaced solely by hydrodynamic force like a catenary. The objective is to investigate how a flexible permeable barrier affects the passing waves in the way they are transmitted and reflected, as observed by the fact that the water inside a fishfarm surrounded by fishnets is significantly calmer than that outside. The boundary value problems are solved by defining the reflection coefficient in terms of velocity potential and then the full solutions are obtained by suitable application of the eigenfunction expansion method and the least squares approximation method. The variations of the reflection coefficient, hydrodynamic pressure, barrier deformation and surface wave elevation are determined with respect to the barrier length, porosity and stiffness. It is observed that as the fishnet gets more flexible, its deformation increases and the reflection coefficient decreases, whereas as the fishnet gets more porous, more water can pass through it and thus the reflection coefficient, barrier deformation and the hydrodynamic force are reduced. The flexibility of the barrier behaves like its porosity by allowing more wave energy to act on it through its deformation and hence reduce the reflection and hydrodynamic force of the incident waves acting on the barrier.     

前板可旋转的双垂板结构水动力特性的理论研究

振荡水柱波能转换装置的最大转换效率往往受到腔内水柱共振机制的直接影响。通过对装置的基本结构进行简化,提出了一种前墙可绕固定轴旋转的双垂板式结构系统,旨在通过前墙的旋转运动进一步加剧水柱的振荡,从而对腔内水柱的共振机制进行调节和控制。基于线性波理论,采用匹配特征函数展开法对波浪与双垂板结构的相互作用进行理论研究,针对流场在结构物尖角附近的奇异性特征,将公共界面上的速度分布基于切比雪夫多项式近似展开,并应用区域间的速度与压力连续条件进行求解。通过分析结构的几何参数对反射透射系数、平均波面高程、前墙旋转振幅以及前墙与水面间相位差的影响,深究其共振机理,为振荡水柱波能转换装置的效率优化机制提供理论依据。结果表明,在所研究的波浪频率范围内,前墙的自由旋转运动会加剧板间的平均波面高程,应用于波浪能转换装置中能进一步拓宽高效频率带宽。     

Interaction between waves and an array of floating porous circular cylinders

The present study theoretically as well as experimentally investigates the interaction between waves and an array of porous circular cylinders with or without an inner porous plate based on the linear wave theory.To design more effective floating breakwaters,the transmission rate of waves propagating through the array is evaluated.Each cylinder in the array is partly made of porous materials.Specifically,it possesses a porous sidewall and an impermeable bottom.In addition,an inner porous plate is horizontally fixed inside the cylinders.It dissipates the wave more effectively and eliminates the sloshing phenomenon.The approach suggested by Kagemoto and Yue(1986) is adopted to solve the multiple-scatter problem,while a hierarchical interaction theory is adopted to deal with hydrodynamic interactions among a great number of bodies,which efficiently saves computation time.Meanwhile,a series of model tests with an array of porous cylinders is performed in a wave basin to validate the theoretical work and the calculated results.The draft of the cylinders,the location of the inner porous plate,and the spacing between adjacent cylinders are also adjusted to investigate their effects on wave dissipation.     

东山湾波浪对悬沙浓度场影响的数值模拟研究

研究了波致底切应力和二维辐射应力对悬沙的作用.首先对东山湾的水动力进行了数值模拟并与实测资料进行了对比检验,然后对东山湾悬浮泥沙进行了考虑波浪和不考虑波浪两种情况下的数值模拟并与实测资料进行了相关对比分析.在模式建立过程中,依据东山湾独特的窄口型半封闭河口海湾的特点,基于ECOMSED模式（2002）建立了东山湾三维水动力模型,并通过第三代海浪模式MASNUM加入了波浪对底切应力及辐射应力的影响,通过ECOMSED中的底边界层模型考虑了波浪增强底摩擦的作用,综合分析了东山湾的水动力及泥沙状况.结果表明在东山湾数值模拟中,该模式能较好地模拟这类海域的水动力及泥沙输运状况.在东山湾模拟计算中,潮流的作用强于波浪的作用,但考虑波浪因素后,泥沙模拟结果更好.在波浪的作用中,底切应力相比于二维辐射应力占有绝对的优势,两者相差2个量级以上,因此可以不考虑二维辐射应力的影响.     

A new model for surface wave propagation over undulating topography

A new model is presented for the propagation of monochromatic surface waves over a region of arbitrary, one-dimensional bottom topography. The smoothly varying bed profile is divided into a series of shelves separated by abrupt steps. The wave fields on either side of each step are related by a “transfer matrix”, and the propagation of waves along the shelf between adjacent steps is described by a “rotation matrix”. Starting from a point where the surface wavefield is known, the step by step application of the appropriate combination of these matrices allows computation of the wavefield over the region of interest. If the individual steps are small then the transfer matrix reduces to a simpler plane-wave form, with considerable savings in computational effort. Comparisons are made with an exact potential solution for single and double steps in order to investigate the accuracy and validity of the matrix method. Finally, the model is applied to the case of wave reflection by fixed sinusoidal bottom undulations, and good agreement is found between its predictions and existing laboratory data.     

Transmission and reflection of the Rossby waves in a stratified ocean with bottom topography

Transmission and reflection coefficients are calculated for Rossby waves incident on a bottom topography with constant slope in a continuously stratified ocean. The characteristics of the coefficients are interpreted in terms of the quasigeostrophic waves on the slope. In the parameter range where only the barotropic Rossby waves can propagate in the region outside the slope, the bottom trapped wave plays the same role as the topographic Rossby wave in a homogeneous ocean, and hence the transmission is weak unless phase matching takes place. When both of the barotropic and baroclinic Rossby waves can propagate outside the slope, the total transmission can be strong. The bottom trapped wave affects the transmission and reflection, and it leads to the possibility that the Rossby wave is transmitted as a mode different from the incident mode. When the number of the wavy modes on the slope is smaller than that of the Rossby wave modes outside the slope, strong reflection occurs.The results for an ocean with linear distribution of the squared Brunt-Väisälä frequency are compared to those in a uniformly stratified ocean. The weakening of the stratification near the bottom is almost equivalent to reducing the effect of the slope.     

Momentum balance in shoaling gravity waves: Comment on ’shoaling surface gravity waves cause a force and a torque on the bottom’ by K. E. Kenyon

In a recent paper, Kenyon (2004) proposed that the wave-induced energy flux is generally not conserved, and that shoaling waves cause a mean force and torque on the bottom. That force was equated to the divergence of the wave momentum flux estimated from the assumption that the wave-induced mass flux is conserved. This assumption and conclusions are contrary to a wide body of observations and theory. Most importantly, waves propagate in water, so that the momentum balance generally involves the mean water flow. Although the expression for the non-hydrostatic bottom force given by Kenyon is not supported by observations, a consistent review of existing theory shows that a smaller mean wave-induced force must be present in cases with bottom friction or wave reflection. That force exactly balances the change in wave momentum flux due to bottom friction and the exchange of wave momentum between incident and reflected wave components. The remainder of the wave momentum flux divergence, due to shoaling or wave breaking, is compensated by the mean flow, with a balance involving hydrostatic pressure forces that arise from a change in mean surface elevation that is very well verified by observations.     

Approximation to the hydrodynamics of floating pontoons under oblique waves

The hydrodynamic properties of long rigid floating pontoon interacting with linear oblique waves in water of finite arbitrary depth are examined theoretically. The flow is idealized as linearized, velocity potentials are expressed in the form of eigen-function expansions with unknown coefficients. The fluid domain is split into three regions, region (1) wave-ward of the structure, region (2) in the lee of the structure, and region (3) beneath the structure. The different hydrodynamic quantities of interest such as the exciting forces, added mass and damping coefficients, reflection and transmission coefficients were studied for an applicable range of wave/structure parameters. Assuming rigid body motions, dynamic responses of the moored structure is approximately calculated through three equations of motion. Floating pontoons proved to be a convenient alternative for protection from waves in shallow water. The present method of solution was found to be computationally efficient, and results are comparable to those obtained through other techniques.