Hydrodynamic characteristics of a single-row pile breakwater

The present paper extends the impedance analytical method to the study of the interaction of regular plane waves with a row of rectangular piles. The dissipative energy is estimated from the flow resistance for the row of piles. Formulas of wave reflection and transmission coefficients and the wave force for the row of piles are derived. Predictions obtained using the present model agree with experimental data in the literature.     

淹没矩形防波堤透反射系数特性研究

采用解析方法研究了斜向入射波作用下淹没矩形防波堤的透反射系数特性.首先利用特征函数展开法导出了绕射势函数的分析解和透反射系数的计算公式,然后利用边界元方法验证了解析解,在此基础上利用解析解分析了若干工况下的防波堤透反射特性.计算结果表明,淹没矩形防波堤截面的宽度、高度和相对位置以及入射角的改变都不同程度影响反射系数和透射系数.在中等深度条件下,对于一定频率的波浪,位置和尺寸适当的淹没矩形堤可以反射大部分斜向入射波.研究结果对设计淹没的矩形防波堤具有重要的参考价值.     

A model for obliquely incident wave interacting with a multi-layered object

This paper presents an analytical solution for scattering of oblique incident, small amplitude, monochromatic wave trains by a stationary rigid multi-layered objects with rectangular cross-section. The object is infinite long and consists of multilayers, which can be either solid or permeable. This paper extends the previous work by Hu and Liu [1] from normal incident wave condition with a special object configuration to oblique incident waves with multi-layered object. The present model is validated with several existing solutions for normal/oblique waves interacting with a single object; excellent agreement is observed. New numerical results are presented to investigate the effects of incidence angle on reflection, transmission and energy loss coefficients for a combined floating and bottom-mounted permeable breakwater. A new floating board-cage breakwater is developed from the present model and its solutions are discussed in detail. A computer program, AWAS-P, has been updated so that it is applicable for both oblique and normal incident waves, while the object is multi-layered.     

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.     

斜向波浪入射角和反射系数确定方法

在海岸工程和水池实验中常常需要同时确定斜向波浪的传播方向和与海岸结构物相遇时的反射系数。应用三点浪高仪测波和迭代求解方法,建立了同时确定斜向波浪入射角和反射系数的分析方法。通过模拟数值信号,研究了测点不同排列方式、不同波浪入射方向、不同入射频率下本方法的分析灵敏程度。数值研究表明当测点间距指标p和q不同时趋于零时,任何一种排列方式求得的波浪反射系数和波浪入射角均具有很高的分析精度。     

Full wave solution for hydrodynamic behaviors of pile breakwater

Rayleigh expansion is used to study the water-wave interaction with a row of pile breakwater in finite water depth. Evanescent waves, the wave energy dissipated on the fluid resistance and the thickness of the breakwater are totally included in the model. The formulae of wave reflection and transmission coefficients are obtained. The accuracy of the present model is verified by a comparison with existing results. It is found that the predicted wave reflection and transmission coefficients for the zero order are all highly consistent with the experimental data (Hagiwara, 1984; Isaacson et al., 1998) and plane wave solutions (Zhu, 2011). The losses of the wave energy for the fluid passing through slits play an important role, which removes the phenomena of enhanced wave transmission.     

桩列透空堤的水动力计算

分析了平面渡与桩列透空堤的相互作用.根据对矩形桩列上力平衡原理和非线性流阻等水动力学特征分析,导出一组计算反射、传递系数和波浪荷载的理论公式.计算公式内所有参数均是已知的,用它们预测的结果与现有的试验数据很好吻合.     

波浪反射系数谱的特征分析

应用斜向不规则波反射系数的改进两点法(MTPM),用模型试验研究了混凝土护面堤和块石护面堤波浪反射系数的频率谱和方向谱,结果表明,分析的反射系数随入射波频率的增加、结构坡度的减小和入射角的加大而减小.给出了波浪反射系数频率谱及其随Iribarren数变化的规律,提出了反射系数三维谱的经验公式,由此可定量地描述斜向不规则波的反射系数随无量纲特征参数Iribarren数和入射波角度的变化规律.     

开孔沉箱与斜向波作用的理论研究和实验验证

应用透空壁内流体速度与壁两侧的压力差成正比的线性模型,研究了无限多个开孔沉箱在斜向波作用下的反射问题。整个流域被分成无限多个子域,在每个子域内应用特征函数展开法对速度势进行展开。对于沉箱内的波浪运动,根据沉箱位置引入相位差概念。在构造反射波模型时,考虑了结构物几何形状周期性的影响。结果表明,当孔隙系数无限大时,开孔墙前后的速度非常接近,反射系数符合能量守恒定律。在低频入射波作用下,沉箱越短,其反射系数越小,反射系数随着角度的变大而减小。     

Wave Reflection Coefficient Spectrum

1 .IntroductionWavereflectionfromstructuresisanimportantfactorforthedesignofthestructures .Therehavebeenmanyresearchesonwavereflectionwithregularwavesandmonochromaticirregularwaves .Miche( 1 951 )proposedanon dimensionalMichenumberMfornormallyincidentirregularwavesconsideringwavebreakingbecauseofthedeepeningofwavesteepnessontheslopeofbreakwaters .ThereflectioncoefficientisproportionaltoM ,i.e .,Kr ∝M =4g( 2π) 5/ 2tan5/ 2 α(Hsf2p) ( 1 )wheregisthegravitationalacceleration ,Hsthesignifican…     

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.     

Interaction of flexural gravity waves with shear current in shallow water

In the present study, the effect of shear current on the propagation of flexural gravity waves is analyzed under the assumptions of linearized shallow-water theory. Explicit expressions for the reflection and transmission coefficients associated with flexural gravity wave scattering by a step discontinuity in both water depth and current speed are derived. Further, trapping and scattering of flexural gravity waves by a jet-like shear current with a top-hat profile are examined and certain limiting conditions for the waves to exist are derived. The effects of change in water depth, current speed, incident wavelength and the angle of incidence on the group and phase velocities as well as on the reflection and transmission characteristics are analyzed through different numerical results.     

基于类海啸波型的岛礁水动力特性数值模拟研究

基于非静压单相流模型NHWAVE建立了高精度二维数值波浪水槽,采用日本2011年实测真实海啸波型系统研究了海啸波在岛礁上传播变形的规律,并且分析了波高、礁坪淹没水深和礁前斜坡坡度等因素对孤立波和真实海啸传播变形的影响。结果表明,相比孤立波,类海啸波的波长明显大于孤立波波长,在测点处引起的水面变化持续时间更长,同等波高情况下真实海啸波型比孤立波能够携带更多的能量,与岛礁的相互作用也更为复杂,在礁坪上形成的淹没水深约为孤立波的两倍。礁前斜坡坡度和礁坪淹没水深均对类海啸波的反射和透射系数有显著影响。随着礁前斜坡坡度的增加,反射系数和透射系数均逐渐增加。随着礁坪淹没水深的增加,反射系数逐渐减小,而透射系数逐渐增大。但是,反射系数和透射系数均随着入射波高的增加而逐渐减小。     

Long Wave Reflection and Transmission over A Sloping Step

This investigation examines long wave reflection and transmission induced by a sloping step. Bellman and Kalaba‘s (1959) invariant imbeddlng is introduced to find wave reflection. An alternative method matching both the surface elevation and its surface slope of each region at the junction is applied to the determination of wave reflection and transmission.The proposed methods are compared with the accurate numerical results of Porter and Porter (2000) and those of Mei (1983) for a vertical step. The wave reflection obtained for a mildly sloping step differs significantly from the result of Mei. The wave reflection is found to fluctuate owing to wave trapping for the ntild sloping step. The height and the face slope of the step are important for determining wave reflection and transmission coefficients.     

双矩形浮子波能装置辐射问题的解析方法

在有限水深下1个漂浮在水中的矩形浮子和1个淹没在水下的浮子构成双矩形波能装置模型。基于特征函数展开法求解了线性入射波作用下双矩形浮子波能装置的辐射问题,得出了双矩形浮子辐射速度势的1种新解析式,然后根据Haskind关系由入射势和辐射势来计算波浪激励力,并且采用数值方法对相同算例进行了计算,得到了完全一致的结果,从而证明这种方法是正确的。研究了在不同工况下的波浪激励力和系统的水动力学系数变化的规律。     

Oblique Wave Scattering by An Undulating Porous Bottom in A Two-Layer Ice-Covered Fluid

The present study analyzes the reflection and transmission phenomenon of water-waves in a two-layer ice-covered system. The upper layer is covered by an ice-sheet, whereas the bottom of the lower layer is undulated and permeable. By using regular perturbation analysis and Fourier transform technique, the problem is solved and the first order reflection and transmission coefficients are determined. It is found that these coefficients depend on the shape as well as the permeability of the undulating bottom. Therefore, from the practical viewpoint, an undulating bottom topography is considered to determine all the aforesaid coefficients. The role of various system parameters, such as porosity, angle of incidence and ice parameters, are discussed to analyze the transformation of incident water wave energy from one layer to another layer. The outcomes are demonstrated in graphical forms.     

Modelling of Random Waves over Submerged Breakwaters and Its Application to Reflection Estimation

1.IntroductionGreat efforts have been devoted to the protection of coastal areas over many years by erectingdikes,seawalls,groin systems,and detached breakwaters.The sea walls,jetties,detached breakwa-ters,etc.are traditionally adopted as absorbingfacilit…     

Interaction of oblique waves with infinite number of perforated caissons

An analytic solution based on the division of the fluid domain is developed for the interaction of obliquely incident waves with infinite number of perforated caissons. The whole fluid domain is firstly divided into infinite sub-domains according to the division of structures, and subsequently eigenfunction expansion is employed to represent the velocity potential in each domain. A phase relation is utilized for the analysis of wave oscillation in each caisson, and the character of structure geometry is considered in setting up the mathematical model of reflection waves. The reflection waves from the present analysis include many propagation waves traveling in different directions when the incident wave frequency is high. Benchmark examinations show that the continuous condition of water particle velocity is satisfied at the front walls of caissons, and the reflection coefficients keep agreement with the energy conservation relation very well when porous effect parameter is infinite. Numerical results show that the reflection coefficients of obliquely incident waves are smaller when the length of caissons is shorter at low frequency. The wave reflection coefficients and the wave forces normal to caissons decrease and the wave forces along caissons increase with the increase of the wave incident angle.     

A Numerical Investigation of the Reduction of Solitary Wave Runup by A Row of Vertical Slotted Piles

To improve the current understanding of the reduction of tsunami-like solitary wave runup by the pile breakwater on a sloping beach, we developed a 3D numerical wave tank based on the CFD tool OpenFOAM in this study. The Navier Stokes equations were applied to solve the two-phase incompressible flow, combined with an LES model to solve the turbulence and a VOF method to capture the free surface. The adopted model was firstly validated with existing empirical formulas for solitary wave runup on the slope without the pile structure. It is then validated using our new laboratory observations of the free surface elevation, the velocity and the pressure around a row of vertical slotted piles subjected to solitary waves, as well as the wave runup on the slope behind the piles. Subsequently, a set of numerical simulations were implemented to analyze the wave reflection, the wave transmission, and the shoreline runup with various offshore wave heights, offshore water depths, adjacent pile spaces and beach slopes. Finally, an improved empirical equation accounting for the maximum wave runup on the slope was proposed by taking the presence of the pile breakwater into consideration.     

Analytical method of radiation by a wave energy device with dual rectangular floating bodies

The system with one floating rectangular body on the free surface and one submerged rectangular body has been applied to a wave energy conversion device in water of finite depth. The radiation problem by this device on a plane incident wave is solved by the use of an eigenfunction expansion method, and a new analytical expression for the radiation velocity potential is obtained. The wave excitation force is calculated via the known incident wave potential and the radiation potential with a theorem of Haskind employed. To verify the correctness of this method, an example is computed respectively through the bound element method and analytical method. Results show that two numerical methods. are in good agreement, which shows that the present method is applicable. In addition, the trends of hydrodynamic coefficients and wave force are analyzed under different conditions by use of the present analytical method.