ANALYTICAL RESEARCH ON THE WAVE DIFFRACTION OF ARC-SHAPED FLOATING BREAKWATERS

1. INTRODUCTIONBreakwaters are generally constructed for thedissipation and reflection of incident wave energyin order to decrease the wave height to protect thecoast against the erosion and to decrease the forceacting on the coastal structures . Compared…     

THE RADIATION AND DIFFRACTION OF WATER WAVES BY A BOTTOM-MOUNTED CIRCULAR CYLINDER IN A TWO-LAYER FLUID

An analytical method was proposed to analyze the radiation and diffraction of water waves by a bottom-mounted circular cylinder in a two-layer fluid. Analytical expressions for added mass and damping coefficients, as well as the wave excitation forces of the circular cylinder were obtained by an eigenfunction expansion method. The hydrodynamic forces on the bottom-mounted circular cylinder in a two-layer fluid include not only the added mass and damping coefficients, but also the wave forces of the surface and internal-wave modes. This is different from the case of a homogenous fluid. Some examples were given, showing that density stratification can have a relative large effect on these hydrodynamic forces over a wide range of frequencies.     

WAVE DIFFRACTION ON ARC-SHAPED BOTTOM-MOUNTED BREAKWATERS

1. INTRODUCTION Various types of breakwaters are common coastal structures to shelter harbors and s mall crafts fromthe direct attack of waves . Of these , the arc-shaped bottom-mounted breakwater is com- mon. This type of breakwaters , whose horizontal section is an arc shape ,is usually situated on the seabed and extended to above the water surface . Many researchers have performed a variety of studies on the wave diffraction performance of many kinds of breakwaters . Penney and Price …     

ANALYTIC SOLUTION FOR WAVE DIFFRACTION OF A SUBMERGED HOLLOW SPHERE WITH AN OPENING HOLE

An investigation is carried out on the interaction of surface waves with a submerged sphere having an opening hole in finite-depth water in this article. Based on the linear wave theory, the method of multipole expansions is used to obtain the fluid velocity potential in the form of double series of the associated Legendre functions with the unknown coefficients of an infinite set. In terms of the body surface boundary condition and the matching condition between the inner and outer flows at the hole, the complex matrix equations for the coefficients of the series are established. The infinite sets of matrix equations are solved by truncating the series at a finite number. The hydrodynamic pressure on the structure surface and the exciting forces acting on the structure are graphically presented. The dynamic pressure on the wave front surface of the sphere varies slightly with angle of opening hole increasing, while that on the wave back surface does obviously. When the angles of opening hole are increasing, the absolute values of the complex exciting forces tend to fall as a whole.     

V形贯底式防波堤上波浪作用力的解析研究

用解析方法计算V形贯底式防波堤在波浪绕射作用下周围流域任意点的速度势,研究波浪作用在V形贯底式防波堤上的波浪力。假定防波堤刚性、薄壁、不透浪、水深恒定。假想的圆柱面将整个流场划分为三个区域,分别在每个区域内将速度势用特征函数展开,然后在公共边界上按照速度连续,速度势连续的原则进行匹配,求得流域中任意一点的速度势和作用在V形贯底式防波堤上的总波力和总波力矩。数值结果给出了作用在防波堤上的波浪力随防波堤张角、入射波波长、入射角变化的曲线。结果表明:作用在V形贯底式防波堤上的波浪力与水深、防波堤的张角、入射波的波长等因素有关。     

水平多孔板导致之近岸陷波

在本文中，利用线性水波理论和本征函数展开方法，我们研究了附有一沉放在一定深度水下的水平多孔介质板之垂直岸壁的水波反射问题，数值模拟了水平多孔板的消浪特性，我们发现，通过在岸会加一水平的多孔人质薄板之后，将增加近岸处波浪反射和散射过程的复杂性，导致陷波现象发生，具有恰当可渗性能的多孔介质薄板将具有消浪特性，这时板的行为就象一个波浪吸收器一样，从而减少了岸壁的反射能力，降低了岸壁处及其临近的波高，板越     

Scattering of gravity waves by a porous rectangular barrier on a seabed

Within the frame of linear potential flow theory, the impact of a porous rectangular barrier on a seabed on the dynamic characteristics of gravity waves is investigated. The porous barrier can be regarded as an abstract representative such as a seabed plant, a wave breaker, inhomogeneous topography, and trussed supporting of ocean engineering platform, etc. In the process of mathematical modeling, the method of matched eigenfunction expansions is employed for analysis, where a newly defined form of inner product is introduced to improve the simplicity of derivation. Under this definition, the inner product is automatically orthogonal, which will provide great simplification to obtain the expansion coefficients. Once the wave numbers for the fluid region and the barrier region are obtained, the reflection and transmission coefficients of the wave motion can readily be calculated.     

多层水平板衰减波浪的影响因素分析

基于线性波浪理论,进行多层水平板对波浪的反射和透射作用研究。通过分解速度势为对称势和反对称势,结合特征函数展开法,在考虑水平板厚度的条件下由匹配条件确定速度势展开式中的待定系数,进而得到结构对波浪的反射系数和透射系数。所得结果与现有相关的理论解、数值解以及试验结果吻合较好。对相对水深、相对宽度、相对厚度以及水平板层数等对结构衰减波浪的影响进行了深入探讨和分析,给出了反射系数和透射系数随上述参数的变化规律。     

FINITE ELEMENT ANALYSIS OF A VERTICAL RECTANGULAR PLATE COUPLED WITH AN UNBOUNDED FLUID DOMAIN ON ONE SIDE USING A TRUNCATED FAR BOUNDARY

The dynamic pressure distribution on a rectangular plate attached to a rigid wall and supporting an infinitely large extent of fluid subjected to a harmonic ground excitation is evaluated in the time domain. Governing equations for the fluid domain are set considering the compressibility of the fluid with negligibly small change in density and a linearized free surface. A far boundary condition for the three-dimensional fluid domain is developed so that the far boundary is truncated at a closer proximity to the structure. The coupled problem is solved independently for the structure and the fluid domain by transferring the acceleration of the plate to the fluid and pressure of the fluid to the plate in sequence. Helmholtz equation for the three-dimensional fluid domain and Mindlin's theory for the two-dimensional plate are used for the solution of the interacting domains. Finite element technique is adopted for the solution of this problem with pressure as nodal variable for the fluid domain and displacement for the plate. The time dependent equations are solved in each of the interacting domain using Newmark-b method. The effectiveness of the technique is demonstrated and the influences of surface wave, exciting frequency and flexibility of the plate on dynamic pressure are investigated.     

NUMERICAL STUDY OF SQUARE-STERN SHIP WAVE IN SHALLOW WATER

This paper employed shallow water equations with moving pressure to calculate water waves generated by a square-stern ship in shallow water. The moving ship is considered as moving pressure on free surface. The finite element method with moving grids is used to solve the shallow water equations based on wave equation model [3]. A non-reflection boundary condition [5]is imposed on open boundaries surrounding the ship. 3-D surface elevations, depth-averaged horizontal velocities are presented. The numerical solutions are physically reasonable. It is found that wave resistance coefficients, draftchange and pitch angle vary rapidly in neighborhood of critical flow (Fh=u/ gh= 0. 9 -1. 1). The numerical results also indicate that the wave resistance coefficients, draft change and pitch angle of square-stern ship are larger than those of sharp-stern ship with the same hull structure at the same speed.     

AN INVERSE PROBLEM OF WATER WAVE GENERATION IN A WAVE TANK

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WAVE MOTION OVER TWO SUBMERGED LAYERS OF HORIZONTAL THICK PLATES

This study investigates the hydrodynamic performance of a submerged two layer horizontal plate breakwater. The plate thickness is considered as non-zero in the study. In the context of linear potential theory, an analytical solution for interaction of water waves with the plates is obtained using the matched eigenfunction expansion method. The solution consists of a symmetric part and an antisymmetric part. Its validity is confirmed by comparing the numerical results of reflection and transmission coefficients for limiting cases with previous predictions. Numerical examples are given to examine the major factors that affect the reflection and transmission coefficients of the plates. Some useful results are presented for engineering design.     

AN ASYMPTOTIC SOLUTION OF VELOCITY FIELD IN SHIP WAVES

1. INTRODUCTION It is well known that behind the ships, V-shaped steady-state ship waves are created while ships move on the water. The classical Kelvin ship wave pattern, which is obtained when a ship is taken as a point impulse moving at a constant velo…     

NUMERICAL SIMULATIONS OF NONLINEAR WAVES OVERTOPPING AN OBSTRUCTION

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AN IMPROVED NUMERICAL METHOD FOR CALCULATIONS IN WAVE KINEMATICS

The prediction of wave kinematics is a necessary basis for ocean engineering design. In this article, an improved method to calculate the wave kinematics especially in the crest region is presented. This method is based on the local approximation method. According to one measured wave surface, the proposed solution focuses on a Fourier series expansion in a somewhat larger segment of the wave surface record. The horizontal and vertical kinematics under the wave crest can be directly predicted. Good agreement between the numerical results and the theoretical Stokes waves verifies the validity of the numerical model. The effectiveness of the numerical method is also proved by the calculation of the wave kinematics of the laboratory focused wave groups.     

水平斜插板透空式防波堤消波性能数值模拟

通过改进已有的防波堤模型，建立了一种新型水平斜板透空式防波堤模型。基于VOF方法建立了波浪与水平斜板防波堤相互作用的数值模型。经数值模拟研究了该新型水平斜板防波堤结构对波浪透射系数的影响，主要考虑了斜板角度、波陡、相对板间距、相对板宽和相对出水高度等因素对防波堤消波效果的影响。模拟结果显示:①水平斜插板透空式防波堤比水平板透空式防波堤的消波效果好。在斜插板作用下，随着斜板角度增大，透射系数逐渐增大，但增幅逐渐减小；②随着波陡增大，透射系数先减后增；③随着水平板间距增加，透射系数增大；④随着防波堤相对板宽的增大，透射系数逐渐减小；⑤随着防波堤出水高度增加，透射系数先减后增。结果表明，该新型结构防波堤的消波效果显著，可以很好地消减波浪，应用前景良好。     

THREE-DIMENSIONAL NUMERICAL SIMULATION OF WAVE SLAMMING ON AN OPEN STRUCTURE

The three-dimensional numerical simulation of wave slamming on an open structure in the splash zone is carried out based upon the Volume Of Fluid (VOF) method.A wave basin is established by solving the...     

NUMERICAL STUDY OF SOLITARY WAVE FISSION OVER AN UNDERWATER STEP

Solitary wave fission over an underwater step is numerically investigated. The numerical model is based on the enhanced Boussinesq equations, which appropriately represent both the nonlinearity and dispersivity of surface water waves. The finite difference method defined on the staggered grid in space with an implicit scheme for time stepping is employed for the numerical solution of the governing equations. It is demonstrated that Boussinesq type equations, though they are vertically integrated, can describe the details of the solitary wave fission process with very good accuracy. Numerical results of the reflected and transmitting wave heights, the number of solitons emitted from the transmitting wave and their amplitudes all agree very well with the analytical solution derived from KdV equation by virtue of a linear long wave approximation in the vicinity of the underwater step.     

THE VOF METHOD FOR STUDY OF WAVE RUN-UP AND BREAKING ON A SLOPING STRUCTURE

The volume of fluid method(VOF method)for numerical simulations describing wave run-up on a sloping structure including the overturning,breaking and.merging phenomena is presented.The flow motions are governed by the classical,two-dimen-sional Navier-Stokes equation for incompressible fluid.Computational results concerning the time evolution of the free surface and pressure distribution along water bed and slope boundary are given,showing how an initial solitary wave undergoes run-up,overturning,breaking and merging on the slope.It is found that most of the wave energy is lost after the wave breaking and merging.     

Numerical study of the wave-induced slamming force on the elastic plate based on MPS-FEM coupled method

Slamming is the phenomenon of structure impacting the water surface. It always results in the extremely high load on the structure. This paper is mainly concerned with the slamming force caused by the wave-plate interaction. In this paper, the process of solitary wave impacting onto the horizontal plate is simulated with the help of the moving particle semi-implicit and finite element coupled method(MPS-FEM). The MPS method is adopted to calculate the fluid domain while the structural domain is solved by FEM method. In the first series of simulations, the profiles of the solitary waves with various amplitudes, which are generated in the numerical wave tank, are compared with the theoretical results. Thereafter the interaction between the solitary waves and a rigid plate is simulated. The effects of wave amplitude, as well as the elevation of the plate above the initial water level, on the slamming force are numerically investigated. The calculated results are compared with the available experimental data. Finally, the interactions between the solitary waves and the elastic plate are also simulated. The effects of the structural flexibility on the wave-induced force are analyzed by the comparison between the cases with elastic and the rigid plate.