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.     

Wave radiation and diffraction by a floating rectangular structure with an opening at its bottom in oblique seas

The radiation and the diffraction of linear waves by a rectangular structure with an opening at its bottom floating in oblique seas of finite depth are investigated. Analytical expressions for the radiated potentials and the diffracted potential are obtained by use of the method of separation of variables and the eigenfunction expansion method, with the unknown coefficients being determined by the boundary conditions and the matching requirement on the interface. The hydrodynamic coefficients and the wave excitation forces are verified using the symmetry properties of coupled hydrodynamic coefficients and one specific example investigated previously. By use of the present analytical-numerical solution, the influences of the angle of incidence, the width of the opening on the wave forces and the hydrodynamic coefficients are investigated. It is also found that in the oblique sea the external excitation frequency that can lead to the resonance of a rectangular tank depends on the wave direction and the wave number of the incident wave.     

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.     

WAVE FORCES ON INCLINED CYLINDER IN REGULAR WAVES

Through a series of model tests,the wave forces on horizontal and inclined circularcylinders are measured and analyzed.Based on Morison Equation and Stokes second order wavetheory,the relationship between the hydrodynamic force coefficients with KC number and sub-merged water depth as well for horizontal cylinders are analyzed,also the relationship betweenthe hydrodynamic force coefficients with KC number,inclined angle and the effect of water freesurface as well for the inclined cylinders are investigated.     

An iterative Rankine boundary element method for wave diffraction of a ship with forward speed

A 3-D time-domain seakeeping analysis tool has been newly developed by using a higher-order boundary element method with the Rankine source as the kernel function. An iterative time-marching scheme for updating both kinematic and dynamic free-surface boundary conditions is adopted for achieving numerical accuracy and stability. A rectangular computational domain moving with the mean speed of ship is introduced. A damping beach at the outer portion of the truncated free surface is installed for satisfying the radiation condition. After numerical convergence checked, the diffraction unsteady problem of a Wigley hull traveling with a constant forward speed in waves is studied. Extensive results including wave exciting forces, wave patterns and pressure distributions on the hull are presented to validate the efficiency and accuracy of the proposed 3-D time-domain iterative Rankine BEM approach. Computed results are compared to be in good agreement with the corresponding experimental data and other published numerical solutions.     

THE WAVE-MAKING CHARACTERISTICS OF A MOVING BODY IN A TWO-LAYER FLUID

The Wave-making characteristics of a moving body in a two-layer fluid with free surface is investigated numerically and experimentally. The numerical analysis is based on the modified layered boundary integral equation system. The wave characteristics on the free surface and interface generated by a moving sphere and an ellipsoid is numerically simulated in both finite depth and infinite depth of lower layer model. The numerical results of the sphere are compared with the analytical results for a dipole with the same velocity in a two-layer fluid of finite depth. The dependence of the wave systems and structures on the characteristic quantities is discussed. Three kinds of measurement techniques are used in model experiments on the internal waves generated by a sphere advancing in a two-layer fluid. The effects of the varying velocity and stratification on the wavelength, wave amplitudes and the maximum half angles of internal waves are analyzed qualitatively.     

开阔海域越洋海啸波高计算的一种简化方法

该文研究了开阔海域中越洋海啸波高的简化计算方法。基于选取具有一系列断裂带长宽比的震源参数,采用Okada弹性变形理论生成初始海底变形,运用基于有限体积法的非线性浅水方程数值模型,模拟地震激发海啸在4 000 m水深的平底地形上的传播过程。通过监测布置在相对震源中心不同距离及方位角上测点的波面时间序列,研究海啸波高在不同距离及方位角上的分布规律,给出不同断裂带长宽比下越洋海啸传播过程中首波幅值的分布关系式;进一步分析了断裂带长宽比对模型参数的影响,得出了归一化的越洋海啸波高计算经验公式,并与日本2011年海啸实际记录进行对比,验证了该近似方法的有效性。     

NONLINEAR DIFFRACTION OF BICHROMATIC WAVES BY A VERTICAL CYLINDER

We present in this paper a semi-analytical solution for second-order wave diffraction by a vertical circular cylinder in bichromatic waves.On the base of the usual assumption of an irrotational flow,the wave-diffraction problems at second-order sum-fre-quency and difference-frequency are considered.The corresponding second-order diffrac-tion potentials are decomposed into three parts,these are associated with the second-order incident wave,the quadratic forcing terms on the free-surface due to the first-order poten-tial,and the linearised'free-wave'component resulting from the boundary condition on the body surface.A particular solution which exactly satisfies the inhomogeneous free-sur-face condition has been derived.Numerical results for the quadratic transfer functions of the second-order force components are given,and are compared with those obtained using numerical solutions(Kim & Yue,1990,Moubayed & Williams 1995).These quadratic functions are useful in calculating the exciting forces on a circula     

TIME-DOMAIN ANALYSIS OF WAVE FORCES ON SHIPS WITH FORWARD SPEED

Analyses of wave forces on Wigley and Series 60 ships at forward speedare presented in time domain which is based on a free surface transient Green functionwith linearized condition. The main effort focus on the investigation of the numerical sta-bility of time stepping calculation and the waterline intergal contribution to the excitingforces. Numerical study shows that the stable results can be obtained when a wall-sided as-sumption is used at the stern only and the effect of waterline can be neglected. Compar-isons have been made between the present time domain calculations and other works. Nu-merical results for the added resistance on a C_B=0.8 ship in short waves are presentedbased on the assumption that the steady disturbance of ship hull can be neglected.     

规则波作用下倾斜桩柱的受力研究

本文通过实验研究,测试了水平桩柱及倾斜桩柱在规则波作用下的波浪力。基于Morison方程和Stokes二阶波理论,分析研究了不同埋深情况下水平桩柱的受力及其水动力系数C_D、C_M随K_C数的变化规律;分析研究了不同倾角情况下,倾斜桩柱的受力及其水动力系数C_D、C_M随K_O数的变化规律,同时还探讨了在同一倾角情况下,桩柱在一端出水和全部埋于水下时,水动力系数C_D、C_M的差别。     

Extreme wave loads on submerged water intakes in shallow water

This paper provides new guidance concerning the hydrodynamic loads on submerged intake structures located in shallow water under breaking and non-breaking waves. Results from a series of experiments conducted in a large wave flume at 1:15 scale to study the hydrodynamic forces exerted on a generic intake structure located on a sloping seabed in shallow water below breaking and non-breaking irregular waves are presented. Based on analysis of the experimental data, empirical relationships are developed to describe the peak loads in terms of characteristic wave parameters such as significant wave height and peak wave period. The distribution of the peak loads across different parts of the intake structure is also described. Drag and inertia force coefficients for the horizontal forcing on the intake structure and for the main structural sub-components are derived and presented. It is shown that the well-known Morison equation, with appropriate drag and inertia force coefficients, can provide reasonable estimates of the moderate horizontal loads, but the peak loads are less well predicted.     

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...     

波浪作用下双孔射流压强特性试验研究

管道污水向海排放是一种典型的射流运动形式。在射流前行的过程中,波浪所引起的水体往复运动明显制约了射流的形成与发展,射流与波浪的相互作用的研究相对较少。利用数字压力传感器对波浪作用下双孔射流进行物理模型试验研究,分析波浪作用下双孔射流横断面压强分布及轴线衰减规律。试验结果表明:波浪条件下双孔射流横断面压强分布规律与静水条件相似,但是波浪条件下的射流压强大于静水条件下的射流压强,波周期越大,压强峰值增加越大;双孔射流的发展经历了单孔主导、双孔射流间的吸附和混掺、合并等过程;单孔主导区,射流压强分布与静水条件相似;吸附和掺混区,各孔衰减呈现出差异,第1孔与单孔射流类似,第2孔压强衰减较第1孔小,合并区双孔射流已为一股射流,其水动力特性与单孔射流类似;波浪对双孔射流的混掺合并有促进影响,随着周期的增大这种促进作用有增强的趋势,波周期的增大也使得射流合并断面提早出现。表明波周期对射流压强特性有显著影响。     

Experimental investigation of the effects of contraction on tsunami-induced forces and pressures on a box section bridge

Many bridges that lie within possible tsunami inundation zones are critical links in transport networks. Some efforts have been made to determine the effects of tsunamis on bridges, but only a limited range of published design guidelines are available. Therefore, it is necessary to further investigate the effects of tsunamis on bridges. In the current study, physical modeling experiments were carried out to measure bore impact forces and pressures for various tsunami bore strengths on a bridge deck with different abutment types (wing wall and spill-through) and different opening and submergence ratios. The experiments were conducted in a wave flume with dimensions of 14 × 1.2 × 0.8 m (length × width × height), equipped with an automatic gate designed to generate a tsunami bore. The horizontal and vertical forces showed an increasing trend with increasing submergence ratio for both types of abutment. However, the horizontal force showed a decreasing trend as the opening ratio decreased, while the vertical force initially increased as the opening ratio decreased, until it reached a peak value, and then it started to decrease. The overall shapes of the results for both types of abutment are similar, with higher values for spill-through abutments due to their lower energy dissipation rates. Based on the experimental data, empirical equations are proposed for estimation of tsunami loads as a function of opening and submergence ratios.     

FREE-SURFACE WAVES AND FAR WAKES GENERATED BY A FLOATING BODY IN A VISCOUS FLUID

1 .　INTRODUCTIONThewavemotionduetoamovingdisturbancehasbeenoflong standinginterest .Butthecorre spondingwakestructuredidnotreceivemuchat tentionuntilthesyntheticapertureradarcollectedanumberofimagesofV likewakepatternsgener atedbyships (Milgram 1988;Brownetal.1989) .Thewakestructuresarethoughttobeclassifiedin tothreecategories :theKelvinwavewakes ,thetrubulentwakesandtheinternalwavewakes(Griffin 1988;Lydenetal.1988;GuandPhillips1994 ) .TheKelvinwakesarethefar fieldwavepatternsgenerate…     

浅水波与圆弧型贯底式防波堤的相互作用

该文基于椭圆余弦波绕射理论,应用特征函数展开法,推导了浅水波对圆弧型贯底式多孔介质防波堤绕射的波势解,并据此解析计算了作用于防波堤的水平波浪载荷与浅水波波面分布。计算结果表明:浅水波入射角与非线性影响参数、海况条件以及防波堤几何条件等因素的相对变化对波浪作用均存在一定的影响,结构透空可以明显减弱防波堤所受波浪作用。与微幅波理论对比可知:在一定浅水条件下采用椭圆余弦波一阶分量模型所计算的最大无量纲波浪力、力矩和波面分布值均明显高于微幅波理论的对应估值,反映了水波非线性因素的影响效应。     

BEM for wave interaction with structures and low storage accelerated methods for large scale computation

The boundary element method(BEM) is a main method for analyzing the interactions between the waves and the marine structures. As with the BEM, a set of linear equations are generated with a full matrix, the required calculations and storage increase rapidly with the increase of the structure scale. Thus, an accelerated method with a low storage is desirable for the wave interaction with a very large structure. A systematic review is given in this paper for the BEM for solving the problem of the wave interaction with a large scale structure. Various integral equations are derived based on different Green functions, the advantages and disadvantages of different discretization schemes of the integral equations by the constant panels, the higher order elements, and the spline functions are discussed. For the higher order element discretization method, the special concerns are given to the numerical calculations of the single-layer potential, the double layer potential and the solid angle coefficients. For a large scale computation problem such as the wave interaction with a very large structure or a large number of bodies, the BEMs with the FMM and p FFT accelerations are discussed, respectively, including the principles of the FMM and the p FFT, and their implementations in various integral equations with different Green functions. Finally, some potential applications of the acceleration methods for problems with large scale computations in the ocean and coastal engineering are introduced.     

波浪力计算中的一个新边界元方法

本文就波浪与结构物作用问题，提出了一个新的高阶边界元方法。较之Ｅａｔｏｃｋ Ｔｏｙｌｏｒ和Ｃｈａｕ的方法，本文在体内附助积分方程中应用了满足刚性水面条件和弱刚性底面条件的简单格林函数。计算速度相应地有所提高；漂浮结构的积分方程更为简洁；计算结果与Ｅａｔｏｃｋ Ｔａｙｌｏｒ和Ｃｈａｕ的方法具有几乎相同的精度和收敛速度。     

EXPERIMENTAL STUDY ON THE SECOND-ORDER DIFFRACTION WAVE PRESSURE AND FORCE ON A CIRCULAR CYLINDER UNDER STOKES WAVE ACTION

This paper presents the model test to measure the second-order wave pressureand forces on a circular cylinder fixed in Stokes wave with a given draught.The distributions ofsecond-order oscillating and steady wave pressure on the wet surface of the cylinder and secondorder oscillating wave forces were obtained in this test,but the second-order steady wave forcewas not able to be measured due to its very small magnitude.The test results also show thatthird-order wave force may be greater than the second-order force when wave frequencies arehigh.The experimental results were compared with the corresponding calculation results of Ref-erence[3].     

REFLECTION OF OBLIQUE INCIDENT WAVES BY PERFORATED CAISSONS WITH TRAVERSE WALL

The interaction of oblique incident waves with infinite number of perforated caissons is investigated. The fluid domain is divided into infinite sub-domains by the caissons, and eigen-function expansion is applied to expand velocity potentials in each domain. A phase relation is introduced for wave oscillation in each caisson, and the structure geometry is considered in constructing the models of reflection waves. The reflected waves with the present analysis include all of the waves traveling in different directions when incident wave period is short. Numerical examinations show that velocities at the inner and outer sides of the front walls of caissons are close to each other, and reflection coefficients satisfy the energy conservation relation very well when porous effect parameter is infinite. Numerical results show that the reflection coefficients of oblique incident waves are smaller for shorter caissons at low frequency, and decrease with the increase of wave incident angle.