直墙前矩形月池水波振荡研究分析

月池内流体存在活塞和晃荡两类振荡现象。基于线性势流理论,推导了波浪斜向入射下,直墙前矩形月池辐射和绕射问题的解析解。通过分离变量法和特征函数展开法求解了速度势函数,根据边界条件来确定速度势函数中的未知系数,由速度势函数计算斜向波与矩形月池相互作用的水动力系数和波浪激励力,对它们的变化规律进行了分析讨论,研究了底部开口大小、波浪入射角度对矩形月池水动力特性的影响以及直墙远近对波浪力的影响。结果表明,月池底部开口大小对流体水平作用的影响较小,而对流体垂直作用的影响较大;波浪入射角度的变化对矩形月池横荡和横摇运动时的水动力特性有一定的影响;在一定条件下,直墙的存在会使得月池在水平方向所受到的波浪力比开敞水域中的要大。     

Radiation and diffraction of linear water waves by an infinitely long submerged rectangular structure parallel to a vertical wall

The radiation and the diffraction of linear water waves by an infinitely long floating rectangular structure submerged in water of finite depth with leeward boundary being a vertical wall are analyzed in this paper by using the method of separation of variables. Analytical expressions for the radiated and diffracted potentials are derived as infinite series with unknown coefficients determined by the eigenfunction expansion matching method. The expressions for wave forces and hydrodynamic coefficients are given. A comparison is made between the results obtained by the present analytical solution and those obtained by the boundary element method. By using the present analytical solution, the hydrodynamic influences of the submergence, the width, the thickness of the structure, and the distance between the structure and the wall on the wave forces and hydrodynamic coefficients are discussed in detail.     

Meshless Method for Analysis of Permeable Breakwaters in the Proximity of A Vertical Wall

In the present work, the improved version of the meshless singular boundary method(ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves and in the proximity of a vertical wall. Both single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with appropriate mixed type boundary conditions, and solved numerically using the ISBM. To model the permeability of the breakwaters fully absorbing boundary conditions are assumed. Numerical results are presented in terms of hydrodynamic quantities of the reflection coefficients. These are firstly validated against the results of a multi-domain boundary element method(BEM) developed independently for a previous study. The agreement between the results of the two methods is excellent. The coefficients of reflection are then computed and discussed for a variety of structural conditions including the breakwaters height, width, spacing, and absorbing permeability. Effects of the proximity of the vertical plane wall are also investigated. The breakwater's width is found to have only marginal effects compared with its height. Permeability tends to decrease the minimum reflections. These coefficients show periodic variations with the spacing relative to the wavelength. Trapezoidal breakwaters are found to be more cost-effective than the rectangular breakwaters. Dual breakwater systems are confirmed to perform much better than single structures.     

A Study of Eddy Viscosity Coefficient in Numerical Tidal Simulation

Based on the fluid motion equations, the physical meaning of eddy viscosity coefficient and the rationality of the Boussinesq hypothesis are discussed in this paper. The effect of the coefficient on numerical stability is analyzed briefly. A semi-enclosed rectangular sea area, with an orthogonal spur dike, is applied in a 2-D numerical model to study the effect of horizontal eddy viscosity coefficient (AH). The computed result shows that AH has little influence on the tidal level and averaged flow velocity, but has obvious influence on the intensity and the range of return flow around near the spur dike. Correspondingly, a wind-driven current pool and an annular current are applied in a 3-D numerical model respectively to study the effect of vertical eddy viscosity coefficient (Av). The computed result shows that the absolute value of Av is inversely proportional to that of horizontal velocity, and the vertical gradient value of Av determines the vertical distribution of horizontal velocity. The distrib     

On the radiation and diffraction of water waves by a rectangular structure with a sidewall

A radiation and diffraction boundary value problem is investigated. It arises from the interaction of linear water waves with a freely floating rectangular structure in a semi-infinite fluid domain of finite water depth with the leeward boundary being a vertical wall. 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. The added masses and damping coefficients for the structure heaving, swaying and rolling in calm water are obtained by use of the corresponding radiated potentials and the wave excitation forces are calculated by use of the diffracted potential. To verify the correctness of the method, a boundary element method is used. A comparison of the analytical results with those obtained by the boundary element method is made and good agreement is achieved, which shows that the analytical expressions for the radiated and diffracted potentials are correct. By use of the present analytical solution, the added mass, damping coefficients, wave excitation force, together with the hydrodynamic effects of the draft, width of the structure and the clearance between the structure and the sidewall are also investigated.     

Numerical investigations of wave overtopping at coastal structures

Under the numerical modelling work package of the EU funded CLASH project, the time accurate, free surface capturing, incompressible Navier–Stokes solver AMAZON-SC has been applied to study impulsive wave overtopping at Samphire Hoe, near Dover in the United Kingdom. The simulations show that the overtopping process on this vertical, sheet pile, seawall is dominated by impulsive, aerated, near vertical overtopping jets. In order to perform the simulations AMAZON-SC has been extended to incorporate an isotropic porosity model and for validation purposes the solver has been applied to study overtopping of a low crested sea dike and a 10:1 battered wall. The results obtained for the battered wall and Samphire Hoe tests are in good agreement both with predicted overtopping discharges calculated using the UK overtopping manual and with available experimental results.     

Wave reflection by a vertical wall with a horizontal submerged porous plate

By applying the linear water wave theory and the eigenfunction expansion method, the wave reflection by a vertical wall with a horizontal submerged porous plate is investigated in this paper. The numerical results, concerning the effects of the dimensionless plate length, the relative water depth, and the porous effect parameter of the plate on the wave loads on the plate and the wave height near the wall as well as the reflection coefficient, are discussed. It is found that the submerged plate increases the complexity of the phenomenon related to the wave reflection and refraction in the close region of the wall, and leads to the occurrence of the phenomenon of wave trapping. The results indicate that there may exist a process of focusing wave energy near the wall for small dimensionless porous effect parameters, whereas the increase of the dimensionless porous effect parameter decreases gradually the wave height until setdown occurs. The behavior of a larger plate with proper porosity is similar to that of a wave absorber which can significantly suppress not only the wave height above the plate but also the reflection waves. The ability of the porous plate to reduce the wave height on the wall surface is, in general, directly proportional to the dimensionless plate length and may be strongest for a proper value of the dimensionless porous effect parameter. It is also demonstrated that the wave loads on a porous plate are smaller than those on an impermeable plate.     

Motion Characteristics of Cavitation Bubble near the Rigid Wall with the Driving of Acoustic Wave

The dynamics of cavitation bubble is analyzed in the compressible fluid by use of the boundary integral equation considering the compressibility.After the vertical incidence of plane wave to the rigid wall,the motion characteristics of single cavitation bubble near the rigid wall with initial equilibrium state are researched with different parameters.The results show that after the driving of acoustic wave,the cavitation bubble near the rigid wall will expand or contract,and generate the jet pointing to the wall.Also,the existence of the wall will elongate time for one oscillation.With the compressible model,the oscillation amplitude is reduced,as well as the peak value of inner pressure and jet tip velocity.The effect of the wall on oscillation amplitude is limited.However with the increment of initial vertical distance,the effect of wall on the jet velocity is from acceleration to limitation,and finally to acceleration again.     

Wave radiation and diffraction by a two-dimensional floating body with an opening near a side wall

The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi-infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for potentials are obtained by the method of variation separation, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The effects of the position of the hole and the gap between the body and side wall on hydrodynamic characteristics are investigated. Some resonance is observed like piston motion in a moon pool and sloshing in a closed tank because of the existence of restricted fluid domains.     

Wave impacts on structures with rectangular geometries: Part 1. Seawalls

This paper considers steep wave impact on seawalls of various geometries. A simple analytical model for the pressure impulse due to a wave of idealized geometry and dynamics is developed and applied to the following geometries: (a) vertical seawall with a berm, (b) vertical seawall with a ditch at its base and (c) vertical seawall with a block missing (damaged condition).The method uses eigenfunction expansions in each of the rectangular regions that satisfy some of the rigid surface conditions and a simplified free-surface condition. Their unknown coefficients are determined from the impact boundary condition, rigid wall conditions and by matching the values and the horizontal derivatives of the solutions in each rectangular region at their mutual boundary. The method yields the pressure impulse throughout the entire region. The overall impulse and moment impulse on the seawall and a simple model for the uprush of the spray jet after the impact are also presented. The effects of different impact regions and different geometries can therefore be quickly estimated and used to show trends in the results. It is shown that berms generally have a beneficial effect on reducing the impulse, moment impulse and uprush, but not the maximum pressure impulse on the seawall, whereas ditches are generally and sometimes strongly detrimental for all effects except uprush. A missing block in the seawall gives an almost constant or linearly decreasing value inside the gap (depending on the boundary condition applied at the rear of the gap being hard or soft respectively); the soft case can affect the pressure impulse on the front face of the seawall, thereby affecting the impulse and moment impulse.     

Step-like structure in temperature and salinity profiles,observed near icebergs trapped by fast ice,Antarctica

Step-like thermohaline structure was observed near icebergs trapped by fast ice in Lützow-Holm Bay, Antarctica. The structure was developed within the draft depth of the icebergs. The typical vertical distance between the succeeding step surfaces is 20–30 m, and the temperature and salinity differences across the step surface are about 0.05–0.06 deg and 0.06–0.10 psu, respectively. The structure appears to be generated by a sea-water/iceberg interaction, and is explainable by a simple model in which an ice wall is placed in the ocean linearly stratified by vertical salinity gradient.     

开孔墙对减小波浪载荷效果的CFD分析

极限波浪载荷是导致海上结构物疲劳失效的主要载荷之一。固定在海洋基础结构物上的直立开孔墙对减小波浪载荷具有一定的效果。基于不可压缩黏性流体流动理论和N-S方程,采用VOF与Level-set相结合追踪自由表面的方法,首先建立数值波浪水槽,然后对开孔墙本身的开孔率和开孔墙与直立墙之间的相对距离,在降低反射系数和波浪力两个方面进行分析。研究结果表明,开孔墙可以明显降低作用在结构物上的波浪力,开孔墙本身的开孔率和与直立墙的相对距离会对其产生明显影响;不同波浪参数下会存在一个最佳的开孔率,但是不同波浪参数时最佳开孔率会略有不同;当开孔墙和直立墙的相对距离在0.2到0.3之间时,开孔墙的消波减载效果最佳。研究结果可为海洋工程相关设计提供一定的参考。     

Wave impacts on structures with rectangular geometries: Part 2 decks,baffles and seawalls with impermeable or porous surfaces

This paper considers wave impacts on baffles, on baffles or decks adjacent to a vertical wall, and on porous seawalls and/or sea beds. For seawalls and vertical baffles, impacts can occur in steep waves, whilst a deck can be struck from below by a rising wave crest either in open sea or in a tank with standing waves (sloshing). A simple analytical model for the pressure impulse, P, due to a wave of idealized geometry and dynamics is developed and applied to the following geometries with impermeable surfaces:

• •horizontal wave impact onto a vertical wall with a deck at the waterline,
• •vertical wave impact under a deck in the same configuration (equivalent to vertical water impact of a horizontal plate),
• •horizontal wave impact onto a surface-piercing vertical baffle in open sea,
• •as for 3. but with the baffle in front of a wall,
• •as for 4. but with a deck extending from the vertical wall to the baffle,
• •bottom-mounted baffle in front of a wall with impact occurring on the wall.

We also consider cases that complement part 1 of this paper to include the effect on impacts on a seawall with a porous sea bed and/or sea wall with/without a berm. Finally we reconsider case 3) above but with a porous baffle.The method uses eigenfunction expansions in each of the rectangular regions that satisfy some of the impermeable or porous surface conditions, and a simplified free-surface condition. Their unknown coefficients are determined from the impact boundary condition, impermeable or porous boundary conditions and by matching the solutions, in any two neighbouring rectangles, along their common boundary. Although the fluid motion is treated rather crudely, the method yields the pressure impulse throughout the entire region. Impulses, I, and moment impulses, M, on all or parts of the structure are also presented.     

Hydrodynamic coefficients of a two-dimensional,truncated rectangular floating structure in shallow water

The paper seeks to examine hydrodynamic coefficients of a rectangular structure in shallow water and to establish analytical formulae for fast computations. A two-dimensional rectangular profile is considered with the under-bottom clearance assumed to be small compared with structure dimensions and the water depth. Following the method of matched asymptotic expansions, the radiation problem is solved under assumptions of the linear wave theory, by matching two ‘outer’ flows with the ‘inner’ flow near the structure edge. Closed asymptotic formulae are obtained for all hydrodynamic coefficients for heave, sway and roll motions. The zero and infinite frequency values of the added mass are examined and formulae are derived intended for quick engineering estimations. Numerical results compare well with those published in literature, and the approach is shown to be consistent with known fundamental relations in the body–wave interaction theory.     

Effects of backfill on seismic behavior of rectangular tanks

The reliability and/or stability of the lifeline structures against failure under seismic loads are of critical concern, and must be studied carefully. Therefore, the main objective of this paper is to demonstrate the commonly encountered backfill effects on the dynamic response of rectangular tanks. However, only the exterior wall of the tank which interacts with both the backfill and fluid is tackled, as each part of the structure shows considerable differences in terms of both the load bearing mechanisms and the geometrical and positional differences. Finite element analyses are employed, taking into consideration the fluid-wall-backfill interaction. The analyses are conducted to observe whether or not both backfill and wall behavior can be affected by variation of the internal friction angle. For that purpose, some comparisons are made on vertical displacements of the backfill, roof displacements, stress responses, etc., by means of internal friction angle variations of the backfill from 25° to 40°. Consequently, it is observed that the variations on maximum vertical displacements are affected considerably. In contrast, the maximum stress responses are affected partially. However, the inertial effects of the backfill show that pseudo-static approximations may be insufficient to understand the dynamic behavior of the backfill-wall-fluid system.     

Wave radiation by a uniform cylinder in front of a vertical wall

In this paper, an exact analytical method is developed for the problem of wave radiation by a uniform cylinder in front of a vertical wall. Based on the image principle, the hydrodynamic problem of a cylinder in front of a vertical wall is transformed into the equivalent problem of double cylinders in unbounded fluid domain. Consequently, an analytical method of eigenfunction expansion is adopted to calculate the radiation of the cylinder due to the motion in surge, sway, roll and pitch, respectively. Moreover, numerical analysis has been carried out in detail in order to discuss the influences of the distance between the cylinder and the vertical wall and water depth on the added mass and radiation damping of the cylinder. It is shown that added mass and damping of the cylinder in front of a vertical wall are evidently different from those in case of the cylinder in unbounded fluid domain from the numerical results. It is also found that the added mass and radiation damping oscillate with wave number, and the oscillating frequency increases with the increasing of the distance between the cylinder and the wall.     

部分反射直墙前二维物体的绕射和辐射问题

基于映像理论将部分反射直墙前物体的散射问题,等效于开敞水域中原物体的散射和关于直墙映像体散射的线性叠加进行求解。采用高阶边界元方法建立了部分反射直墙前二维任意形状物体波浪绕射和辐射问题的数值分析模型,通过与已发表的海底方箱和淹没圆柱结果的对比验证了数值模型的准确性。应用该模型研究了直墙反射系数幅值及相位、方箱与墙间距离等参数对水面方箱上波浪激振力、附加质量和辐射阻尼的影响。结果表明：直墙反射系数幅值越大,波浪激振力、附加质量和辐射阻尼的波动越大,附加质量在一些频率下出现负值;相位角的变化会改变波浪激振力、附加质量和辐射阻尼曲线的偏移,在低频区对升沉附加质量有显著影响;方箱距离直墙越远,方箱上的波浪激振力、附加质量和辐射阻尼随波数振荡的频率越快,峰值频率向低频侧移动。     

Experimental study on bubble pulse features under the combined action of horizontal and vertical walls

The pulse features of a bubble have a close connection with the boundary condition. When a bubble moves near a rigid wall, it will be attracted by the Bjerknes force of the wall, and a jet pointing at the wall will be generated. In real application, the bubble may move under the combined action of walls in different directions when it forms at the corner of a pipe or at the bottom of a dam. The motion of the bubble shows complex and nonlinear characteristics under these conditions. In order to investigate the bubble pulse features near complex walls, a horizontal wall and a vertical wall are put into the experimental water tank synchronously, and an electric circuit with 200 voltages is designed to generate discharge bubbles, and then experimental study on the bubble pulse features under the combined action of horizontal and vertical walls is carried out. The influences of the combined action of two walls on the bubble shape, pulse period, moving trace and inside jet are obtained by changing the distances from bubble center to the two walls. It aims at providing references for the relevant theoretical and numerical research.     

A hydraulic model of the Korea Strait bottom cold current

A one and a half layer inviscid hydraulic model was introduced to study the dynamics of the flow that brings the bottom cold water southward into the Korea Strait. Two different channel geometries were considered; a rectangular channel and a channel with a sloping western wall, which represents the continental slope near the Korean coast. The lower layer water in the rectangular channel separates from the eastern wall when the depth of the channel,H _o, becomes shallower than a critical value donwstream. Hydraulic control of the flow is possible after the flow separation, if the channel becomes shallow enough. Before hydraulic control, the width of the flow decreases asH _o decreases, but the effect of the slope of the western wall is negligible. After the control, however, the width increases asH _o decreases or the slope becomes weaker. If the slope becomes weak enough or the channel becomes deep enough, which is determined by upstream conditions, the lower layer is observed only over the sloping western wall. This simple model shows that the continental slope between the East Sea (Japan Sea) and the Korea Strait makes the southward flowing North Korean Cold Water bank against the Korean coast in the Korea Strait. The model also shows that the sloping bottom near the Korean coast makes the bottom cold water of the Korea Strait appear only over the continental slope away from the trough of the strait.     

Impact pressure of breaking waves on vertical and sloping walls

Laboratory tests are conducted to measure the impact pressures of breaking waves on vertical, 5° forward, and 5, 10, 20, 30, and 45° backward sloping walls. The base structure of the wall has a foreshore slope of . Regular waves are used throughout the experiments for all wall angles. The maximum impact pressures on the wall are shown to satisfy the log-normal probability distribution. It is found from the present experiments that the impact pressures and resulting forces on sloping walls can be greater than those on a vertical wall. On the seven different walls tested, the maximum impact pressures occur most frequently slightly below the still-water level. The pattern of the impact pressure history does not change with the slope of the wall, and as the probability of maximum impact pressure decreases, the pressures around the peak pressure region of the impact pressure histories remain longer.