The vertical mode method in the problems of flexural-gravity waves diffracted by a vertical cylinder

The linear three-dimensional problem of ice loads acting on a vertical circular cylinder frozen in an ice cover of infinite extent is studied. The loads are caused by an uni-directional hydroelastic wave propagating in the ice cover towards the cylinder mounted to the see bottom in water of constant depth. There are no open water surfaces in this problem. The deflection of the ice cover is described by the Bernoulli–Euler equation of a thin elastic plate of constant thickness. At the contact line between the ice cover and the surface of the cylinder, some edge conditions are imposed. In this study, the edge of the ice plate is either clamped to the cylinder or has no contact with the cylinder surface, with the plate edge being free of stresses and shear forces. The water is of finite constant depth, inviscid and incompressible. The problem is solved by both the vertical mode method and using the Weber integral transform in the radial coordinate. Each vertical mode corresponds to a root of the dispersion relation for flexural-gravity waves. It is proved that these two solutions are identical for the clamped edge conditions. This result is non-trivial because the vertical modes are non-orthogonal in a standard sense, they are linearly dependent, the roots of the dispersion relation can be double and even triple, and the set of the modes could be incomplete. A general solution of the wave-cylinder interaction problem is derived by the method of vertical modes and applied to different edge conditions on the contact line. There are three conditions of solvability in this problem. It is shown that these conditions are satisfied for any parameters of the problem.     

波浪对透空外双壁筒柱的绕射

应用透空壁内流体速度与两壁间压力差成正比的线性模型，建立了外壁透空的双筒圆柱对波浪绕射的解析解。通过数值计算研究了外壁透空率的大小、内外柱半径之比等因素对桩柱上总波浪作用力和波面高度的影响。数值结果表明圆柱外壁透空系数的增加，将明显地降低圆柱周围的波浪高度和圆柱上的波浪力；内外柱径之比的大小对波浪力和波高的最大值无太大影响，而对波浪力剧烈衰减区的位置和波高的振荡周期有决定作用。     

波浪对直墙前垂直圆柱的绕射

应用映像原理，将直墙前单个圆柱对波浪的绕射问题，变换为双柱对双向波浪的绕射问题，应用速度势的特征展开方法，建立了直墙前垂直圆柱对波浪绕射的解析解。通过数值计算研究了圆柱与直墙间距离大小、波浪入射角等因素对圆柱上总波浪作用力的影响。计算结果表明，直墙前圆柱上的波浪力将成倍地增加，且随着波数的变化而发生振荡。     

聚焦波作用下半浸没圆柱所受波浪载荷理论研究

由于畸形波的物理机制较复杂,有关畸形波-结构物相互作用的理论研究进展缓慢。然而对于较简单的畸形波模型与规则结构体,可以给出畸形波-结构物相互作用的理论解。本文基于畸形波的一种基本模型聚焦模型,采用解析方法研究其对半浸没圆柱体产生的波浪载荷。为保留畸形波的大部分特征,聚焦模型采用高斯包络描述。通过流场分隔给出绕射势,进而给出圆柱所受水平波浪力与波浪弯矩。采用适当方法简化理论公式,并与数值结果进行对比验证。此外,系统分析了聚焦程度、浸没深度与聚焦位置等参数对波浪载荷的影响。     

波浪作用下沙质海床上大直径圆筒结构动态响应的实验研究

通过物理模型实验,对沙质海床上沉入式大直径圆筒结构对波浪的动态响应进行了较系统的实验研究。实验中考虑了大直径圆筒、波浪和海床三者之间的耦合作用,并实时记录了大直径圆筒结构的动态响应。实验数据分析表明,大直径圆筒在波浪作用下的动态响应以大圆筒随波浪的前后摆动为主,其摆动轴心并不是固定不变的。最后通过回归分析给出了估算大直径圆筒摆动转角幅值的经验公式。     

Measurements of higher harmonic wave forces on a vertical truncated circular cylinder

Wave forces on a vertical truncated circular cylinder in Stokes waves with the wave slopes ranging from 0.06 to 0.24, are measured in a wave tank. The higher harmonic wave forces are compared with the available values from theories of the FNV (Faltisen–Newman–Vinje) model and Varyani solution. The first harmonic horizontal forces measured are much larger than the theoretical values from the FNV model, while the first harmonic vertical forces are well predicted by the Varyani theory. It was also found that the FNV model significantly overpredicts the second harmonic horizontal forces in high frequency waves, but under predicts the third harmonic forces. The differences between the actual measurement and the theory, in the second and third harmonic horizontal forces, become smaller at low wave frequencies as the wave slope increases. In addition, the transverse instabilities in the incoming waves with high wave slope were observed, which is due to the nonlinear modulation. Measurements were, thus, carried out before the instability occurred.     

Numerical simulation of nonlinear wave radiation by a moving vertical cylinder

In this paper the fully nonlinear potential model based on a finite element method is used to investigate the nonlinear wave motion around a moving circular cylinder. The results for the cylinder in transient motion are compared with the experimental data and a much better agreement than the linear theory is found. Further simulation for a circular cylinder in sinusoidal motion is made. It is found that when the ratio of the cylinder diameter D to the wavelength L is relatively small at a fixed motion amplitude the nonlinear components of the runup on the cylinder surface at the second- and third-harmonic frequencies become more important and this is confirmed by the experimental data. Results for the hydrodynamic force are also provided for a cylinder oscillating in a channel. It is noticed that when the frequency of the cylinder motion in a channel is between the first and the second natural frequencies of the symmetric mode, the time history has components not only at the frequency of the cylinder motion but also at the first natural frequency. The latter remains significant over the period that the simulation is made. This has important implications to model testing. If measurement is to be made at such a frequency it may take long time for the motion to become periodic at the frequency of the cylinder motion.     

Numerical simulation of solitary wave scattering by a circular cylinder array

The interaction of a solitary wave with an array of surface-piercing vertical circular cylinders is investigated numerically. The wave motion is modeled by a set of generalized Boussinesq equations. The governing equations are discretized using a finite element method. The numerical model is validated against the experimental data of solitary wave reflection from a vertical wall and solitary wave scattering by a vertical circular cylinder respectively. The predicted wave surface elevation and the wave forces on the cylinder agree well with the experimental data. The numerical model is then employed to study solitary wave scattering by arrays of two circular cylinders and four circular cylinders respectively. The effect of wave direction on the wave forces and the wave runup on the cylinders is quantified.     

Experimental and numerical investigations of monopile ringing in irregular finite-depth water waves

In storm conditions, nonlinear wave loads on monopile offshore wind turbines can induce resonant ringing-type responses. Efficient, validated methods which capture such events in irregular waves in intermediate or shallow water depth conditions are needed for design. Dedicated experiments and numerical studies were performed toward this goal. The extensive experimental campaign at 1:48 scale was carried out for Statoil related to the development of the Dudgeon wind farm, and included both a rigid model and a flexible, pitching-type, single degree-of-freedom model. Twenty 3-hour duration realizations for 4 sea states and 2 water depths were tested for each model. A high level of repeatability in ringing events was observed. Uncertainties in the experimental results were critically examined. The stochastic variation in the 3-hour maximum bending moment at the sea bed was significantly larger than the random variation in repetition tests, and highlighted the need for a good statistical basis in design. Numerical simulations using a beam element model with a modified Morison wave load model and second order wave kinematics gave reasonable prediction of the ringing response of the flexible model, and of the measured excitation forces on the rigid model in the absence of slamming. The numerical model was also used to investigate the sensitivity of the responses with respect to damping and natural period. A simple single degree-of-freedom model was shown to behave similarly to a fully flexible model when considering changes in natural frequency and damping.     

Experimental and numerical investigation of local scour around a submerged vertical circular cylinder in steady currents

Local scour around a submerged vertical circular cylinder in steady currents was studied both experimentally and numerically. The physical experiments were conducted for two different cylinder diameters with a range of cylinder height-to-diameter ratios. Transient scour depth at the stagnation point (upstream edge) of the cylinder was measured using the so-called conductivity scour probes. Three-dimensional (3D) seabed topography around each model cylinder was measured using a laser profiler. The effect of the height-to-diameter ratio on the scour depth was investigated. The experimental results show that the scour depth at the stagnation point is independent on cylinder height-to-diameter ratio when the later is smaller than 2. The increase rate of equilibrium scour depth with cylinder height increases with an increase in Shields parameter.     

Experimental investigation of pressure distribution on a cylinder due to the wave diffraction in a finite water depth

The experimental investigations on the pressure distribution around a large vertical cylinder fixed on a wave channel, piercing the free surface and subjected to regular waves have been carried out. Recently, considerable advances have been made in the development of analytical techniques for studying non-linear wave loading phenomena on large structures. However, there is a lack of high quality experimental data that may be used for validating the analytical and numerical solutions obtained. This paper describes the design and execution of an experiment conducted at the Hydraulics Laboratory in the Civil Engineering Department of the Istanbul Technical University. Experimental measurements of pressures at different locations are presented including comparisons with the computational results. This study showed that the experimental and computational results generally exhibited better correlation, however, the measured pressure values diverged from the computational results while approaching the free surface.     

Numerical study on cnoidal wave run-up around a vertical circular cylinder

A finite element model of Boussinesq-type equations was set up, and a direct numerical method is proposed so that the full reflection boundary condition is exactly satisfied at a curved wall surface. The accuracy of the model was verified in tests. The present model was used to further examine cnoidal wave propagation and run-up around the cylinder. The results showed that the Ursell number is a nonlinear parameter that indicates the normalized profile of cnoidal waves and has a significant effect on the wave run-up. Cnoidal waves with the same Ursell number have the same normalized profile, but a difference in the relative wave height can still cause differences in the wave run-up between these waves. The maximum dimensionless run-up was predicted under various conditions. Cnoidal waves hold entirely distinct properties from Stokes waves under the influence of the water depth, and the nonlinearity of cnoidal waves enhances rather than weakens with increasing wavelength. Thus, the variations in the maximum run-up with the wavelength for cnoidal waves are completely different from those for Stokes waves, and there are even significant differences in the variation between different cnoidal waves.     

In-line response of vertical cylinders in regular and random waves

The in-line response of a vertical flexibly mounted cylinder in regular and random waves is reported.Both theoretical analyses and experimental measurements have been performed.The theoretical predictions are based on the Morison equation which is solved by the incremental harmonic balance method.Experiments are then performed in a wave flume to determine the accuracy of the Morison equation in predicting the in-line response of the cylinder in regular and random waves.The interaction between waves and vibrating cylinders are investigated.     

系泊方柱在畸形波与波群伴生波浪作用下运动响应试验研究

畸形波与波群伴生波浪作用于系泊浮体,和常规随机波浪作用比较,运动响应时频域特征均将发生显著变化。基于物理模型试验,采用小波方法计算伴生波浪和常规随机波浪作用下系泊浮体运动响应的时频域特征变化及波群因子与浮体运动响应时频域特征的定量关系。结果表明:伴生波浪作用下浮体运动响应显著大于常规随机波浪的作用结果,且波群因子G A对浮体运动响应时频域特征有显著影响;伴生波浪作用下浮体纵荡运动的广义能量谱E(t)统计特征值E max(t)、E 1/10(t)、E 1/3(t)、E average(t)均明显大于相同波谱下常规随机波浪的结果,且随着波群因子G A增大显著增大;伴生波浪作用下各运动响应能量集中度δE显著大于常规随机波浪作用结果,且能量集中时域分布范围参数ΔT E以纵荡运动分量最为显著。     

Numerical investigation on the dynamics of a vertical wall defenced by an offshore breakwater

The numerical and experimental investigations on the performance of an offshore-submerged breakwater in reducing the wave forces and wave run-up on vertical wall are presented. A two-dimensional finite-element model is employed to study the hydrodynamic performance of the submerged breakwater under the action of regular and random waves. The numerical prediction has been supported with experimental measurements. The wave forces and wave run-up on the vertical wall were measured for different breakwater configurations. The applicability of linear theoretical model in the prediction of wave forces on the wall by a submerged breakwater has been discussed.     

Wave propagation through dense vertical cylinder arrays: Interference process and specific surface effects on damping

The purpose of this research work is to study the effect of specific surface s, the fluid–solid contact surface per volume unit, on the wave energy dissipation by porous structures consisting in dense arrays of emergent vertical cylinders. Experiments have been carried out in a 10 m long wave flume. Three cylinder diameters D are considered in order to study the effects of the specific surface while keeping the porosity constant. In a first series, the length of the porous zone is kept constant for the three cylinder diameters tested. The measurements, which include various wave steepness conditions, demonstrate the role of specific surface s on both wave attenuation and interference processes. The larger the specific surface is, the stronger the wave damping is. Damping is found to be almost proportional to 1/D when laminar, turbulent and inertial effects are of same order. Results are compared to numerical calculations based on either a constant rate of wave damping within the porous medium per unit wavelength or a quadratic damping developed using a force expression based on the work of [26]. This latter model, calibrated with drag and inertia coefficients, shows a good agreement with measurements. In a second series, both porous length and water depth are kept proportional to the cylinder diameter for the three diameters. Scale effects are then discussed and underline the importance of the flow regime within the porous medium.     

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.     

可渗透海床单桩孤立波破碎波浪力数值研究

当波浪传播至近岸浅水区时易发生破碎,波浪破碎后水体直接拍击单桩结构,其波浪作用力显著增大,可能导致结构失稳破坏。首先建立包括斜坡海床的数值波浪水槽,并与已有研究进行对比验证。进而开展考虑斜坡海床可渗透性的孤立波数值模拟,分析孤立波传播与浅水化破碎特征,着重研究竖直单桩上破碎波浪力的特性,及其与单桩位置、海床渗透率的关联性。数值研究发现:对于低渗透率海床,随着单桩位置由深水向岸线位置变动,其所受波浪力先增后减,所受波浪力最大的桩体位置随海床渗透率增加而从波浪破碎点前方移动至破碎点后1D处,而在高渗透率海床上不同位置处桩体所受波浪力均较小;随海床渗透率等梯度增加,海床消波作用逐渐增强,波浪破碎进程延缓,波浪破碎点向岸线方向加速移动,单桩上破碎波浪力呈整体下降趋势,但可能因波浪破碎点的位置变动导致部分位置桩体所受波浪力异常增大。     

波浪对上部开孔带内柱的圆筒结构的绕射

应用透空壁内流体速度与两壁间压力差成正比的线性模型和特征函数展开方法,建立了外壁上部开孔并带有内柱的圆筒结构对波浪绕射的解析解.通过数值计算研究了外壁开孔率的大小、圆筒与内柱半径之比、筒内水深等因素对圆筒上总的波浪作用力和圆筒周围波浪高度的影响.经数值研究发现随着外壁开孔率的增大圆筒迎浪端的波浪高度和圆筒结构上总的波浪力明显减小,外壁孔隙特性G虚部的增加对波高和波浪力的衰减也有一定的影响;增加圆筒内部的水深可减小圆筒周围的波浪高度,降低圆筒结构上的总波浪力.     

亚临界区雷诺数下圆柱绕流场电磁力控制数值研究

在亚临界区雷诺数下,采用脱体涡模拟方法对弱电解质中电磁力作用下圆柱绕流场及其升阻力特性进行了数值模拟与分析。结果表明,电磁力可以提高圆柱体边界层内的流体动能,延缓圆柱体近壁面流动分离,减弱绕流场中流向和展向大尺度涡的强度,减小圆柱体阻力及其升力脉动幅值;当电磁力作用参数大于某个临界值后,流动分离角消失,在圆柱体尾部产生射流现象,电磁力产生净推力作用,出现负阻力现象,而且升力脉动幅值显著减小且接近于零。