Hydrodynamics of a body floating in a two-layer fluid of finite depth. Part 1. Radiation problem

A linearized 2-D radiation problem was considered for a general floating body in a two-layer fluid of finite depth. A boundary integral-equation method was developed for directly computing the velocity potential on the wetted surface of a body which is immersed in both the upper and lower layers as a general case. To do this, appropriate time-harmonic Greens functions were derived, and an efficient numerical method of evaluating those functions is proposed. Based on Greens theorem, hydrodynamic relations such as the energy-conservation principle were derived theoretically for a case of finite depth, and we confirm that those relations are satisfied numerically with very good accuracy. Experiments were also carried out using water and isoparaffin oil as the two fluids and a Lewis-form body. Measured results for the added mass, the damping coefficient, and the amplitude of the generated waves are compared with the computed results, and a favorable agreement is found.     

复杂地形下平台水弹性响应研究

在以往的研究中,波浪对浮体的水动力响应作用大多采用有限均匀水深或无限水深情况进行计算,考虑实际复杂地形对浮体性能影响的研究较少,但事实上地形的变化对浮体影响不可忽略,尤其岛礁附近区域珊瑚礁地形复杂,需要考虑地形对波浪场的影响。文章先从简单情况入手,入射波浪采用有限水深均匀入射波,使用有限水深格林函数求解源强,但加入了地形对浮体波浪绕射和辐射的影响。基于这些假定,验证了该方法计算结果的准确性,进而对某浮式平台在复杂地形下的水动力进行计算,并与均匀有限水深的结果进行比较,两者总体趋势吻合。结果表明,地形的存在对低频区运动响应影响较大,相比均匀水深波动较大。该文可以为浮体在实际地形下水动力响应计算研究工作的开展提供一个参考。     

On the application of the Haskind-Hanaoka relations to hydroelasticity problems

The Haskind-Hanaoka relations for obtaining the wave-exciting forces, given the incoming and radiation potentials in floating rigid-body dynamics, are extended to deformable-body dynamics in the presence of a free surface and within the assumption of linear potentials theory. These relations are applied to the mode-superposition and the direct methods of solution of hydroelasticity problems. In other words, it is shown that regardless of the structural analysis method used in a hydroelasticity problem, the Haskind-Hanaoka relations can be used to calculate the wave-exciting forces without solving for the diffraction potential explicitly. These relations can also be used in the composite singularity distribution method to increase further the computational efficiency.     

Experimental study of freak wave impacts on a tension-leg platform

This study investigates the freak wave impinging on a tension-leg platform through wave flume experiments. The freak waves are generated using the focused wave theory. By adjusting the wave focusing location, different incident wave scenarios at the structure location are produced. Simultaneous measurements of wave shape evolutions upon impingement, wave impact pressures on the platform deck, platform motions and tether forces are carried out for synchronized analyses of the wave kinematics/dynamics and structural responses. The variation of these parameters with the incident wave profile is studied. It is found that although applying less intensive local impact pressures as compared to the highly-breaking freak wave, the slightly-breaking or non-breaking freak wave imposes the same level of adverse effect on the platform's global stability in terms of motions and tether forces. In addition, the high-crest freak wave causes violent motions of the floating platform, which are likely to induce snap loads of large amplitude and high occurrence frequency in tethers. The published results would provide useful benchmarks for validating numerical and analytical models.     

冰盖下两层流体水波与可渗透起伏海床的作用(英文)

The scattering problem involving water waves by small undulation on the porous ocean-bed in a two-layer fluid,is investigated within the framework of the two-dimensional linear water wave theory where the upper layer is covered by a thin uniform sheet of ice modeled as a thin elastic plate.In such a two-layer fluid there exist waves with two different modes,one with a lower wave number propagate along the ice-cover whilst those with a higher wave number propagate along the interface.An incident wave of a particular wave number gets reflected and transmitted over the bottom undulation into waves of both modes.Perturbation analysis in conjunction with the Fourier transform technique is used to derive the first-order corrections of reflection and transmission coefficients for both the modes due to incident waves of two different modes.One special type of bottom topography is considered as an example to evaluate the related coefficients in detail.These coefficients are depicted in graphical forms to demonstrate the transformation of wave energy between the two modes and also to illustrate the effects of the ice sheet and the porosity of the undulating bed.     

两层介质中运动潜体内波的数值计算

基于势流理论,采用Hess-Smith方法,对两层介质中运动潜体内波的进行数值计算研究,得到表面波和内波波形与水深佛鲁德数、潜深之间的对应关系。并通过计算无限水深中运动椭球体引起的兴波阻力对自编程序进行验证。     

Oblique wave trapping by vertical permeable membrane barriers located near a wall

The effectiveness of a vertical partial flexible porous membrane wave barrier located near a rigid vertical impermeable seawall for trapping obliquely incident surface gravity waves are analyzed in water of uniform depth under the assumption of linear water wave theory and small amplitude membrane barrier response. From the general formulation of the submerged membrane barrier, results for bottom-standing and surface-piercing barriers are computed and analyzed in special cases. Using the eigenfunction expansion method, the boundary-value problems are converted into series relations and then the required unknowns are obtained using the least squares approximation method. Various physical quantities of interests like reflection coefficient, wave energy dissipation, wave forces acting on the membrane barrier and the seawall are computed and analyzed for different values of the wave and structural parameters. The study will be useful in the design of the membrane wave barrier for the creation of tranquility zone in the lee side of the barrier to protect the seawall.     

潜伏式高速船型变航态自航数值模拟

针对一种具有半潜-水面航态变换功能的新型潜伏式高速船型,基于非稳态RANS方程组与VOF模型求解粘性流场,结合动态流域边界与滑移网格技术,对目标船在垂直面内三自由度运动及其喷水推进器叶轮随船定轴高速旋转的耦合运动进行数值模拟。结果表明：在相同主机平均转速条件下,所预报自航点体积傅氏数与自航模型试验结果的相对误差在7%以内;从半潜到水面的航态变换过程中,船体有显著的纵倾与升沉,船体主要克服压差阻力,船体兴波由相互叠加的首波、肩波、尾波逐渐发展为首尾分明的两个波系,在喷水推进器射流区内捕捉到生成和发展的高强度涡系。     

Wave scattering by undulating bed topography in a two-layer ocean

The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating at both the free surface of the upper layer and the interface between the two layers. Due to a wave train of a particular mode incident on an obstacle which is bottom-standing on the lower layer, reflected and transmitted waves of both modes are created by the obstacle. For small undulations on the bottom of the lower layer, a perturbation method is employed to obtain first-order reflection and transmission coefficients of both modes for incident wave trains of again both modes in terms of integrals involving the bed-shape function. For sinusoidal undulations, numerical results are presented graphically to illustrate the energy transfer between the waves of different modes by the undulating bed. U. BASU was born in 1949. She is a professor in the Department Applied Mathematics, Calcutta University, India. Her current research interests include water wave problems, continuum mechanics, etc.     

孤立波作用于V形薄壁防波堤的绕射波浪力

在一定条件下浅水波可能以孤立波形态作用于离岸结构。基于波浪绕射理论,推导V形薄壁防波堤的一阶孤立波绕射理论解。通过对孤立波作用于防波堤的波浪力进行计算,研究孤立波对V形防波堤的作用规律。通过对180°张角的有限长薄壁V形堤足够长时的绕射波浪力计算,与无限长直立薄壁堤的孤立波反射波浪力进行有效的相似性比较。结果表明:孤立波的最大无量纲波浪力明显大于相同浅水条件下Airy微幅波理论的对应结果,由此反映浅水波的非线性效应;孤立波入射角、V形堤张角、防波堤臂长与水深比以及孤立波特征参数等因素的变化均将对波浪荷载产生一定的影响。     

带有月池的非对称结构物水波辐射和激励力（英文）

A highly efficient "hybrid integral-equation method" for computing hydrodynamic added-mass, wave-damping, and wave-exciting force of general body geometries with a vertical axis of symmetry is presented. The hybrid method utilizes a numerical inner domain and a semi-infinite analytical outer domain separated by a vertical cylindrical matching boundary.Eigenfunction representation of velocity potential is used in the outer domain; the three-dimensional potential in the inner domain is solved using a "two-dimensional" boundary element method with ring sources and ring dipoles to exploit the body symmetry for efficiency. With proper solution matching at the common boundary, both radiation and diffraction potentials can be solved efficiently while satisfying the far-field radiation condition exactly. This method is applied to compute the hydrodynamic properties of two different body geometries: a vertical-walled moonpool with a bottom plate that restricts the opening and a spar-like structure with a diverging bottom opening inspired by designs of floating Oscillating Water Columns. The effects of the size of the bottom opening on the hydrodynamic properties of the body are investigated for both geometries. The heave motion of the floater as well as the motion of the internal free surface under incident wave excitation are computed and studied for the spar-like structure.     

近水面波浪力作用下潜体的非线性运动响应

通过对潜体近水面航行波浪力作用下非线性运动响应进行建模和计算，揭示了由于二阶波浪力民低速时潜艇操纵面舵力之不足，潜体的定深控制可能难于实现，产生逐渐上浮与露出波面的非线性现象。计算结果与自由自航模的试验结果相当吻合。     

Green water loading on a floating structure with degree of freedom effects

The aim of the present work is to investigate whether the degree of freedom (DOF) of a floating body has a notable effect on the maximum impact pressure due to green water on deck. The analysis is carried out for a box-shaped floating structure with a deckhouse, using experimental and numerical means to model the green water load. Green water on deck and impact on the deckhouse is generated by the impingement of a focusing wave group on a floating structure. Computations are performed using a two-dimensional constrained interpolation profile-based model solving the Navier–Stokes (N–S) equations with free surface boundary condition to deal with nonlinear water–structure interactions. The free surface is captured by a volume of fluid (VOF)-type tangent of hyperbola for interface capturing/slope weighting (THINC/SW), which is more accurate than the original THINC scheme. The verifications of the simulation through a series of model-to-model comparisons are performed in a two-dimensional glass-wall wave tank. Experimental water surface elevations, body motions and impact pressure are compared satisfactorily with the computed results for different DOFs cases. As a result, the peak impact pressure due to green water decreases rapidly with the increasing DOF.     

A B-spline Galerkin scheme for calculating the hydroelastic response of a very large floating structure in waves

This paper presents an effective scheme for computing the wave-induced hydroelastic response of a very large floating structure, and a validation of its usefulness. The calculation scheme developed is based on the pressure-distribution method of expressing the disturbance caused by a structure, and on the mode-expansion method for hydroelastic deflection with the superposition of orthogonal mode functions. The scheme uses bi-cubic B-spline functions to represent unknown pressures, and the Galerkin method to satisfy the body boundary conditions. Various numerical checks confirm that the computed results are extremely accurate, require relatively little computational time, and contain few unknowns, even in the region of very short wavelengths. Measurements of the vertical deflections in both head and oblique waves of relatively long wavelength are in good agreement with the computed results. Numerical examples using shorter wavelengths reveal that the hydroelastic deflection does not necessarily become negligible as the wavelength of incident waves decreases. The effects of finite water depth and incident wave angle are also discussed.     

基于双层Boussinesq方程的聚焦波数值模型

基于高精度双层Boussinesq方程,建立了聚焦波的时域波浪数值水槽。时间积分采用混合4阶Adams-BashforthMoulton预报-校正格式,聚焦波生成则采用累加不同频率规则波的内部造波源项法。针对Baldock等的聚焦波试验进行数值计算,计算结果与试验数据吻合较好。利用验证后模型进一步考察了非线性对数值计算聚焦波的影响,其中考虑了强非线性、弱非线性以及线性3种情况,结果表明非线性对精确模拟聚焦波至关重要,强非线性模型给出的结果最好,弱非线性次之,线性最差。     

超大型浮体结构考虑非线性项的波浪力响应计算

为求解超大型浮体结构波浪响应问题,将其简化成弹性梁板模型。以有限元软件为基础来建立超大型浮体结构的弹性梁板模型,在势流理论的基础上,将速度势分解为入射势、绕射势和辐射势三部分,并利用格林函数法推导出一阶、二阶波浪速度势的表达式。以此为理论基础,编制了相应的计算程序来计算浮体结构所受到的二阶波浪力,最后建立了梁板模型的水弹性响应方程,对非线性波浪力作用下的浮体结构的水弹性响应进行求解分析,并分析了波向对响应振幅的影响。     

船体湿表面脉动压力预报的三维非线性方法

本文给出了一种预报船体湿表面脉动压力响应的三维非线性时历模拟方法.计及瞬时物面变化引起的各种非线性因素,在时域内建立船体非线性运动方程.在每一时刻,认为船体以其瞬时平均湿表面为平衡位置做简谐振荡运动,利用三维线性频域解来简化运算.在此基础上,进一步将绕射和辐射问题在静平衡位置求解,仅考虑占主导地位的入射波和静恢复力变化的非线性,作为一种兼顾工程需要的计算精度和计算效率的简化方法.以此方法为基础编制了计算机程序,对实船进行了计算,并与模型试验进行了对比.分析比较表明,该方法能够给出令人满意的船体湿表面脉动压力响应预报结果.     

Second-order hydrodynamic effects on an arrangement of two concentric truncated vertical cylinders

The second-order diffraction problem by a piston-like arrangement that consists of two concentric surface piercing cylinders is considered. The developed matched axisymmetric eigenfunction expansion solution methodology in cylindrical co-ordinates is based on the semi-analytical formulation of the velocity potentials in the various fluid regions which are defined by the geometry of the two-body arrangement. The main difficulty associated with the specific configuration originates from the fact that the geometry defines two fluid regions that extend up to the free surface in which the inhomogeneous second-order free surface boundary condition has to be fulfilled. To this end the associated velocity potentials in these regions are decomposed into a number of components defining the so-called ‘free’ and ‘locked’ waves. The latter are calculated by solving the resulting Sturm–Liouville problems. The seek second-order velocity potential in the whole fluid domain is then derived by enforcing matching conditions for the radial velocities and the fluid pressures at the cylindrical boundaries of adjacent fluid domains. Numerical results concerning the second-order hydrodynamic loading and the wave run-up on the cylinders are given, whereas special attention is given at incident wave frequency regions where the first-order exciting wave forces attain maximum values due to the resonant fluid motions in the moonpool.     

数值波浪水池及顶浪中船舶水动力计算

基于粘流理论建立了三维数值波浪水池,模拟了非线性波浪,并对规则波顶浪中前进的拘束船模的水动力进行了计算.数值模拟中,控制方程-RANS方程和连续性方程使用有限体积法离散,非线性自由面采用VOF方法处理;在入口边界模拟柔性造波板运动产生入射波,使用位于波浪水池尾部的人工阻尼区消波.给出了非线性规则波的模拟结果以及规则波顶浪中前进的拘束船模的水动力计算结果,并与理论解及DUT(Delfi University of Technology)的试验数据进行了比较,二者吻合良好.