Diffraction of oblique water waves by small uneven channel-bed in a two-layer fluid

Obliquely incident water wave scattering by an uneven channel-bed in the form of a small bottom undulation in a two-layer fluid is investigated within the frame work of three-dimensional linear water wave theory. The upper fluid is assumed to be bounded above by a rigid lid, while the lower one is bounded below by a bottom surface having a small deformation and the channel is unbounded in the horizontal directions. Assuming irrotational motion, perturbation technique is employed to calculate the first-order corrections to the velocity potentials in the two fluids by using Fourier transform approximately, and also to calculate the reflection and transmission coefficients in terms of integrals involving the shape function representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that the reflection coefficient is an oscillatory function of the ratio of twice the component of the wave number along x-axis and the ripple wave number. When this ratio approaches one, the theory predicts a resonant interaction between the bed and interface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of incident wave energy occurs if this number is large.     

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.     

经过海峡的双层流体由底部波动产生的斜向波散射问题研究(英文)

The problem of oblique wave(internal wave) propagation over a small deformation in a channel flow consisting of two layers was considered.The upper fluid was assumed to be bounded above by a rigid lid,which is an approximation for the free surface,and the lower one was bounded below by an impermeable bottom surface having a small deformation;the channel was unbounded in the horizontal directions.Assuming irrotational motion,the perturbation technique was employed to calculate the first-order corrections of the velocity potential in the two fluids by using Green’s integral theorem suitably with the introduction of appropriate Green’s functions.Those functions help in calculating the reflection and transmission coefficients in terms of integrals involving the shape function representing the bottom deformation.Three-dimensional linear water wave theory was utilized for formulating the relevant boundary value problem.Two special examples of bottom deformation were considered to validate the results.Consideration of a patch of sinusoidal ripples(having the same wave number) shows that the reflection coefficient is an oscillatory function of the ratio of twice the x-component of the wave number to the ripple wave number.When this ratio approaches one,the theory predicts a resonant interaction between the bed and the interface,and the reflection coefficient becomes a multiple of the number of ripples.High reflection of incident wave energy occurs if this number is large.Similar results were observed for a patch of sinusoidal ripples having different wave numbers.It was also observed that for small angles of incidence,the reflected energy is greater compared to other angles of incidence up to.These theoretical observations are supported by graphical results.     

Water wave scattering by a sphere submerged in uniform finite depth water with an ice-cover

Using the multipole method, we formulate the problem of water wave scattering by a submerged sphere in uniform finite water depth with an ice-cover, the ice-cover being modelled as an elastic plate of very small thickness. This leads to an infinite system of linear equations which are solved numerically by standard techniques. The vertical and horizontal forces on the sphere are obtained and depicted graphically against the wave number for various values of the depth of water and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover and also the effect of varying depth of water on these quantities. When the flexural rigidity is taken to be zero, the numerical results exactly coincide with the curves of the vertical and horizontal forces on the sphere for the cases of uniform finite depth water with a free surface.     

浅水中下潜物体有航速辐射问题的数值解

开发了一种基于非均匀有理B样条(NURBS)的Rankine源高阶面元法用于求解浅水中下潜物体有航速辐射问题。基于势流理论,流场中的扰动速度势用物体表面和自由面上分布的Rankine源来表达,同时用映像法计及水底的影响;采用NURBS曲面精确表达物面和自由面,在求出边界面上的未知源强后,物体表面的速度势分布用B样条表示;采用配置方法对边界积分方程进行求解,采用高斯—勒让德公式计算方程中的积分,同时开发了一种解决数值积分中奇异性问题的方法。采用文中数值方法求解了浅水中下潜圆球的有航速辐射问题,计算得到了下潜圆球水动力系数和自由面波形,所得水动力系数计算结果和他人的计算结果进行了比较,其吻合程度良好,从而验证了文中开发方法的有效性。     

Effects of wave directionality and choice of wave spectrum on the extreme response of a deep water jacket

Wave-induced load effects in an idealized deep water jacket are considered. The structure is selected more to examine the worst effects of wave-induced uncertainties than to represent a realistic North Sea installation. The largest natural period is about 5 9 s and the structural response is significantly affected by dynamics. The structural system is linearized and response extremes are predicted by means of a stochastic, dynamic long term response analysis. A realistic modelling of ocean waves for long term response calculations is outlined. Various possibilities concerning the choice of wave spectrum are included and the corresponding effects on the predicted extremes are demonstrated. A sensitivity study is carried out both for the quasi-static response and for the resulting dynamic response. Finally, the effects of accounting for wave directionality are indicated. This includes both the introduction of a varying main wave direction and the modelling of the shortcrestedness for a given sea state.     

渗透海床上波浪传播特性的研究

波浪在渗透海床上传播时会发生波高的衰减.基于Dean和Dalrymple(1984年)提出的渗透海床上波浪传播的理论模型,推导了波浪运动的速度势表达式和色散关系,并采用迭代方法,提出了一种求解色散方程的简单高效的数值算法,从而求得波浪的空间衰减系数(即复波数虚部).在此基础之上,研究了不同渗透系数和不同水深条件下波高的衰减规律,结果表明,波浪在传播过程中波高按指数衰减,衰减速率随渗透系数的增大和相对水深的减小而增大,但由于波浪的空间衰减系数较小,波浪的衰减也较为缓慢,通常情况下,只有当波浪长距离传播时,海床渗透导致的波高衰减才较为显著.     

计入船体变形及齿间摩擦的齿面接触疲劳强度

船舶在波浪中航行时,船体总弯曲变形会使沿船体纵向布置的齿轮机构的轴承支座中心距产生缩减.在一定条件下,这种中心距缩减会导致互相啮合的两齿轮间产生附加径向压力.本文导出了计入这种附加径向压力、齿间摩擦及轴承间隙综合影响的船用齿轮齿面接触疲劳强度优化计算公式.利用此公式计算齿面接触疲劳强度可使船用齿轮的设计更合理,更安全.     

Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean with ice-cover

Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace＇s equation by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.     

A rational analysis of intact stability hazards involving small inland passenger ferries in Bangladesh

The safety of inland passenger vessels operating in Bangladesh has been investigated. By thorough analysis of past accident data, the main causes of intact stability failures have been determined: adverse weather conditions and overloading, likely resulting in crowding to one side. Historical series of wind data were gathered and their analysis suggests that an increase in the wind speed presently used in the Weather Criterion in force in Bangladesh could be advisable. A model of a small passenger ship typically operated in Bangladesh has been analyzed in order to identify the most relevant hazards under intact ship conditions. A strongly jeopardizing effect of overloading under intact ship conditions has been detected when analyzing the hazard from the crowding of people to one side.     

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.     

舟山群岛海域潮波传播变形和不对称性探讨

舟山海域属于多岛屿海域,潮波受岛屿地形条件影响复杂。根据舟山海域4个潮位站2017年一个月实测逐时潮位以及7个临时测站的大潮、小潮短期逐时潮位资料,采用调和分析及偏度指标计算法,确定了舟山本岛至穿山半岛之间海域的分潮特征及潮汐不对称变化;通过分析浅水潮波方程中的各非线性项,确定了舟山海域浅水分潮产生的主要动力机制;评估了不同频率分潮组合产生的潮汐不对称性贡献值。研究表明,潮波方程中非线性摩擦项是舟山群岛海域浅水分潮变化和潮波变形的主要动力来源;明确了该海域潮汐以M_2和S_2天文半日潮主导,浅水分潮以M_4、MS_4分潮为主但潮幅较小,潮波传播过程中耗散潮波能量同时,潮能存在由低频分潮向高频分潮转移,呈现低频天文分潮潮幅沿程减小,高频浅水分潮潮幅增加;潮汐不对称性表现为涨潮占优,大潮期不对称性较小潮期明显,天文半日分潮M_2、S_2与浅水分潮MS_4、M_4组合是潮汐不对称性的最大贡献者。     

An upper-bound solution to the problem of plate tearing

An upper-bound solution is derived for the problem of the tearing of a metal plate by a rigid wedge. These newly proposed formulas, with no fracture parameters being used, provide an explanation to the problem of plate tearing, which is a phenomenon that occurs in the process of ship grounding. This paper starts with the proposition of a new kinematic model. Based on the fact that in many experiments there is no evidence of cracks extending ahead of the wedge tip, this new kinematic model assumes no separation between the wedge tip and the crack tip in the plate. Another characteristic of this model is that out-of-plane deformation is assumed for the region around the tip, which correlates well with the experimental observations. Rupture of the metal plate is assumed to occur ahead of the wedge tip due to ductile failure. In the case of longitudinally stiffened panels, an equivalent plate thickness is employed to take the effect of stiffeners into consideration. From comparisons of calculations with existing experimental results, it is clear that the present upper-bound solution is effective in predicting resistance force and energy absorption in the process of plate tearing, and that it can provide predictions that are close to those obtained from empirical formulas and from the theoretical formulas of Wierzbicki and Thomas, who assume that cracks run ahead of the wedge tip.     

甲板室围壁焊接波浪形变形的控制

介绍了甲板室围壁在各工序阶段因焊接引起的波浪形变形的特点 ,减小波浪变形的工艺措施包括制定正确的装焊工序、选用合适的材料、提高配缝质量、在确当的位置上安装临时工艺材并选择正确的焊接方法。对水火矫正变形进行了详细的介绍。     

双层开孔斜挡板透空式防波堤消浪性能研究

针对一种新型双层开孔斜挡板透空式防波堤消浪性能问题,研究挡板开孔率和挡板倾斜角度对防波堤消浪性能的影响。采用物理模型试验方法,得出其反射和透射系数、波能分布和堤后波幅频谱特征结果。结果表明,斜挡板开孔率越大,防波堤透射系数也越大,但在试验范围内,透射系数均小于0. 5;该类型防波堤对波浪有较好的消能性,对较长周期波以反射为主,较短周期波以消浪室消能为主,整体透射系数较短周期波略大;防波堤设计斜挡板比平挡板透射系数小,具有更好的消浪性能,最小透浪仅为后者的39%。     

波浪水池中畸形波生成的研究综述

畸形波具有异常大的波高,容易对海洋结构物造成巨大破坏。世界各大海域均有畸形波发生及其引起的海难记录,其生成机理正引起人们越来越多的关注。在实测畸形波时历的基础上,有必要在实验室中实现畸形波的生成,从而揭示畸形波的生成机理及其对海洋结构物的作用机理。目前,国内外许多学者根据畸形波所产生的海洋环境条件提出了多种多样的畸形波成因假说,并相应地形成了多种畸形波生成模型。色散聚集方法通过控制成分波相位使波浪能量定时定点聚集,简单高效,仍为大多数的畸形波生成研究的首选。在此基础上,部分学者提出或应用了迭代方法对畸形波模拟结果进行优化,以修正非线性波波作用引起的相位、幅值偏离。另一方面,薛定谔方程呼吸子解作为畸形波的一个原型,也在畸形波的生成模拟中得到成功应用。该文针对上述畸形波在数值波浪水池或物理水池中的模拟方法作了综述,可为进一步开展畸形波的机理研究及其对海洋结构物作用机理研究提供基础。     

A note on the age of radioactive tracers

The age of a water mass is often estimated experimentally using the radio-age computed from the distribution of a radioactive tracer (radiocarbon, helium–tritium). Deleersnijder et al. [J. Mar. Syst. 28 (2001) 229.] have shown that the radio-age underestimates the age of the water and is larger than the age of the radioactive tracer used for its evaluation. This result is generalized here to radio-ages computed from the ratio of two radioactive tracers. The differences between the different ages are also studied analytically and numerically as functions of the decay rate of the radioactive tracers.For small decay rates, the difference between the age of the water mass and the radio-age is shown to be proportional to the decay rate. It depends also on the level of mixing in the system; even radioactive tracers with small decay rates can provide poor estimates of the age of the water mass in a strongly diffusive flow. For small half lives, both the radio-age and the age of radioactive tracers decrease as the inverse of the square root of the decay rate.The same analysis applies to some extent to the estimates of the age of a water mass from stable tracers with known time dependent sources (e.g. chloroflurocarbons).     

结构物出水过程中的自由液面变形研究

利用有限体积法( FVM)研究了圆柱形物体垂直出水的问题.物体以恒定速度垂直出水时,初始自由液面会受到物体的抬升作用而发生变形.自由液面的峰值变化与物体的初始深度有关,但当初始深度Y＞5R时其对液面变形的影响不变.研究还发现液面变形的峰值与物体的长度无关,与物体的头、尾部形状及宽度关系较大.头部平整的物体出水时的液面峰值很大,而头部尖锐的物体出水时液面峰值较小,在双30°锥角形下,液面可以看到明显的波纹.