Trapped Modes in a Three-Layer Fluid

In this work, trapped mode frequencies are computed for a submerged horizontal circular cylinder with the hydrodynamic set-up involving an infinite depth three-layer incompressible fluid with layer-wise different densities. The impermeable cylinder is fully immersed in either the bottom layer or the upper layer. The effect of surface tension at the surface of separation is neglected. In this set-up, there exist three wave numbers: the lowest one on the free surface and the other two on the internal interfaces. For each wave number, there exist two modes for which trapped waves exist. The existence of these trapped modes is shown by numerical evidence. We investigate the variation of these trapped modes subject to change in the depth of the middle layer as well as the submergence depth. We show numerically that two-layer and single-layer results cannot be recovered in the double and single limiting cases of the density ratios tending to unity. The existence of trapped modes shows that in general, a radiation condition for the waves at infinity is insufficient for the uniqueness of the solution of the scattering problem.     

三层流体中的捕获模态分析（英文）

In this work, trapped mode frequencies are computed for a submerged horizontal circular cylinder with the hydrodynamic set-up involving an infinite depth three-layer incompressible fluid with layer-wise different densities. The impermeable cylinder is fully immersed in either the bottom layer or the upper layer. The effect of surface tension at the surface of separation is neglected. In this set-up, there exist three wave numbers: the lowest one on the free surface and the other two on the internal interfaces. For each wave number, there exist two modes for which trapped waves exist. The existence of these trapped modes is shown by numerical evidence. We investigate the variation of these trapped modes subject to change in the depth of the middle layer as well as the submergence depth. We show numerically that two-layer and single-layer results cannot be recovered in the double and single limiting cases of the density ratios tending to unity. The existence of trapped modes shows that in general, a radiation condition for the waves at infinity is insufficient for the uniqueness of the solution of the scattering problem.     

A study of fatigue crack propagation at a web stiffener on a longitudinal stiffener

Predicting fatigue crack growth after its detection during in-service inspection is necessary to prevent a loss of serviceability, such as the oil and/or water tightness of critical compartments. This paper focuses on the most typical fatigue cracks that start at the weld joint between a flat bar stiffener on a transverse web frame and the flange of a longitudinal stiffener on a bottom plate or inner bottom plate. An experiment is carried out to observe the fatigue crack propagation for two kinds of flat bars at the abovementioned connection. The experimental results, especially the surface crack growth on the flange (which dominates during the total fatigue life of the longitudinal stiffener), are compared with crack growth curves predicted using a few existing formulas. Based on the comparative study, a formula that shows the best agreement with the experiment results is selected. Weld toe magnification factors for the web stiffener are computed from the crack propagation rates measured in the experiment, and two equations for the magnification factors versus crack depth are developed for two types of web stiffeners. The selected existing formula and the proposed equations are applied to two connections at the inner bottom and side longitudinal bulkhead of an LNG carrier. The equivalent stress approach based on a long-term distribution is employed to avoid the complexity involved in dealing with the actual stress history. Using this prediction, the remaining service life until an oil or water leakage occurs at a tank boundary can be estimated when a fatigue crack at the connection is detected.     

洋山深水港区四期工程接岸结构冲刷分析

水工建筑物前沿底部冲刷严重,将对建筑物的稳定性造成巨大威胁。洋山深水港区四期工程接岸结构西端区域进行了定期的水下地形测量,本文根据取得的实测数据资料,对洋山水域的水深变化趋势进行分析及分类拟合预测,并与现行规范理论计算结果进行对比、分析得出相关结论,供洋山附近及类似工程参考。     

水底地形变化对摇板造波的影响

In the present paper,the effect of a small bottom undulation of the sea bed in the form of periodic bed form on the surface waves generated due to a rolling oscillation of a vertical barrier either partially immersed or completely submerged in water of non uniform finite depth is investigated.A simplified perturbation technique involving a non dimensional parameter characterizing the smallness of the bottom deformation is applied to reduce the given boundary value problem to two independent boundary value problems upto first order.The first boundary value problem corresponds to the problem of water wave generation due to rolling oscillation of a vertical barrier either partially immersed or completely submerged in water of uniform finite depth.This is a well known problem whose solution is available in the literature.From the second boundary value problem,the first order correction to the wave amplitude at infinity is evaluated in terms of the shape function characterizing the bottom undulation,by employing Green’s integral theorem.For a patch of sinusoidal ripples at the sea bottom,the first order correction to the wave amplitude at infinity for both the configuration of the barrier is then evaluated numerically and illustrated graphically for various values of the wave number.It is observed that resonant interaction of the wave generated,with the sinusoidal bottom undulation occurs when the ratio of twice the wavelength of the sinusoidal ripple to the wave length of waves generated,approaches unity.Also it is found that the resonance increases as the length of the barrier increases.     

Trapped waves within the blocking frequency under compressed sea ice and two-dimensional current

The existence of trapped modes due to a horizontal submerged rigid cylinder placed below a compressed ice-covered surface is shown to exist within the frequency band of wave blocking by employing linearized water wave theory and with the inclusion of the effects of a two-dimensional current and the obliqueness of the propagating wave. A new modified multipole expansion method catering to the multiple propagating modes is proposed. The impact of different choices of propagating modes at a fixed frequency within the above-mentioned band on the trapped modes is detailed. Multiple trapped modes whose number depends on the direction and magnitude of the current exist within the frequency band. Out of the three choices of current types considered, while two of them result in the generation of trapped modes for all three possible choices of the propagating wave, the remaining one shows that only one propagating mode can generate a trapped wave. A break in the continuous spectrum of the trapped mode frequency due to the wave blocking and at the point of inflexion is presented. There exists a region of angle of propagation within which an abundance of the trapped mode is shown. The surface profiles for different angles of propagation and choices of propagating modes are illustrated graphically. The trapped modes associated with a higher angle of propagation decay at a faster rate.     

大范围直线运动梁的非线性共振响应计算

以两端铰支直梁的大范围直线运动为研究对象,建立了直梁纵横运动的动力学模型,利用多尺度法,求解了纵横向运动微分方程,解决了纵向运动对横向运动的耦合影响关系,为研究非线性动力学特性奠定了基础,并计算了主共振响应.通过对文中的算例结果与非线性有限元计算结果比较,得出两种计算结果相差很小,证明该动力学模型是正确的.从计算结果可知,在一阶共振外部激振条件下,2,3阶振幅同样为零.     

Vortex-induced vibration of a tension leg platform tendon: Multi-mode limit cycle oscillations

This paper studies the application of mathematical models to analyze the vortex-induced vibrations of the tendons of a given TLP along the Indian coastline, by using an analytical approach, analyzed using MATLAB. The tendon is subjected to a steady current load, which causes vortex-shedding downstream, leading to cross-flow vibrations. The magnitude of the excitation (lift and drag coefficients) depends on the vortex-shedding frequency. The resulting vibration is studied for possible resonant behavior. The excitation force is quantified empirically, the added mass by potential flow hydrodynamics, and the vibration by normal mode summation method. Non-linear viscous damping of the water is considered. The non-linear oscillations are studied by the phase-plane method, investigating the limit-cycle oscillations. The stable/unstable regions of the dynamic behavior are demarcated. The modal contribution to the total deflection is studied to establish the possibility of resonance of one of the wet modes with the vortex-shedding frequency.     

A numerical study of the effects of bottom and sidewall stiffeners on sloshing behavior considering roll resonant motion

In the present study, aiming to provide practical guidance for the structural design, the effects of the small bottom and sidewall stiffeners on sloshing loads in shallow and intermediate liquid conditions are investigated numerically. The interaction between the highly nonlinear free surface flow and a large number of small stiffeners is modeled based on the Moving Particle Semi-implicit method. 2D models of a rectangular clean tank and tanks with small sidewalls or bottom stiffeners are considered. For filling ratios ranging from 5% to 20%, harmonic angular motions with periods around the analytical sloshing resonant ones are applied. Simulation snapshots and computed pressure time series, pressure variation, wave run-up, maximum fluid velocity, and kinetic energy were provided to clarify the complex interaction between the small baffles and the shallow free surface flow. As a result, except for the tanks with bottom stiffeners in shallow liquid conditions, in which the response under actual resonant frequency should be considered, the response computed using the clean tank excited by its resonant period can be adopted as a conservative estimation for the sloshing loads of actual tanks with small stiffeners.     

Bathymetric influences on the lower Chesapeake Bay hydrography

Observations of salinity and density in the lower Chesapeake Bay are used to describe the bathymetric influence on the transverse hydrographic structure in the area. Current velocity observations of high spatial resolution are also used to relate the flow structure to the hydrographic structure. Tidal flow characteristics in the lower bay are affected by the combination of bathymetry and hydrography. Increased stratification over channels relative to shoals may increase M₂ ellipticity with depth over channels but not over shoals. It is found that three consistent hydrographie features can be related to the transverse structure of the longitudinal flow: (1) persistent stratification over channels due to differential tidal advection of density gradients, (2) development of bottom front separating net inflows from net outflows at the region south of Chesapeake Channel, and (3) outflow of low salinity water at the northern end of a lower bay section. Based on these hydrographie features, two basic hydrographic regimes are proposed to exist throughout the year in the lower Chesapeake Bay: (1) a low buoyancy-high mixing energy regime of stratification restricted to channels, a northward monotonical increase in salinity, and a weak bottom front, and (2) a high buoyancy-weak mixing energy regime of stratified conditions everywhere, a large region of northward salinity decrease at the northern half of the section, and a robust bottom front. The dynamics in the transverse direction for the former regime is ageostrophic, and in the latter regime the contribution by geostrophy is approximately 50% as bathymetric influences become less evident.     

河北曹妃甸近海区地貌与沉积特征分析

依据现场调查资料与前人的研究成果,对该海区的沉积分布特征进行了分析,认为该区沉积物自岸向海的粒径分布呈由粗而细的分布特征。近岸浅滩为细砂,深水区为粉砂质粘土,自东向西的分布,也显示了由粗而细的分布特征,粒径最细的区域在曹妃甸西南侧的深水区。拟建港区水深条件优越,可利用岸线长,并有天然的进出港航道,具有非常良好的开发前景。     

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.     

对称波形底箱型水面防波堤性能试验研究

为了提高箱型水面防波堤的消波性能,将箱型水面防波堤的主体底部外形进行了改造,即将主体底部由平底改造为对称波形底,提出了一种对称波形底水面防波堤。对平底和对称波形底箱型防波堤分别进行了物理模型试验研究。试验时,将平底和对称波形底的方箱型消波主体通过支架固定在小型波浪水槽中,保持水槽水深不变,改变箱体吃水、波陡、波长,进行了系列试验。给出两种模型的透射系数、反射系数和能量损耗系数随相对宽度BL的变化规律。通过比较发现:对称波形底的消波性能比平底的优良,增加的消波效果高达60%左右;两种模型的反射系数相差无几,说明改变箱型底部结构对于防波堤反射性能的影响不大;对称波形底对于波能的损耗作用要强于平底。     

基于边界元理论模型的舰船腐蚀相关电场衰减规律

基于边界元理论,建立了舰船与腐蚀相关的电场模型,初步研究了舰船腐蚀相关电场在深海环境中随水平距离及深度的衰减规律。结果表明,电场横向分量与垂直分量随纵向距离的衰减速率要大于纵向分量。随正横距离的增加,电场纵向分量与垂直分量的衰减速率逐渐减小,而横向分量为先增大,后逐渐减小。正横距离一定时,电场各分量随深度的增加,衰减速率逐渐减小。     

洋山港区域挟沙力公式研究*

利用基于能量平衡观点推导的挟沙力公式,考虑到洋山港海域涨落潮期间悬沙浓度存在一定差异,分别建立了 该区域涨潮时期及落潮时期挟沙力公式。利用计算底部通量切引力公式与挟沙力公式相等方法,估算了实测期间水体挟沙 力值,并以洋山港2003年10月实测的水沙资料进行率定。最后,采用洋山港2005年7月实测含沙量资料对公式计算结果进行 验证。验证结果表明,所建立的挟沙力公式具有较高精度,其计算的含沙量变化与洋山港实际情况较为符合。     

浅底远程海底混响(英文)

The method of coupled mode is introduced for investigation of bi-static distant bottom reverberation of impulsive source in shallow water, which will not contradict with principle of reciprocity in all cases. And the method of multi-pole for directional source is also introduced. It shows that in case of layered medium, intensity of bi-static bottom reverberation will decease according to the cubic power of receiving time t, and the transverse spatial correlation of bottom reverberation is a little greater than longitudinal correlation for equal separation of receivers, and both vary in form with the receiving time.     

大连大窑湾港湾振荡数值模拟研究

采用Boussinesq数值波浪模型,模拟得到大窑湾不同水域的固有频率。模拟了不规则波入射时全湾水面响应状况,结果表明:谱峰周期较小的不规则波入射大窑湾港内,经过一定长的时间,波能会在局部地区发生高频到低频的传递,从而诱发局部低频波动。外海波浪入射不会导致全湾水域整体振荡,但湾底及南岸小港池易发生局部水体振荡。采用减小边界反射系数的措施,可有效降低局部水域的波动幅度。     

海港工程疏浚对波浪传播的影响

针对海港工程疏浚边界处大角度入射波浪的显著折射和类似"全反射"现象,及其可能对航道、防波堤及港内不同位置产生的不利影响,采用Boussinesq方程建立典型数学模型,并对相关控制性试验要素进行无量纲处理,试验得出不同条件下的波浪场分布及各要素的影响规律。结果显示,各类影响要素中,入射波高-水深比、海底坡度、入射角对最大波高值及波能聚集位置的影响相对显著。     

浅海宽带声源深度判决方法

被动声呐系统具备区分水面和水下目标的能力是十分重要的。针对此问题,文章提出了一种在浅海环境下利用单水听器区分水面和水下目标进行分类的方法。声源深度判决问题可以看作二元分类问题,在理想浅海波导的相干多途信道模型下,推导了海底和海面反射声与直达声时延差比值的关系式,并基于该比值构建了与声源距离无关的深度判决统计量,利用该统计量与预设门限进行对比,可以对水面和水下声源进行区分。在宽带噪声源的假设下,接收信号的功率谱中含有与多途时延量有关的周期分量,对功率谱进行稀疏性约束,可利用正交匹配追踪算法对海底和海面反射声时延进行估计。计算机仿真给出了时延估计性能,分析了时延估计误差对算法的影响性能,同时利用蒙特卡罗试验方法验证了所提声源深度判决方法的有效性。     

通州湾港区一港池回淤对策

通州湾港区一港池建在辐射沙洲南缘腰沙高滩上,港池航道开挖后的回淤问题是工程设计关注的焦点.设计时通过研究工程海域潮流、波浪、泥沙、底质等自然特征,分析影响回淤的主要因素,从挡沙堤平面布置、备淤深度确定、维护疏浚、船舶吃水控制等方面提出一系列针对性措施.研究认为:通州湾港区一港池建在粉砂质浅滩上,港池航道开挖必会出现回淤...