On response of structures to random waves

The solution to the non-linear, stochastic, ordinary differential equation governing the dynamic response of offshore structures to random waves, hitherto achieved by the statistical equivalent linearization method, is approached in a different manner. It is shown that the correlation function of the response is governed by a non-linear integral equation which can be solved successively. To the first order of approximation, the solution coincides with that of the statistical equivalent linearization method. This equation is solved up to the second order.     

非线性载荷对船中弯矩响应影响

给出舰船结构水弹性分析的通用公式,分析典型高速船的水弹性响应,将总响应分为线性和非线性,前者用线性势流理论计算,后者用船体—流体系统脉冲响应函数的卷积积分和水动力非线性修正得到。计算表明线性解答过高地估计了共振点刚体运动,从而导致弯矩预报不准确,而非线性模拟的中拱/垂弯矩均与实验吻合较好。     

An inverse method for reconstructing the density and sound speed profiles of a layered ocean bottom

A standard inverse problem in underwater acoustics is the reconstruction of the ocean subbottom structure (e.g., the density and sound speed profiles) from an aperture- and bandlimited knowledge of the reflection coefficient. In this paper we describe an inverse solution method due to Candel et al. [12] which is based on the scattering of acoustic plane waves by a one-dimensional inhomogeneous medium. As a consequence of applying the forward scattering approximation to a local wave representation of the acoustic field, they obtain an expression for the reflection coefficient in the form of a nonlinear Fourier transform of the logarithmic derivative of the local admittance. Inversion of this integral transform enables the recovery of the admittance profile via the numerical integration of two first-order differential equations which require as reflection data a single impulse response of the medium. Separate recovery of both the density and sound speed profiles requires two impulse responses for two different grazing angles. In this case, four differential equations need to be integrated instead of two. To illustrate the capability of the method, we present numerical reconstructions which are based on synthetic reflection data for a geoacoustic model that represents the acoustic properties of the surficial sediments for a site in the Hatteras Abyssal Plain.     

The transient response of an ocean to moving wind field

The paper studies the short period response of an unbounded and uniform ocean to moving wind field. Firstly, it is shown that the response disturbance has two kinds of motion, one is geostrophical and other is inertial gravity wave. Secondly, this paper studies the disturbance source caused by a circular wind field which moves rapidly in a straight path on a horizontal plane. It is shown that the disturbance source is mainly determined by the distribution of the curl of wind stress. Thirdly, this paper studies the solution of disturbance equation with nonhomogeous term of disturbance source as an impulse. It is shown that the oceanic response is determined by disturbance source. Finally, by calculating numerically the current velocity and surface elevation in time, it is shown that the intensity, spatial scale and duration of the response are closely related to wind field.     

A numerical study on the generation of the small meander of the Kuroshio off southern Kyûshû

The generation of small meanders of the Kuroshio off southern Kyûshû is investigated. Basing on the fact that the small meanders tend to follow an increase in velocity of the Kuroshio in the Satsunan region (Sekine andToba, 1981), the influence of this velocity increase on the quasi-stationary path of the Kuroshio is studied numerically. Simplified bottom and coastal topographies are employed in a two layer model ocean. A quasi-stationary numerical solution with a constant inflow is used for the initial condition, and a temporal increase in the inflow with corresponding leakage is employed as the boundary condition to investigate nonlinear effects due to the increase in current velocity. Experiments for four different physical models are carried out to determine the specific roles of the continental slope, the planetary-effect, and density stratification. Temporal increase in the inflow tends to cause offshore shift of the current path. But the topographic effect of the continental slope is strong enough that no significant shift of the current path occurs in the case of the barotropic ocean. However, in the case of a baroclinic ocean, temporal increase in the inflow does cause generation of small meanders, because density stratification diminishes the topographic effect. A larger density stratification provides more favorable condition for the appearance of the small meander, and a cyclonic eddy is formed on the continental side of the small meander path.     

Theoretical Analysis of A Buoyant Jet Interacting with Small Amplitude Waves

A new theoretical solution is presented here for the dynamic characteristics of a buoyant jet due to opposing small amplitude waves.The conservation equations of mass,tangential momentum and vertical momentum are solved by the integral method which encompasses the Gaussian profiles of velocity and density.The action of waves is incorporated into the equations of motion as an external force and a new exact solution is obtained to predict the trajectory,velocity distribution and boundary thickness of the buoyant jet over an arbitrary lateral cross section.It is found that the velocity along the centerline is inversely proportional to the ratio of the momentum of the wave to the buoyant jet.The averaged boundary width varies with the fluctuation of the boundary width,the distance from the orifice and the velocity correction function.Owing to the motion d waves,the fluctuation of the boundary width is proportional to the wave steepness.     

层化流体中半板造波的内波解

为了形象地说明内波的传播模式,研究给出了内波水槽中由半板造波所形成的内波解。结合Ｖａｅｉｓａｅｌａｅ频率Ｎ（ｚ）＝ｃｏｎｓｔ和简化Ｈｏｌｍｂｏｅ两种密度剖面模式讨论了内波场的传播图案。在内波水槽中成功地形成了上述两种密度剖面,相应的实验印证了本文分析的正确性。     

A numerical method for the solution of a line source under a free surface

A modified source-and-dipole type singularity panel method is proposed to calculate the flow properties for an oscillating arbitrary body in the presence of a free surface. The technique is based on Green's identity whereby the boundary value problem is expressed as a boundary integral equation which is solved numerically. The free-space Green function is used in the integral equation. To demonstrate the feasibility of the method, the problem of a pulsating submerged line source under a free surface is treated and results are compared with the exact solution.An excellent agreement with the theory is obtained for panel density of about ten panels per wavelength and paneled water surface length of two wavelengths with very low computing times, indicating the feasibility of the method for unsteady water wave problems.     

光透射-光反射方法的光程放大校正因子研究

光透射-光反射方法是获取水体悬浮颗粒物吸收系数的重要方法,文中阐述利用积分球装置获取测量悬浮颗粒物吸收系数测量的关键参数——光程放大校正因子,验证与比对效果表明,这个结果与传统的光程放大校正因子可比。     

Dynamic Plastic Response of Circular Plates Resting on Fluid with Finite Deformation

This paper concerns the dynamic plastic response of a circular plate resting on fluid subjectedto a uniformly distributed rectangular load pulse with finite deformation.It is assumed that the fluid isincompressible and inviscous,and the plate is made of rigid-plastic material and simply supported along itsedge.By using the method of the Hankel integral transformation,the nonuniform fluid resistance is de-rived as the plate and the fluid is coupled.Finally,an analytic solution for a circular plate under a mediumload is obtained according to the equations of motion of the plate with finite deformation.     

岛屿环流理论发展回顾及展望

为了寻找岛屿环流理论进一步发展的突破口,使其在长期气候变化背景下海洋的响应以及深海环流等海洋领域前沿研究方向中继续起到指导作用,首先回顾了岛屿环流理论的发展过程,对其重要的发展里程碑和实际应用进行了系统梳理。同时,对岛屿环流理论未来进一步丰富发展的重点方向进行了展望。分析结果显示,该理论仍存在深入发掘的潜力,可在积分路径设计、时间变化项的影响和地形及斜压效应的影响等多方面进行细节修正和补充,拓展其应用的时间和空间尺度。     

Reflection of surface waves by submerged cylinders

Reflection from submerged cylinders are studied by means of integral equations. By expressing the solution as a distribution of vortices, the integral equations become non-singular for closed contours. It is shown that the method gives a short and easy proof for the classical result that no reflection occurs for the circular cylinder. The reflection power for the elliptic contour and the flat plate are studied when the bodies are situated deeply below the surface.     

Adiabatic density surface,neutral density surface,potential density surface,and mixing path*

In this paper,adiabatic density surface,neutral density surface and potential density surface are compared.The adiabatic density surface is defined as the surface on which a water parcel can move adiabatically,without changing its potential temperature and salinity.For a water parcel taken at a given station and pressure level,the corresponding adiabatic density surface can be determined through simple calculations.This family of surface is neutrally buoyant in the world ocean,and different from other surfaces that are not truly neutrally buoyant.In order to explore mixing path in the ocean,a mixing ratio m is introduced,which is defined as the portion of potential temperature and salinity of a water parcel that has exchanged with the environment during a segment of migration in the ocean.Two extreme situations of mixing path in the ocean are m=0(no mixing),which is represented by the adiabatic density curve,and m=1,where the original information is completely lost through mixing.The latter is represented by the neutral density curve.The reality lies in between,namely,0m1.In the turbulent ocean,there are potentially infinite mixing paths,some of which may be identified by using different tracers(or their combinations)and different mixing criteria.Searching for mixing paths in the real ocean presents a great challenge for further research.     

A nonlinear viscoelastic bend stiffener steady-state formulation

Bend stiffeners are essential components of a flexible riser system, employed to ensure a smooth transition at the upper connection and to protect the riser against over bending and from accumulation of fatigue damage. The highly nonlinear rate dependent behavior of these structures directly affects the integrity assessment of the riser in one of its most critical regions, the top connection. A steady-state formulation (disregarding inertial forces) and numerical solution procedure is developed in this work employing the perturbation method for a nonlinear viscoelastic bend stiffener large deflection beam model subjected to harmonic loading conditions. For stochastic loading conditions, the response is calculated employing the superposition principle by summing up the steady-state result of a number of individual frequency components. A time domain formulation is also derived employing the state-variable approach for the numerical solution of the resulting hereditary integral in the governing equations. A case study is presented for the top connection system of a 4″ ID flexible riser using relaxation and tensile experimental data obtained from a typical class of bend stiffener polyurethane. Harmonic and stochastic input loading conditions are employed for time and frequency domain model comparison/validation and to assess loading history and frequency influence in the curvature response.     

沉箱基础对摇板式波浪能装置水动力性能影响研究

摇板式波浪能转换装置具有频率响应范围广、可靠性好、常规海况下转换效率高、建造成本低等优点。基于势流理论建立具有沉箱基础的摇板式波浪能装置水动力性能的解析解。将解析结果与文献中已有结果和边界元数值结果进行了对比,验证了解析解求解过程的正确性。通过算例分析,研究了波浪入射频率、沉箱基础高度、沉箱基础宽度、摇板位置、摇板厚度和摇板密度对装置能量俘获效率的影响。研究结果表明：采用合适高度的沉箱基础能显著提升装置性能;长波海况下,摇板铰接在沉箱基础背浪侧上表面时装置性能更佳,而短波海况下,摇板铰接在沉箱基础迎浪侧上表面更为合理;沉箱基础宽度的推荐值为0.5到1.0倍水深;适当减小摇板厚度能够提升装置性能;应优先选用密度较大的摇板。     

一种基于Roe格式的有限体积法在二维溃坝问题中的应用

溃坝属于典型的非恒定含间断的浅水问题。应用有限体积法离散二维浅水控制方程的守恒型方程组,将基于近似黎曼解的Roe格式用于数值计算溃坝问题,并利用MUSCL方法构造二阶空间积分格式和预测-校正二步法构造二阶时间格式,从而使数值解的整体达到二阶,提高了精度。文中算法在一维溃坝的Stoker问题的数值结果与解析解进行对比,结果证明了此方法的可行性。应用此方法在二维溃坝问题上的结果,说明了此算法可有效模拟溃坝水流的演进过程。     

水深有陡变的人工港域内波高分布的数值计算方法

首次将单源点法应用于水深有陡变的人工港域内波高分布的数值计算,结果与一维理论解符合极好,并与工程实例的物理模型试验结果符合也很好.     

Determination of the statistical characteristics of the specular points of 3 dimensional Gaussian sea surface

The inverse problem in the form of Fredholm integral equation of the first kind for determining the distribution density of the number of specular points of 3-D Gaussian sea surface is formulated and solved. The kernel of this equation is determined by the characteristic function of the distribution of radii of curvature at the specular points. On the basis of numerical experiments, and also by using images of the Sun glitters it is shown that on the known distribution density of the intensity of reflected light it is possible to define the distribution densities of both the number of specular points and the radii of curvature at the specular points.     

A novel decomposition of the quadratic transfer function (QTF) for the time-domain simulation of non-linear wave forces on floating bodies

In the present study, a novel method is proposed for the separation of the second-order sum- and difference-frequency wave forces—that is, quadratic transfer functions (QTFs)—on a floating body into three components due to wave–wave, wave–motion, and motion–motion action. By applying the new QTF components, the second-order wave forces on a floating body can be strictly computed in the time domain. In this work, the boundary value problems (BVPs) corresponding to the three kinds of QTF components were derived, and non-homogeneous boundary conditions on the free surface and the body surface were obtained. The second-order diffraction potentials were determined using the boundary integral equation method. In the solution procedure, the highly oscillatory and slowly converging integral on the free surface was evaluated in an accurate and effective manner. Furthermore, the application of the QTF components in the time domain was demonstrated. The second-order exciting forces in the time domain were divided into three parts. Each part of these forces was computed via a two-term Volterra series model based on the incident waves, the first-order motion response, and the QTF components. This method was applied to several numerical examples. The results demonstrated that this decomposition yields satisfactory results.     

Solution of the problem of propagation of water waves over a pair of asymmetrical rectangular trenches

The problem of propagation of obliquely incident surface water waves over a pair of asymmetrical rectangular trenches in a channel of finite depth is examined for its solution. The mathematical problem is handled for its numerical solution with the aid of a system of singular integral equations of first kind. The resulting integral equations are solved numerically by using suitably designed polynomial approximations of the unknown functions. System of linear algebraic equations is obtained by utilizing the zeros of Chebyshev polynomial of first kind as collocation points and hence the occurrence of ill-conditioned matrix is avoided. The effectiveness of the pair of trenches is studied by analyzing the physical quantities namely the reflection and transmission coefficients. As a special limiting case, the results for a single trench problem are derived and are found to be in excellent agreement with the results available in the literature. The effect of various parameters are analyzed through different graphs for a pair of asymmetrical trenches. The energy balance relation is derived and used to check the accuracy of numerical results.