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.     

能量耗散效应的多域边界元法(英文)

The wave diffraction and radiation around a floating body is considered within the framework of the linear potential theory in a fairly perfect fluid.The fluid domain extended infinitely in the horizontal directions but is limited by the sea bed,the body hull,and the part of the free surface excluding the body waterplane,and is subdivided into two subdomains according to the body geometry.The two subdomains are connected by a control surface in fluid.In each subdomain,the velocity potential is described by using the usual boundary integral representation involving Green functions.The boundary integral equations are then established by satisfying the boundary conditions and the continuous condition of the potential and the normal derivation across the control surface.This multi-domain boundary element method(MDBEM) is particularly interesting for bodies with a hull form including moonpools to which the usual BEM presents singularities and slow convergence of numerical results.The application of the MDBEM to study the resonant motion of a water column in moonpools shows that the MDBEM provides an efficient and reliable prediction method.     

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.     

有限水深中垂直下潜弹性薄板的水波散射(英文)

The problem of water wave scattering by a thin vertical elastic plate submerged in uniform finite depth water is investigated here.The boundary condition on the elastic plate is derived from the Bernoulli-Euler equation of motion satisfied by the plate.Using the Green’s function technique,from this boundary condition,the normal velocity of the plate is expressed in terms of the difference between the velocity potentials(unknown)across the plate.The two ends of the plate are either clamped or free.The reflection and transmission coefficients are obtained in terms of the integrals’involving combinations of the unknown velocity potential on the two sides of the plate,which satisfy three simultaneous integral equations and are solved numerically.These coefficients are computed numerically for various values of different parameters and depicted graphically against the wave number in a number of figures.     

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.     

Scattering of Oblique Surface Waves by the Edge of Small Deformation on a Porous Ocean Bed

The scattering of oblique incident surface waves by the edge of a small cylindrical deformation on a porous bed in an ocean of finite depth, is investigated here within the framework of linearized water wave theory. Using perturbation analysis, the corresponding problem governed by modified Helmholtz equation is reduced to a boundary value problem for the first-order correction of the potential function. The first-order potential and, hence, the reflection and transmission coefficients are obtained by a method based on Green’s integral theorem with the introduction of appropriate Green’s function. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number along x-direction and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the free-surface, and the reflection coefficient becomes a multiple of the number of ripples. Again, for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. It is also observed that the reflected energy is somewhat sensitive to the changes in the porosity of the ocean bed. From the derived results, the solutions for problems with impermeable ocean bed can be obtained as particular cases.     

带有变化率的同轴圆柱体受到的波浪力研究(英文)

Wave diffraction of two concentric porous cylinders with varying porosity was studied by using an analytical method based on eigenfunction matching.The fluid domain around the cylinders is divided into three sub-domains and in each sub-domain an eigenfunction expansion of the velocity potential is obtained by satisfying the Laplace equation,the boundary conditions on the free surface and on the sea bed.The unknown coefficients of eigenfunction expansions are determined by boundary conditions on the porous hulls.In the paper,the boundary conditions are based upon the assumption that the flow in the porous medium is governed by Darcy’s law.Two porous-effect parameters applied on two porous cylinders are functions of the vertical coordinate instead of the constant.Wave loading on the outer and inner cylinder is presented in the numerical results.     

Coupled motions of two ships in irregular waves in time domain

A three-dimensional time domain approach is used to study the coupled motions of two ships with forward speed in waves. In this approach, the boundary condition is satisfied on the mean wetted hull surface of the moving bodies and the free surface condition is linearized. The problem is solved by using a transient free-surface Green function source distribution on the submerged hulls. After solving the response amplitude operator, the method of spectral analysis is employed to clearly express the motion energy spectrum and significant amplitude of two ships. For verifying the code, two same circular cylinders at beam wave are selected to calculate coupled motions by comparison with the results obtained by 3D frequency method which has been proved to be efficient for solving such problems.Two Wigley ships of different sizes with the same forward speed are chosen for numerical calculation of the interaction effect, and some useful suggestions are obtained for underway replenishment at sea.     

Ship hull plate processing surface fairing with constraints based on B-spline

The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plane curve fairing. The algorithm can be applied to global and local curve fairing. It can constrain the perturbation range of the control points and the shape variation of the curve, and get a better fairing result in plane curves. In this paper, a new fairing algorithm with constraints for curves and surfaces in space is presented. Then this method is applied to the experiments of ship hull plate processing surface. Finally numerical results are obtained to show the efficiency of this method.     

基于B样条应用的船舶波浪增阻计算（英文）

Making an exact computation of added resistance in sea waves is of high interest due to the economic effects relating to ship design and operation. In this paper, a B-spline based method is developed for computation of added resistance. Based on the potential flow assumption, the velocity potential is computed using Green's formula. The Kochin function is applied to compute added resistance using Maruo's far-field method, the body surface is described by a B-spline curve and potentials and normal derivation of potentials are also described by B-spline basis functions and B-spline derivations. A collocation approach is applied for numerical computation, and integral equations are then evaluated by applying Gauss–Legendre quadrature. Computations are performed for a spheroid and different hull forms; results are validated by a comparison with experimental results. All results obtained with the present method show good agreement with experimental results.     

水波与双圆型透水板的相互作用（英文）

In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green's integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cum-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.     

Scattering of oblique surface water waves by thin vertical barrier over undulating bed topography

The present study deals with the scattering of oblique surface water waves by small undulation on the bottom in the presence of a thin vertical barrier. Here, three different configurations of vertical barriers are investigated. Perturbation analysis is employed to determine the physical quantities, namely, the reflection and transmission coefficients. In this analysis, many different Boundary Value Problems (BVPs) are obtained out of which the first two bvps are considered. The zeroth order bvp is solved with the aid of eigenfunction expansion method. The first order reflection and transmission coefficients are derived in terms of the integrals by the method of the Green’s integral theorem. The variation of these coefficients is plotted and analyzed for different physical parameters. Furthermore, the energy balance relation, an important relation in the study of water wave scattering, is derived and checked for assuring the correctness of the numerical results for the present problem.     

A note on the solution of water wave scattering problem involving small deformation on a porous channel-bed

The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within the framework of linearized water wave theory. In such a situation, there exists only one mode of waves propagating on the porous surface. A simplified perturbation analysis, involving a small parameter ε ( ? 1), which measures the smallness of the deformation, is employed to reduce the governing Boundary Value Problem (BVP) to a simpler BVP for the first-order correction of the potential function. The first-order potential function and, hence, the first-order reflection and transmission coefficients are obtained by the method based on Fourier transform technique as well as Green’s integral theorem with the introduction of appropriate Green’s function. Two special examples of bottom deformation: the exponentially damped deformation and the sinusoidal ripple bed, are considered to validate the results. For the particular example of a patch of sinusoidal ripples, the resonant interaction between the bed and the upper surface of the fluid is attained in the neighborhood of a singularity, when the ripples wavenumbers of the bottom deformation become approximately twice the components of the incident field wavenumber along the positive x-direction. Also, the main advantage of the present study is that the results for the values of reflection and transmission coefficients are found to satisfy the energy-balance relation almost accurately.     

有限水深格林函数及其导数的改进Gauss-Laguerre算法

文中对计算有限水深自由面格林函数及其导数主值积分的Gauss-Laguerre算法进行了两点改进,一是通过约分从被积函数中分离出可由公式直接求解的部分,降低了被积函数其余部分中积分变量的阶数,二是采用无限水深格林函数的主值积分和指数积分相结合的方式来消除被积函数的奇异性,这两点改进不仅极大地改善了被积函数的收敛性,使获得满意精度所需要的高斯积分点数目大大降低,计算效率显著提高,而且解决了传统方法中计算频率较高时计算结果失真的问题.计算结果表明,该改进方法求得的水动力系数和法国BV船级社的Hydrostar软件的计算结果吻合良好.     

双材料中矩形裂纹问题的超奇异积分方程方法

使用超奇异积分方程方法,对双材料空间中垂直于界面的矩形裂纹Ⅰ型问题进行了研究.首先根据双材料空间的弹性力学基本解,使用边界积分方程方法,在有限部积分的意义下导出了以裂纹面位移间断为未知函数的超奇异积分方程.根据裂纹面上位移函数的分布特性,通过将位移间断函数表示为特征函数和一组多项式乘积的形式,为其建立了数值方法.数值结果表明,该方法不仅具有较好的收敛性和较高的数值计算精度,而且能够精确满足裂纹面上的边界条件.在此基础上,对不同材料组合界面对裂纹前沿应力强度因子的影响进行了分析,取得了较好的数值结果.