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.     

冰盖下近圆柱产生的水波散射分析（英文）

Assuming linear theory, the two-dimensional problem of water wave scattering by a horizontal nearly circular cylinder submerged in infinitely deep water with an ice cover modeled as a thin-elastic plate floating on water, is investigated here. The cross-section of the nearly circular cylinder is taken as r=a(1+δC(θ)), where a is the radius of the corresponding circular cross-section of the cylinder, δ is a measure of small departure of the cross-section of the cylinder from its circularity and C(θ) is the shape function. Using a simplified perturbation technique the problem is reduced to two independent boundary value problems up to first order in δ. The first one corresponds to water wave scattering by a circular cylinder submerged in water with an ice-cover, while the second problem describes wave radiation by a submerged circular cylinder and involves first order correction to the reflection and transmission coefficients. The corrections are obtained in terms of integrals involving the shape function. Assuming a general Fourier expansion of the shape function, these corrections are evaluated approximately. It is well known that normally incident wave trains experience no reflection by a circular cylinder submerged in infinitely deep water with an ice cover. It is shown here that the reflection coefficient also vanishes up to first order for some particular choice of the shape function representing a nearly circular cylinder. For these cases, full transmission occurs, only change is in its phase which is depicted graphically against the wave number in a number of figures and appropriate conclusions are drawn.     

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.     

具有惯性表面的两层流体的柯西-泊松问题(英文)

This paper is concerned with the generation of waves due to initial disturbances at the upper surface of a two-layer fluid, as the upper layer is covered by an inertial surface and the lower layer extends infinitely downwards. The inertial surface is composed of thin but uniform distribution of non-interacting material. In the mathematical analysis, the Fourier and Laplace transform techniques have been utilized to obtain the depressions of the inertial surface and the interface in the form of infinite integrals. For initial disturbances concentrated at a point, the inertial surface depression and the interface depression are evaluated asymptotically for large time and distance by using the method of stationary phase. They are also depicted graphically for two types of initial disturbances and appropriate conclusions are made.     

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.     

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.     

线性连续分层流体中水波与截断圆柱浮体的相互作用

研究了在线性连续分层流体中水波与截断圆柱浮体相互作用的问题.在Boussinesq近似下,基于分离变量法,表明了对给定的频率,当它大于浮力频率时,流场中只有一种模态的平面前进波,当它小于浮力频率时,流场中有无数多个模态的平面前进波.基于特征函数匹配理论,建立了作用在截断圆柱浮体上水动力的计算方法.对作用在截断圆柱浮体上的水平波浪力、垂向波浪力和力矩进行了数值计算分析,表明了在某个频率范围内,流体的线性连续分层效应对这些水动力量的影响是不可忽视的.特别地,在入射波频率小于浮力频率时,高阶模态入射波对截断圆柱浮体水动力的影响也是重要的,在海洋工程的实践中应予以特别关注.     

双层开孔消浪板结构消能性能分析

双层开孔消浪板是一种新型消能结构,其结构通过上层开孔板和下层实心板两部分来解决结构的消能问题．文中通过模型试验的方法来验证结构的消能性能,同时,对双层开孔消浪板结构在规则波作用下的消能系数随3个主要影响因子（相对板宽B／L,相对开孔A／A0,波陡H／L）变化的结果进行分析．通过分析和比较消能系数与影响因子之间的相互关系,证明双层开孔消浪板结构具有较好的消能效果．     

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。     

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。     

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.     

两层流体中运动物体的兴波特性

研究了在两层流体中定常运动的三维物体产生的内波尾流场特性.在势流理论假设下,基于Green第三公式,建立了一组基于Rankine源的分层变形边界积分方程,提出了一种基于四节点双线性等参元的数值实现方法,有效地处理了在场点处立体角的计算和数值积分中的奇异性问题.对定常运动三维球体产生的表面波和内界面波进行了数值模拟,并与定常运动点源的结果进行了比较.