Wave Scattering by Porous Bottom Undulation in a Two Layered Channel

The scattering of plane surface waves by bottom undulations in channel flow consisting of two layers is investigated by assuming that the bed of the channel is composed of porous material. The upper surface of the fluid is bounded by a rigid lid and the channel is unbounded in the horizontal directions. There exists only one wave mode corresponding to an internal wave. For small undulations, a simplified perturbation analysis is used to obtain first order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom. For sinusoidal bottom undulations and exponentially decaying bottom topography, the first order coefficients are computed. In the case of sinusoidal bottom the first order transmission coefficient is found to vanish identically. The numerical results are depicted graphically in a number of figures.     

双层通道中可渗透底部起伏的波浪散射(英文)

The scattering of plane surface waves by bottom undulations in channel flow consisting of two layers is investigated by assuming that the bed of the channel is composed of porous material. The upper surface of the fluid is bounded by a rigid lid and the channel is unbounded in the horizontal directions. There exists only one wave mode corresponding to an internal wave. For small undulations, a simplified perturbation analysis is used to obtain first order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom. For sinusoidal bottom undulations and exponentially decaying bottom topography, the first order coefficients are computed. In the case of sinusoidal bottom the first order transmission coefficient is found to vanish identically. The numerical results are depicted graphically in a number of figures.     

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 Nearly Circular Cylinder Submerged Beneath an Ice-cover

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 plat...     

斜向规则波与单列桩的相互作用

文章讨论了斜向入射波与桩列相互作用。根据流体通过孔隙结构传递波角小于入射波角以及压力和体积速度连续原理,利用波阻抗和桩列的流阻分析,导出反射系数、传递系数和波浪荷载的解析公式。公式内所有参数均是已知的。用文中公式预测结果与其他研究者的正向入射波试验数据对比,理论与试验很好地吻合。     

双层流中由小型不平坦河床引起的斜向入射水波绕射研究（英文）

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.     

纵向位移波穿过微极流体中微极弹性板的传播特性研究

基于微极流体理论和微极固体弹性理论,研究了纵向位移波通过微极流体中微极弹性板时的纵向位移波、耦合波一和耦合波二等三种微极弹性波的反射和透射特性。理论分析和数值计算结果表明:在一般情况下,各种反射和透射波的振幅比是入射波的入射角、频率和介质材料特性的函数;正入射时只有纵向位移波穿过固体板,而不存在其它波的传播;掠入射时仅有入射波沿界面传播而无反射、折射和透射现象发生。文章同时还讨论了反射、折射和透射系数随入射角的变化规律。     

冰盖海洋中多孔海底结构上微小起伏边缘产生的波浪散射分析(英文)

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.     

Damping of Oblique Ocean Waves by a Vertical Porous Structure Placed on a Multi-step Bottom

Oblique ocean wave damping by a vertical porous structure placed on a multi-step bottom topography is studied with the help of linear water wave theory. Some portion of the oblique wave, incident on the porous structure, gets reflected by the multi-step bottom and the porous structure, and the rest propagates into the water medium following the porous structure. Two cases are considered： first a solid vertical wall placed at a finite distance from the porous structure in the water medium following the porous structure and then a special case of an unbounded water medium following the porous structure. In both cases, boundary value problems are set up in three different media, the first medium being water, the second medium being the porous structure consisting ofp vertical regions-one above each step and the third medium being water again. By using the matching conditions along the virtualvertical boundaries, a system of linear equations is deduced. The behavior of the reflection coefficient and the dimensionless amplitude of the transmitted progressive wave due to different relevant parameters are studied. Energy loss due to the propagation of oblique water wave through the porous structure is also carried out. The effects of various parameters, such as number of evanescent modes, porosity, friction factor, structure width, number of steps and angle of incidence, on the reflection coefficient and the dimensionless amplitude of the transmitted wave are studied graphically for both cases. Number of evanescent modes merely affects the scattering phenomenon. But higher values of porosity show relatively lower reflection than that for lower porosity. Oscillation in the reflection coefficient is observed for lower values of friction factor but it disappears with an increase in the value of friction factor. Amplitude of the transmitted progressive wave is independent of the porosity of the structure. But lower value of friction factor causes higher transmission. The investigation is then carried out for the second ca     

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.     

波浪对二层海水中的直立圆弧形透空防波堤的绕射

基于二层海水的微幅波绕射理论,应用特征函数展开法,推导了在二层海水中波浪对直立圆弧形透空防波堤绕射的波势解析解,并据此分别计算了作用于防波堤的表面波与内波载荷以及最大波面分布。计算结果表明:在防波堤结构表面适度布孔既可以明显减小所受到的表面波与内波载荷,又可改变绕射水波的最大波面分布。而表面波与内波各自作用于防波堤上的无量纲最大波浪载荷可能具有相同量级,说明内波作用不可忽视。海况与波浪条件以及防波堤几何条件等因素的相对变化对波浪的绕射均有一定影响,而表面波与内波在波浪作用的变化规律上存在一定差异。     

浅水高速船舶引起的波浪和压力场研究

基于浅水兴波理论,在线性条件下对高速薄船引起的兴波和水底压力变化进行了计算.研制了表面波和水底压力联合测量系统,对船模引起的波浪和压力场进行了测量和分析.通过计算和实验结果的比较,明确了理论模型的适用范围.     

全回转起重船风浪流中系泊运动性能预报

针对一艘全回转起重船在渤海湾区域风浪流中系泊作业的安全要求,考虑到首吊900t和侧吊400t作业时特殊性,建立了模型试验方法,并基于卡明斯六自由度运动方程建立了预报方法,对该船首吊900t和侧吊400t风浪流中系泊运动性能进行了预报,结果对比表明理论预报与模型试验结果吻合较好,验证了理论预报方法的实用价值。同时基于模型试验和理论预报的结果,对该船在渤海湾区域作业提出了建议,可为该船安全作业提供指导和参考。