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.     

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。     

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.     

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.     

Hydrodynamics of a body floating in a two-layer fluid of finite depth. Part 2. Diffraction problem and wave-induced motions

A linearized two-dimensional diffraction problem in a two-layer fluid of finite depth was solved for a general floating body and relevant wave-induced motions were studied. In a two-layer fluid, for a prescribed frequency, incident waves propagate with two different wave modes. Thus the wave-exciting forces and resulting motions must be computed separately for each mode of the incident wave. The boundary integral equation method developed by the authors in the Part-1 article was applied to directly obtain the diffraction potential (pressure) on the body surface. With the computed results, an investigation was carried out on the effects of the fluid density ratio and the interface position on the wave-exciting forces on the body and the motions of the body, including the case in which the body intersects the interface. By a systematic derivation using Green's theorem, all the possible reciprocity relations were derived theoretically in explicit forms for a system of finite depth; these relations were confirmed to be satisfied numerically with very good accuracy. Experiments were also carried out using water and isoparaffin oil as the two fluids and a Lewis-form body. Measured results for the sway- and heave-exciting forces and the heave motion were compared with the computed results, and a favorable agreement was found.     

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.     

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.     

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.     

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.     

斜向不规则波对斜坡堤堤头作用的试验研究

在物理模型试验的基础上,描述斜向不规则波对斜坡式防波堤堤头的作用形态,分析冲击波流的形成原因,找出不同波向所产生冲击波流的影响范围及对护面块体的影响,为同类工程的设计提供借鉴.     

分段式造波机生成斜向波浪特性的理论研究*

分段式造波机是实验室模拟真实海浪以及研究波浪特性的重要设备。单元造波板的相对宽度和波浪周期是影响分段式造波机生成波质量的重要因素。通过数值模型研究分段式造波机生成斜向波浪的理论特性,分析了波浪周期与相对造波板宽度对波浪传播的影响,总结分段式造波机的有效区域范围的变化规律,可为实际试验提供参考。     

Statistical and dynamical analyses of propagation mechanisms of solitary internal waves in a two-layer stratification

The blocking effect of submarine ridges on the propagation of internal solitary waves (ISWs) over the topography of the seabed results in the fission of the solitary waves that accompany the generation of reflected and transmitted waves. In this study, multivariate analysis of variance (MANOVA) is used to investigate the inseparable relationship between the transmission and reflection. An examination of the error sums of squares and cross-products (SSCP) matrix and the correction matrix shows that the correlation between the transmission (at/ai) and reflection coefficients (ar/ai) is quite low (0.284). Moreover, from multivariate testing, including Pillai’s trace, Wilks’ lambda, Hotelling’s trace and Roy’s largest root, we conclude that the ridge height has a large effect (η = 0.456) on both the amplitude of the transmitted and reflected waves, as well as large (η = 0.411) and very large (η = 0.469) effects on the amplitudes of the transmitted and reflected waves, respectively. In conclusion, the results in the present study highlight the importance of the role played by ridge height in coherent ISW transmission and reflection during oceanic wave–ridge interactions.     

Amplitude decay and energy dissipation due to the interaction of internal solitary waves with a triangular obstacle in a two-layer fluid system: the blockage parameter

Experiments were carried out in a wave flume to examine the propagation of depression-type internal solitary waves (ISWs) over a submerged triangular-shaped obstacle. We observed the distortion and breaking of the ISW depression in a two-layer stratified fluid system as induced by the obstacle on the bottom. Physical factors, such as the amplitude of the wave, the thickness of the two layers, and the height of the submerged obstacle were utilized in our analysis of the wave–obstacle interaction. Wave breaking was determined in relation to input parameters arranged before the experimental runs. A classification scheme based on the blockage parameter ζ was proposed. The various degrees of ISW-obstacle interaction were visually classified with three schematic forms (ζ < 0.55 for a weak encounter; 0.55 < ζ < 0.7 for a moderate encounter; and 0.7 < ζ for wave breaking). Furthermore, the reflection and transmission coefficients were utilized to explore the resultant influence on changes in amplitude and energy of an ISW. The wave characteristics (e.g., amplitude-based wave reflection, energy-based reflection, amplitude-based transmission, and energy-based transmission) during the wave–obstacle interaction showed an approximately linear relation with the blockage parameter. Influenced by the submarine obstacle, the transmitted waves were found to always consist of a leading pulse (solitary wave) followed by a dispersive wave train. Moreover, due to bottom friction the energy budget of the leading pulse was reduced by a factor of at least 5% which could approach 50% in cases with strong breaking.     

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．     

Stochastic averaging for estimating a ship roll in random longitudinal or oblique waves

In this work, the C11 container ship is taken as an example to analyze its rolling performances in random longitudinal or oblique waves. Firstly, a dynamic model of C11 roll in random waves is improved, and it is verified by the model test and numerical simulation. Mathematically, this dynamic model is a one-dimensional stochastic differential equation with random parametric (and external) excitation. Secondly, an enhanced stochastic averaging method is proposed to solve this stochastic differential equation. The validity of the solutions was verified by Monte Carlo simulation. At last, the probabilistic characteristics of the extreme rolling response were investigated based on the calculated results using enhanced stochastic averaging method. According to the analysis, some advices for ship's manoeuvring can be put forward when ships are navigating in random waves.     

斜向浪作用下潜堤透射系数的计算公式

在港口水工建筑物布置中,波浪大多数是斜向作用于建筑物的,考虑斜向浪的作用更符合实际。针对这一问题,分析杨正己计算公式、Daemrich计算公式、邹红霞计算公式对本试验结果的拟合效果,并分析规则波正向入射时各影响因素对潜堤透射系数的影响,拟合出相应的计算公式。在此基础上,根据斜向规则波作用于潜堤的试验结果,分析得出斜向规则波作用下潜堤透射系数的计算公式。分析斜向不规则波试验结果,提出斜向不规则波作用下潜堤透射系数的计算公式,经检验,公式合理,可为我国潜堤结构设计提供科学的参考依据。     

Hydrodynamics of a body floating in a two-layer fluid of finite depth. Part 1. Radiation problem

A linearized 2-D radiation problem was considered for a general floating body in a two-layer fluid of finite depth. A boundary integral-equation method was developed for directly computing the velocity potential on the wetted surface of a body which is immersed in both the upper and lower layers as a general case. To do this, appropriate time-harmonic Greens functions were derived, and an efficient numerical method of evaluating those functions is proposed. Based on Greens theorem, hydrodynamic relations such as the energy-conservation principle were derived theoretically for a case of finite depth, and we confirm that those relations are satisfied numerically with very good accuracy. Experiments were also carried out using water and isoparaffin oil as the two fluids and a Lewis-form body. Measured results for the added mass, the damping coefficient, and the amplitude of the generated waves are compared with the computed results, and a favorable agreement is found.     

斜向和多向不规则波作用于直墙堤上的波浪荷载

基于三维波浪物理模型实验研究的结果,参照国内外已有的研究成果,探讨了波浪斜向性和多向性对不规则波作用于直墙堤上波浪荷载的影响,表明波浪是否在堤前破碎其影响波浪荷载的规律是不同的.建议了斜向和多向不规则波作用于直墙堤上波浪荷栽的实用计算方法.     

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.