旋转地球上不可压缩流体惯性重力波的频率方程

用微扰动方法对旋转地球上不可压缩流体的控制方程组进行线性化，得到了扰动解和流体界面上惯性重力波的频率方程。表面惯性重力波和惯性重力内波的相速公式都是这个更普遍的频率方程的特殊情况。     

旋转地球上不可压缩流体惯性重力波的频率方程

用微扰动方法对旋转地球上不可压缩流体的控制方程组进行线性化,得到了扰动解和流体界面上惯性重力波的频率方程。表面惯性重力波和惯性重力内波的相速公式都是这个更普遍的频率方程的特殊情况。     

波浪在缓变海底上传播的一个简单数学模型

基于Liu和Shi(2008)的波浪势函数零阶、一阶近似解,采用四阶龙格-库塔法,对缓变海底上一维波浪传播理论模型进行了数值求解,并对波浪在定常坡度的斜坡地形、双曲正切地形为例的传播、变形进行了研究。为了更逼真地描述流体质点的波动特性,将在Euler坐标系下得到的解转换至Lagrange坐标下的解,并绘制Lagrange坐标下坡度为0.2的海滩上的一个波周期内临近破碎前的波形的详细变化过程。此外,计算得到了变水深区域波浪速度势以及自由面的分布,并与Athanassoulis and Belibassakis[34]的结果进行了对比,表明本文模型比保留了六个瞬息项的后者更有效。     

周期性内波对横置圆柱体作用的试验研究

本文对分层流体中周期性内波与水下横向放置圆柱体模型的相互作用进行了试验研究。采用摇板法进行了内波造波试验,通过染色试验配合CCD系统得到周期性内波的相关波要素;利用测力系统对圆柱体模型在内波作用下的受力进行测量分析,得到了横置圆柱体模型上垂向力随周期性内波作用及水深的变化规律,同时对圆柱体模型垂向力和水平力进行了耦合分析。结果表明:圆柱体的垂向力会随着周期性内波的变化而变化,其最大值也会随着水深发生变化。密度跃层处横置圆柱体模型水平力的主要频率是垂向力主要频率的两倍,两个方向的内波作用力耦合后呈现"8"字形态。     

两层流体中内波作用下Spar平台运动响应

研究两层流体中Spar平台在内波作用下的运动响应问题。在线性势流理论框架,提出在内波作用下Spar平台运动响应及分段式悬链线系泊张力特性的计算方法。数值分析两层流体内界面位置、入射内波的波长以及系泊索初始预张力对Spar平台运动响应及其系泊索张力特性的影响规律,结果表明内波对Spar平台纵摇运动响应的影响是小的,但对Spar平台纵荡与垂荡运动响应及其系泊索张力的影响是不可忽视的。因此,在Spar平台的设计中,考虑内波的影响是重要的。     

内孤立波数值模拟方法研究

本文选用RNGk-ε湍流模型封闭二维不可压缩N-S方程组,选用KdV、mKdV理论作为输入条件进行内孤立波造波模拟。运用流体模拟软件Fluent建立二维内波数值水槽,用动网格手段实现网格变形模拟物理边界造波法,用VOF方法进行密度分层流体的内界面追踪,对不同非线性强度的二相流内孤立波进行了数值模拟。并将数值模拟结果与KdV、mKdV理论波形以及内波试验水槽所造内孤立波进行对比,验证了此套造波方法在Fluent中进行内孤立波模拟的可行性。     

Gerris在海洋大振幅内孤立波数值模拟中的应用

本文运用基于自适应网格的流体动力学开源软件Gerris,来建立基于Boussinesq近似下的二维不可压缩Euler方程组的数值模型,以模拟不同层化条件下稳定状态的完全非线性大振幅内孤立波。文中比较了完全非线性的用Gerris实现的Euler模型与弱非线性的KdV理论模型在刻画大振幅内孤立波结构及特征参数上的差异,说明在模拟大振幅内孤立波时,高阶非线性不应忽略。Euler模型模拟结果表明,完全非线性大振幅内孤立波的等密度面半宽度随深度变化,这使得基于KdV方程解析解、利用卫星SAR(Synthetic Aperture Radar)图像提取内孤立波极值间距来反演内波振幅的可行性存疑,需要重新评估。此外,本文用两组实测数据验证了用Gerris实现的Euler模型模拟大振幅内波的有效性。     

层结流体中的非线性内波

十多年来,用摄动法研究非线性波已经取得了相当大的成就.在流体力学方面研究较多的是浅水表面波,在大气科学方面研究较多的是Rossby波.对层结流体中的内波,则研究较少.大家知道,海洋和大气都是密度随深度或高度变化的层结(分层)流体.许多重要的自然现象,如台风、飑线、积云、湍流、海洋中的温跃层等,都和重力内波有关.随着卫星技术的发展,非线性重力内波已经在大气和海洋中观测到[1,2].从理论上研究非线性重力内波较早的是Benney(1966)[3]和Benjamin(1966[4],1967[5]),最近Maslowe和Redekopp(1980)[6]对层结剪切流动的非线性内波作了系统详细的研究.     

分层流水槽箱内垂荡板式内波造波模拟研究

提出了一种新型内波造波方法——箱内垂荡板式造波。应用 FLUENT 软件的有限体积法,采用 k-ε两方程湍流模型封闭 RANS 方程作为求解控制方程,建立二维数值内波水槽。通过模仿物理造波机运动的数值模拟结果比较表明：箱内垂荡板式造波机生成的内波与理论解十分吻合,与双板联动式造波和平板拍击式造波相比,控制简单,对自由水面的扰动小,对水槽水深的变化和分层界面位置的改变适应性好,不会造成分层水体的掺混。     

海洋内波对水声场的扰动

针对海洋内波对水声传播影响的问题，在简要引出内波方程，水声方程和内波解，射线理论之后，以水深2100m等Vaisala频率的全板造波内波解对双线性水声剖面情况计算了内波和内波对声场及声线传播的影响，结果表明，内波对声线传播的路径和时间的影响是不可忽略的。     

四层成层水域内波的研究

运用小振幅波理论研究了四层成层水域的内波运动，给出了四层成层状态下的各界面波波面位移和各层速度势的解析表达式及各层深度平均流速分布和内波波动频散关系，并与三层成层水域内波的解析结果进行了比较。     

Second-order random interfacial wave solutions for two-layer fluid with a free surface

1 Introduction Interfacial waves travelling along the interface between two fluids of different densities can be often observed in subsurface layers of the ocean since the upper subsurface layer is warmer over much of the o- cean (Umeyama, 2002). They are…     

Internal generation of waves for extended Boussinesq equations

It is studied whether the mass transport or energy transport is the proper viewpoint for internally generating waves in the extended Boussinesq equations of Nwogu [J. Waterw., Port, Coastal Ocean Eng. 119 (1993) 618–638]. Numerical solutions of the Boussinesq equations with the internal generation of sinusoidal waves show that the energy transport approach yields the required wave amplitude properly while the mass transport approach yields wave amplitude different from the required one by the ratio of phase velocity to energy velocity. The waves which pass through the wave generation point do not cause any numerical distortion while the incident waves are generated. The technique of internal generation of waves shows its capability of generating nonlinear cnoidal waves as well as linear sinusoidal waves.     

A modified Euler–Lagrange transformation for particle orbits in nonlinear progressive waves

This paper presents a modified Euler–Lagrange transformation method to obtain the third-order trajectory solution in a Lagrangian form for the water particles in nonlinear water waves. We impose the assumption that the Lagrangian wave frequency is a function of wave steepness and an arbitrary vertical position for each water particle. Expanding the unknown function in a small perturbation parameter and using a successive expansion in a Taylor series for the water particle path and the period of a particle motion, the third-order asymptotic expressions for the Lagrangian particle trajectories, the mass transport velocity and the period of particle motion can be derived directly in Lagrangian form. The wave frequency and mean level of the particle motion in Lagrangian form differ from those of the Eulerian. Finally, the third-order asymptotic solution obtained is uniformly valid in contrast with early works containing resonant terms presented by Wiegel [1964. Oceanographical Engineering. Prentice-Hall, New Jersey, pp. 37–40] (Eqs. (B.1) and (B.1), (B.2) in Appendix B) or Chen et al.[2006. Theoretical analysis of surface waves shoaling and breaking on a sloping bottom. Part 2 nonlinear waves. Wave motion, 43, 356–369] based on a straightforward expansion for two-dimensional progressive waves.     

Experimental study on internal waves in a stratified shear flow

This paper describes experiments on interfacial phenomena in a stratified shear flow having a sharp velocity shear at a density interface. The interface was visualized in vertical cross-section using dye, and the flow pattern was traced using aluminum powder. Two kinds of internal waves with different phase velocities and wave profiles were observed. They are here named p(positive)-waves and n(negative)-waves, respectively. By means of a two-dimensional visualization technique, the following facts have been confirmed regarding these waves. (1) The two kinds of waves propagate in the opposite direction relative to a system moving with the mean velocity at the interface, and their dispersion relations approximately agree with the two solutions of interfacial waves in a two-layer system of a linear basic shear flow. (2) The p-wave has sharp crests and flat troughs, and the n-wave has the reverse of this. This difference in wave profile is due to the finite amplitude effect. (3) Phase velocity of each wave lies within the range of the mean velocity profile, so that a critical layer exists and each wave has a “cat's eye” flow pattern in the vicinity of the critical layer, when observed in a system moving with the phase velocity. Consequently, these two waves are symmetrical with respect to the interface. The mechanisms of generation of these waves, and the entrainment process are discussed. It is inferred that when the “cat's eye” flow pattern is distorted and a stagnation point approaches the interface, entrainment in the form of a stretched wisp from the lower to the upper layer occurs for the p-wave, and from the upper to the lower layer for the n-wave.     

Hydroelastic interaction between obliquely incident waves and a semi-infinite elastic plate on a two-layer fluid

The hydroelastic response of a semi-infinite thin elastic plate floating on a two-layer fluid of finite depth due to obliquely incident waves is investigated. The upper and lower fluids with different densities separated by a sharp and stable interface are assumed to be inviscid and incompressible and the motion to be irrotational. Simply time-harmonic incident waves of the surface and interfacial wave modes with a given angular frequency are considered within the framework of linear potential flow theory. With the aid of the methods of matched eigenfunction expansion and the inner product of the two-layer fluid, a closed system of simultaneous linear equations is derived for the reflection and transmission coefficients of the series solutions. Based on the dispersion relations for the gravity waves and the flexural–gravity waves in a two-layer fluid and Snell’s law for refraction, we obtain a critical angle for the incident waves of the surface wave mode and three critical angles for the incident waves of the interfacial wave mode, which are related to the existence of the propagating waves. Graphical representations of the series solutions show the interaction between the water waves and the plate. The effects of several physical parameters, including the density and depth ratios of the fluid and the thickness of the plate, on the wave scattering and the hydroelastic response of the plate are studied. It is found that the variation of the thickness of the plate may change the wave numbers and the critical angles. The density ratio is the main factor to influence the wave numbers of the interfacial wave modes. Finally, the stress state is considered.     

Mass Transport in a Thin Layer of Bi-Viscous Mud Under Surface Waves

The mass transport in a thin layer of non-Newtonian bed mud under surface waves is examined with a two-fluid Stokes boundary layer model. The mud is assumed to be a bi-viscous fluid, which tends to resist motion for small-applied stresses, but flows readily when the yield stress is exceeded. Asymptotic expansions suitable for shallow lluid layers are applied, and the second-order solutions for the mass transport induced by surface progressive waves are obtained numeri-cally. It is found that the stronger the non-Newtonian behavior of the mud, the more pronounced intermittency of the flow. Consequently, the mass transport velocity is diminished in magnitude, and can even become negative (i. e. , oppo-site to wave propagation) for a certain range of yield stress.     

Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a twolayer fluid system

Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a flat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. (2004. Science in China, Ser. D, 47(12):1147-1154) for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth''s rotation both on the surface wave solutions and the interfacial wave solutions should be considered.     

Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a two-layer fluid system

Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer .uid with a top free surface and a .at bottom. The solutions were deduced from the general form of linear .uid dynamic equations of two-layer .uid under the f -plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. (2004. Science in China, Ser. D, 47(12): 1147–1154) for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the in.uence of the earth’s rotation both on the surface wave solutions and the interfacial wave solutions should be considered.     

Particle trajectories of nonlinear gravity waves in deep water

The paper presents a numerical method for calculating the particle trajectories of nonlinear gravity waves in deep water. Particle trajectories, mass-transport velocity and Lagrangian wave period can be accurately determined by the proposed method. The high success rate of the proposed method is examined by comparing the present results with those of (a) Longuet-Higgins, M.S., 1986, 1987. Eulerian and Lagrangian aspects of surface waves. Journal of Fluid Mechanics 173, 683-707 and (b) Lagrangian moments and mass transport in Stokes waves. Journal of Fluid Mechanics 179, 547-555. It is shown that the dimensionless mass-transport velocity can exceed 10% for large waves, and the Lagrangian wave period is much larger than the Eulerian wave period for large waves.