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.     

Second-Order Solutions for Random Interfacial Waves Under Steady Uniform Currents

1.Introduction Owingtothesimilaritiesbetweenthesurfacewaveandtheinterfacialwave,itisnaturaltoapply themethodsdevelopedforsurfacewavestothestudyofinterfacialwavesasreviewedbyUmeyama (1998;2000).Recently,Song(2004)derivedsecond ordersolutionsforrandominterfacialwavesat aconstantdepthinatwo layerfluidsystemwitharigidlidusinganexpansiontechnique,analogousto thatusedbyLonguet Higgins(1963)andSharmaandDean(1979),tostudyrandomsurfacewaves. Inthispaper,Song’sresultsareextendedtoamoregeneralcaseoft…     

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.     

剪切流中界面波的二阶Stokes波解

考虑了均匀剪切流场中强非线性界面波,建立了基于任意水深处速度而不是通常所用的平均速度为速度变量的模型,分析了其色散关系,并求得了各层速度的二阶渐近解和界面内波波面位移的二阶Stokes解,揭示了波流之间的非线性相互作用和界面波解之间的非线性相互作用。     

两层流体中矩形箱浮体的附加质量和阻尼系数

研究了两层流体中矩形箱浮体的辐射问题。基于特征函数匹配理论,针对矩形箱浮体的三种振荡运动模式(横荡、垂荡和横摇),建立两层流体中矩形箱浮体辐射势的求解方法,导出矩形箱浮体附加质量和阻尼系数的计算公式。对所建立的求解模型进行了数值计算分析,结果表明在矩形箱浮体的某个振荡频率范围内,流体的分层效应对其附加质量和阻尼系数有显著影响的。     

Higher-order Boussinesq-type equations for interfacial waves in a two-fluid system

Interfacial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa’s results (1999). The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. (1991) and Schaffer and Madsen (1995a). It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer (1998). By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa’s (1999) results, and the applicable scope of water depth is deeper.     

两层流体中多个圆柱浮体波浪力的解析方法

采用解析方法研究了线性入射波作用下两层流体中多个圆柱形淹没浮体的渡浪力特性.首先基于多极子展开方法,建立了散射势函数的解析表达式,并进一步得到浮体散射渡浪力的计算公式,然后利用边界元方法验证了本文的解析解,最后分析了不同参数的变化对双圆柱形浮体结构波浪力的特有影响.     

Hydroelastic response of a circular plate in waves on a two-layer fluid of finite depth

The hydroelastic response of a circular, very large floating structure （VLFS）, idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the plate-covered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presentedto investigate the effects of different physical quantities, such as the thickness of the plate, Young＇s modulus, the ratios ofthe densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid.Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.     

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。     

Green functions with pulsating sources in a two-layer fluid of finite depth

The derivation of Green function in a two-layer fluid model has been treated in different ways.In a two-layer fluid with the upper layer having a free surface,there exist two modes of waves propagating due to the free surface and the interface.This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating.The source point is located either in the upper or lower part of a two-layer fluid of finite depth.The derivation is carried out by the method of singularities.This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present.Furthermore,experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results.Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower,for each case.The effect of the density on the internal waves is demonstrated.Also,it is shown how the surface and internal wave amplitudes are compared for both the wave modes.The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.     

两层粘性流体中圆柱体受迫振荡数值模拟

研究两层粘性流体中无限长水平圆柱体的受迫振荡问题。在湍流模式下,采用VOF方法追踪两层流体的内界面,基于动网格技术模拟圆柱体的运动边界,对均匀流中横向振荡圆柱体的绕流场进行了数值模拟。计算受迫振荡圆柱体的升力系数、阻力系数随时间的演化曲线和圆柱体的尾涡分布,以及圆柱体的受迫振荡激发两层流体内界面的扰动,并与均匀流体的情况进行了比较分析。研究表明,流体的两层分层效应对受迫振荡圆柱体的升阻力系数和尾涡分布特性都有显著影响,在水下输油气管道涡激振动特性的工程评估中,应考虑流体的密度分层效应。     

拉格朗日描述下三层流体系统中界面内波的三阶渐近解

在流体力学中,描述流体运动有Lagrange方法和Euler方法.Euler方法是通过观测通过空间各固定位置点处流体质点的运动行为来描述流体运动规律,而Lagrange方法是跟踪各个流体质点,通过观测它们在时空运动中所走过的路径来描述流体的运动规律.在数学处理上,Euler方法较Lagrange方法简单,但Lagrange方法可以完全描述流体运动的整个流场的所有特性,而Euler方法却无法描述每个流体质点的运动轨迹.本文,我们研究具有刚性边界的三层流体系统中的界面内波,其中上层流体的密度比下层流体的密度大.通过在界面处引入朗格朗日匹配条件并使用微扰法得到了拉格朗日描述下的界面内波的一阶解、二阶解及三阶解,给出了质量输运速度、波频率、平均水平和质点运动轨迹的解.结果表明对于质量输运速度、波频率、平均水平和质点运动轨迹在界面处会有不连续性,但是我们发现在满足一定的三层流体水深比和密度比条件时这种不连续性将会消失.     

两层流体中内孤立波与潜体相互作用数值模拟

提出基于双推板的内孤立波数值造波方法,对两层流体中内孤立波与潜体的相互作用进行了数值模拟,分析不同潜深下潜体所受的内孤立波载荷特性.结果表明,内孤立波对水下潜体的载荷作用是不可忽视的.特别地,当潜体位于内孤立波中时,其所受的垂向力要远比潜体位于内孤立波下时的大.     

两层流体中振荡水平圆柱潜体水动力特性

研究了有限深两层流体中水平圆柱潜体的振荡辐射问题。在线性势流理论框架内,建立求解辐射势的多极展开理论,提出附加质量和阻尼系数的计算方法,进行了数值计算分析,并且与均匀流中的情况进行比较。结果表明,在圆柱潜体的某个振荡频率范围内,流体的分层效应对其附加质量和阻尼系数是有重要影响的。同时,对水平圆柱潜体振荡产生的自由面和内界面波动特性进行了数值分析。     

未破碎变浅随机海浪的波面高度概率分布

利用青岛海洋大学物理海洋实验室现代化的大型水槽,设计进行了多种海浪强度下,由深水传入近岸不同坡度水底上的变浅随机海浪的实验.依据实验资料分析结果表明,对变浅非正态海浪过程而言,其波面高度分布取Gram-Charlier级数前3项,所得结果与实验分布符合良好.该分布中σ、λ₃、λ₄3个参量是测点水深和波浪强度的函数,并获得了与无因次参量Hs/d之间的经验关系,为预测变浅随机海浪的波面高度分布提供了可能.     

有限深两层流体内孤立波非线性数值模拟入口边界条件研究

基于有限深两层流体KdV(Korteweg-de Vries)、eKdV(extended KdV)和MCC(Miyata-Choi-Camassa)理论,以内孤立波诱导上下层深度平均水平速度为入口边界条件,采用理想流体完全非线性欧拉方程,建立了两层流体中内孤立波生成的CFD(Computational Fluid Dynamics)数值模拟方法。以系列数值模拟结果为依据,结合内孤立波非线性和色散参数的组合条件,给出了选择合适内孤立波理论解作为CFD数值模拟入口边界条件的方法,从而实现了振幅与波形可控的内孤立波完全非线性数值模拟。     

Probability distribution of surface slope for nonlinear random sea waves and calculation of whitecap coverage

Based on the nonlinear model of two-dimensional random sea waves, a statistical distribution of wave surface slope exact to the third order is derived by using the expansion of the characteristic function and direct calculations of each order moment. Based on the distribution of wave surface slope derived in this paper, a whitecap coverage is proposed by using the limit surface slope as a criterion of wave breaking. The whitecap coverage expressed by the model depends on three parameters which can be determined in principle by the linear wave spectrum and three kinds of wave-wave interaction.     

The retrieval of the nonlinear random waves from the non-Gaussian characteristics of the sea surface elevation distribution

In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.     

Nonlinear wave interaction with a vertical circular cylinder: wave forces

Second-order wave forces on a large diameter vertical circular cylinder, computed according to a semi-analytic nonlinear diffraction theory, are compared to results of 22 laboratory experiments with regular waves. In general, predicted forces agree quite well with measured forces. In most tests, both measured and predicted maximum forces exceeded linear theory by 5 to 15%. In a few cases, however, the measured forces were less than those predicted by linear theory, in contrast to the second-order predictions. It is shown that these results are related to the phasing of various linear and nonlinear wave force components, and are consistent with those obtained by other investigators.