深水斯托克斯波的一种近似解析解

本文给出斯托克斯波的一种新的近似解法,得到了与经典三阶以上斯托克斯波不同弥散关系和波面函数.在与经典斯托克斯波比较后,它被证明是一种更好的逼近解析解.它对精确确定斯托克斯波解,特别是确定高阶斯托克斯波的表达形式有重要应用价值.     

基于二阶斯托克斯波理论的辐射应力垂向分布

基于二阶斯托克斯波理论推导了辐射应力的垂向分布表达式,通过算例讨论了辐射应力在深水和有限水深条件下的垂向分布规律,并与基于微幅波理论的辐射应力进行了比较.结果表明,在波浪非线性不强时,基于二阶斯托克斯波理论的辐射应力与基于微幅波理论的辐射应力表达式计算结果接近;而当水深较浅波浪非线性较强时,基于二阶斯托克斯波理论的辐射应力在近表面处明显大于基于微幅波理论的辐射应力.采用二阶斯托克斯波理论推导的波浪辐射应力更为合理地反映了波浪非线性效应.     

深水中极限波峰下速度场快速算法

基于五阶斯托克斯规则波理论,提出了一种快速求解深水极限波峰下速度场的数学模型.研究中,按照上跨零点和下跨零点的方法由计算或实测的极限波浪波面时间历程确定包含极限波峰的相邻两个周期的平均值为五阶斯托克斯规则波的波浪周期,然后根据极限波峰反推确定波浪入射波幅.通过与已有的数值结果和实验数据对比,验证了所建立的数值模型可以快速准确的计算出极限波峰下的速度场,相比其他模型,更适合于工程应用.     

精确边界条件导出的最优化五阶斯托克斯波

本文应用变分原理的方法，根据精确的动力自由表面边界条件导出五阶斯托克斯波。所得 边界条件的误差平方和最不意义的最优化解，本文还讨论了确定伯努利方程中的示知函数ｆ（ｔ）的方法。     

水平圆柱上波压力的非线性分析

本文运用二阶斯托克斯波浪理论和非线性补偿流理论,对水平圆柱上波压力的水平分力进行非线性分析。根据实测的最大水平分力及其相位角的试验资料,确定水平圆柱的惯性系数、阻力系数及其比值,得到了它们沿水深变化的函数关系式,为水平小直径圆柱上应用莫利逊公式计算波压力的水平分力提供了可能性。     

水重力波统一变分原理导出的流函数波

在应用水重力波统一变分原理导出线性波、弧立波和五阶斯托克斯波的基础上,应用水重力波统一变分原理导出流函数波。本文将直接处理运用自由表面边界条件和动力自由表面边界条件,而不应用条件Σ（Ｑａｖ－Ｑｉ）＾２＝ｍｉｎ,及相应的极值条件方程组,并得出最优化解。当波高Ｈ、周期Ｔ、水深Ｄ和阶数给定后,原有的流函数解也就确定了,如果发现其与实际情况不符,也不能再进行调整。但本文方法则可以增加几个约束条件进行调整,     

计算波群折射的方法及其应用

根据汪炳祥１９８提出的普遍几何群速概念和波群波向线及其波向线散开因子方程，提出一种计算和绘制波群折射的数值方法。为使本方法较具普遍性，将旋转坐标系引入控制方程并予以变形与简化。数值计算采用Ｒｕｎｇｅ－Ｋｕｔｔａ法。将上述方法应用于胶州湾湾口附近海域的波群折射计算并绘制其折射图。将计算结果分别与依几何群速建立的波群折射和单频率波折射结果比较，可明显地看出基本方法的结果优于后两者。     

水重力波统一变分原理导出的风生斜剖面波浪

考虑到目前应用的规则波具有对称于垂直坐标轴的波剖面,这与实际的风生海浪有较大差别,在应用水重力波统一变分原理导出线性波、弧立波、五阶斯托克斯波和流函数波的基础上,本文应用水重力波统一变分原理导出风生斜剖面波浪。其特点是波剖面在风压的作用下,不对称于垂直坐标轴,而是呈向前倾斜的形状。     

分段式造波机生成波的方法和特性

本文叙述了分段式造波机生成波的理论和方法，通过试验确定了造波板前过渡段的长度，研究了分段式造波机生成波浪的特性，并将规则波的试验结果与理论结果进行了比较，给出了有效实验区的范围，可供实际应用时参考。     

五阶斯托克斯波的简化解法及改进解

由于Ｓｋｊｅｌｂｒｅｉａ导出的确定五阶斯托克斯波的二个方程不易求解，本文将其简化为确定ｄ／Ｌ的一个方程：ｆ（Ｈ，Ｔ，ｄ，ｄ／Ｌ）＝０。根据这一简化解法，发现Ｓｋｊｅｌｂｒｅｉａ方程组的解有３种情况；存在唯一的精确解精确解不止一个；不存在精确解（但存在满足Ｓｋｊｅｌｂｒｅｉａ方程组方面的最佳近似解）。当精确解不止一个时，可应用变分原理的方法差别出合理的解，应用变分原理的方法还可将Ｓｋｊｅｉｌｂｒｉａ     

Singularity and Breaking of the Third Order Stokes Waves

1 .ＩｎｔｒｏｄｕｃｔｉｏｎＡｓａｖｉｖｉｄｔｈｅｏｒｙｏｆｗａｔｅｒｗａｖｅｓｗｉｔｈｆｉｎｉｔｅａｍｐｌｉｔｕｄｅｓ ,ＳｔｏｋｅｓｗａｖｅｓｈａｓｂｅｅｎｓｔｕｄｉｅｄｔｈｏｒｏｕｇｈｌｙａｎｄａｐｐｌｉｅｄｗｉｄｅｌｙｉｎｍａｒｉｎｅｓｃｉｅｎｃｅａｎｄｅｎｇｉｎｅｅｒｉｎｇｓｉｎｃｅＳｔｏｋｅｓｐｒｏｐｏｓｅｄｉｔｉｎ 1 84 7.Ｒａｙｌｅｉｇｈ(1 876 )ｄｅｖｅｌｏｐｅｄｔｈｅｔｈｅｏｒｙｉｎａｓｉｍｐｌｉｆｉｅｄｗａｙ .Ｍｉｃｈｅｌｌ (1 893)ｄｅｄｕｃｅｄｌｉｍｉｔｉｎｇＳｔｏｋｅｓｗａｖ…     

高频表面波对定常Ekman流解的影响

基于Jenkins(1989)建立的包含Stokes漂流、风输入和波耗散影响的修正Ekman模型,采用Paskyabi等(2012)使用的推广的Donelan等(1987)中的谱和波耗散函数,并利用Paskyabi等(2012)中修正方法给出的包含高频波的风输入函数,在粘性不依赖于水深及粘性随深度线性变化的条件下,研究了包含高频毛细重力波的随机表面波对Stokes漂流和Song(2009)导出的波浪修正定常Ekman流解的影响。结果表明高频表面波使Stokes漂流在海表面剪切加强,对定常Ekamn流解的影响通常不能忽略,但对Ekman流场的角度偏转影响很小。最后,将考虑高频表面波尾谱影响所估算的定常Ekman流解与已有观测结果以及经典Ekman解进行了比对分析。     

A new approximate solution to the surface wave problem

Recent measurements of wave kinematics, showing that the horizontal velocity under the trough is in absolute value greater than the velocity under the crest, can not be explained by the Stokes theories up to and including the fifth order theory which are normally used by the offshore industry in the design process. This has led to a reconsideration of the surface wave problem. By applying a Green function technique a solution is obtained which reflects these recent experimental results on wave kinematics. This solution and the Stokes higher order solutions represent different approximate solutions to the surface wave problem. It turns out, however, that this new approximate solution gives a better fit to the measurements than do the approximate solutions obtained from the Stokes higher order theories. In the present paper deep water waves are discussed, but the method of solution can just as well be applied to the finite water depth case.     

On the Fifth-Order Stokes Solution for Steady Water Waves

This paper presents a universal fifth-order Stokes solution for steady water waves on the basis of potential theory. It uses a global perturbation parameter, considers a depth uniform current, and thus admits the flexibilities on the definition of the perturbation parameter and on the determination of the wave celerity. The universal solution can be extended to that of Chappelear (1961), confirming the correctness for the universal theory. Furthermore, a particular fifth-order solution is obtained where the wave steepness is used as the perturbation parameter. The applicable range of this solution in shallow depth is analyzed. Comparisons with the Fourier approximated results and with the experimental measurements show that the solution is fairly suited to waves with the Ursell number not exceeding 46.7.     

Study on the Interaction of Water Waves with Semi-Circular Breakwater

—The present study investigates the interaction of steep waves with semi-circular breakwaterwith the complex plane＇s Cauchy boundary integral theorem.The boundary integral method is used totransform the calculation in fluid domain into its boundary alone.In the calculation the computation do-main is moved with the propagation of waves.A numerical solution is obtained for incident Stokes wavespassing the submerged obstacles.This method has been extended to the calculation of wave run-up on aslope for estimating wave overtopping.     

Nonlinear effects in the process of propagation of internal waves in the presence of turbulence

In the Boussinesq approximation, we study the nonlinear effects observed in the process of propagation of internal waves in the presence of turbulence. The space damping factor of the waves is evaluated. The Stokes drift velocity and the Euler velocity of the mean current induced by waves due to the presence of nonlinearity are determined. It is shown that the principal contribution to the wave transfer is made by the horizontal velocity of the induced current. The Stokes drift is significant only near the bottom. The vertical component of the Stokes drift velocity obtained with regard for the turbulent viscosity is nonzero.     

三维完全非线性波浪水槽的数值模拟

用有限元求解拉普拉斯方程,建立了三维完全非线性数值波浪水槽.跟踪流体自由表面的方法为满足完全非线性自由表面条件的半拉格朗日法,对离散单元采用20节点的六面体二次等参数单元.并把数值计算结果与水面初始升高产生箱体内流体运动解析解和二阶斯托克斯波理论解进行了对比,结果表明该模型是稳定的、守恒的,能精确模拟非线性波浪的产生和传播.     

Transparent boundary condition for simulating nonlinear water waves by a particle method

Open boundaries are important when simulating water waves. In this study, a transparent boundary condition at an open boundary was developed for simulating nonlinear water waves propagating to a distant area using the Moving Particle Semi-implicit method. The novelty of this study is that the technique of wave analysis used in the experiment was introduced into the particle simulation to absorb incident waves; the simulation cost was reduced by employing inflow and outflow regions instead of a long dissipation region. Incident waves in front of the boundary were evaluated using Fourier analysis, and the particles on the transparent boundary were forced to move at the velocity of the analytical solution for Stokes waves in order to absorb the incident waves. The analysis was restricted to periodic waves. Wave propagation was simulated for two wave periods using the developed transparent boundary condition. The results showed that this transparent boundary transmitted the incident waves with small reflection and the simulation cost was lower than that for wave damping by a conventional highly viscous region.     

Nonlinear wave profiles of wave–wave interaction in a finite water depth by fixed point approach

In this paper, a superposition of two periodic wave profiles in a finite water depth was investigated. This paper is focused on the improvement of a wave profile on the linear superposition of two waves. This improvement was realized by introducing an iterative method, which was based on a fixed point approach. Application of the fixed point approach to the wave superposition made it possible to obtain a wave profile of wave–wave interaction. The improved result of the wave profile was in good agreement with that of the nonlinear perturbation solution of the second order. It was interesting that the improved result revealed the higher-order nonlinear frequencies for two interacting Stokes waves while Dalzell's solution by a perturbation method could not predict them.