Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid

This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.     

三层流体界面内波的二阶Stokes解

以小振幅波理论为基础，利用摄动方法研究了三层密度成层状态下的界面内波，求得了三层成层状态下各层速度势的二阶渐近解及界面内波波面位移的二阶Stokes解.结果表明：一阶解为正弦波解，与传统线性理论的结果相一致；二阶解描述了界面波的二阶非线性修正及两界面波之间的非线性相互作用；一阶解及二阶解都依赖于各层流体的厚度及密度.Umeyama导出的理论结果为本文的特殊情形. 关键词： 三层密度成层流体 内波 二阶Stokes解 小振幅波理论     

三层流体系统非线性界面内波传播理论的研究

基于波陡很小的假设, 利用摄动法, 讨论了任意深度的二维不可压缩、无黏性、无旋的三层流体系统. 在刚性上边界、平底不可渗透条件下, 给出了界面内波传播的统一理论以及描述其波剖面的近似非线性演化方程(NEEs). 最后讨论了几种特殊情形下的近似NEEs.结果表明文献导出的理论结果为本文的特殊情形.     

Effects of Buoyancy on Langmuir Circulation

Based on the Navier-Stokes equation, an equation describing the Langmuir circulation is derived by a perturbation method when the influences of Coriolis force and buoyancy force are both considered. The approach used in the analysis is similar to the works carried out by Craik and Leibovieh [3. Fluid Mech. 73 （1976）401], Leibovieh [3. Fluid Mech. 79 （1977） 715] and Huang [3. Fluid Mech. 91 （1979） 191]. Potential applications of the equation proposed are discussed in the area of Antarctic circumpolar current.     

A set of Boussinesq-type equations for interfacial internal waves in two-layer stratified fluid

Many new forms of Boussinesq-type equations have been developed to extend the range of applicability of the classical Boussinesq equations to deeper water in the study of the surface waves. One approach was used by Nwogu (1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618--638) to improve the linear dispersion characteristics of the classical Boussinesq equations by using the velocity at an arbitrary level as the velocity variable in derived equations and obtain a new form of Boussinesq-type equations, in which the dispersion property can be optimized by choosing the velocity variable at an adequate level. In this paper, a set of Boussinesq-type equations describing the motions of the interfacial waves propagating alone the interface between two homogeneous incompressible and inviscid fluids of different densities with a free surface and a variable water depth were derived using a method similar to that used by Nwogu (1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618--638) for surface waves. The equations were expressed in terms of the displacements of free surface and density-interface, and the velocity vectors at arbitrary vertical locations in the upper layer and the lower layer (or depth-averaged velocity vector across each layer) of a two-layer fluid. As expected, the equations derived in the present work include as special cases those obtained by Nwogu (1993, J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638) and Peregrine (1967, J. Fluid Mech. 27, 815-827) for surface waves when the density of the upper fluid is taken as zero.     

THE CALCULATION OF EIGENVALUES FOR THE STATIONARY PERTURBATION OF COUETTE－POlSEUILLEFLOW

ＴＨＥＣＡＬＣＵＬＡＴＩＯＮＯＦＥＩＧＥＮＶＡＬＵＥＳＦＯＲＴＨＥＳＴＡＴＩＯＮＡＲＹＰＥＲＴＵＲＢＡＴＩＯＮＯＦＣＯＵＥＴＴＥ－ＰＯｌＳＥＵＩＬＬＥＦＬＯＷＳｏｎｇＪｉｎｂａｏ（宋金宝）ＣｈｅｎＪｉａｎｎｉｎｇ（陈建宁）（ＲｅｃｅｉｖｅｄＤｅｃ．３...     

THE CALCULATION OF EIGENVALUES FOR THE STATIONARY PERTURBATION OF COUETTE－POISEUILLE FLOW

ＴＨＥＣＡＬＣＵＬＡＴＩＯＮＯＦＥＩＧＥＮＶＡＬＵＥＳＦＯＲＴＨＥＳＴＡＴＩＯＮＡＲＹＰＥＲＴＵＲＢＡＴＩＯＮＯＦＣＯＵＥＴＴＥ－ＰＯＩＳＥＵＩＬＬＥＦＬＯＷＳｏｎｇＪｉｎｂａｏ（宋金宝）ＣｈｅｎＪｉａｎｎｉｎｇ（陈建宁）（ＲｅｃｅｉｖｅｄＤｅｃ．３...     

Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random interfacial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order asymptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen （2006） as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song （2005） for second-order solutions for random interfacial waves with steady uniform currents if N = 2.     

A theory of nonlinear AC response in coated composites

A method for determining effective dielectric responses of Kerr-like coated nonlinear composites under the alternating current (AC) electric field is proposed by using perturbation approach. As an example, we have investigated the composite with coated cylindrical inclusions randomly embedded in a host under an external sinusoidal field with finite frequency ω. The local field and potential of composites in general consists of components with all harmonic frequencies. The effective nonlinear AC responses at all harmonics are induced by the coated nonlinear composites because of the nonlinear constitutive relation. Moreover, we have derived the formulae of effective nonlinear AC responses at the fundamental frequency and the third harmonic in the dilute limit.     

二维水槽中岩石坠落激发表面波的生成机制

针对二维水槽中岩石坠落激发表面波的生成机制进行数值和实验室研究,其中数值模型使用边界元方法求解完全非线性势流函数,实验室研究测得不同时刻的波面位移并用于检验数值模型.研究表明,数值结果和实验结果比对良好,这种基于势流函数理论的数值模型能够有效模拟水中岩石坠落激发表面波的生成过程.进一步数值研究了生成波最大位移随岩石大小、密度、初始位置和下落角度的变化,结果发现：岩石大小和密度对生成波最大位移的影响非常重要,而岩石初始位置和下落角度对生成波最大位移的影响较为显著.当岩石大小变大,密度变大,岩石初始位置更靠近 关键词： 水中岩石坠落 波浪生成 边界元方法 波浪破碎