有流存在时三层流体界面波的二阶Stokes波解

以小振幅波理论为基础，利用摄动方法研究了有背景流场存在时密度三层成层状态下的界面内波，得到了各层流体速度势的二阶渐近解及界面内波波面位移的二阶Stokes波解，并讨论了界面波的Kelvin-Helmholtz不稳定性.结果表明：有流存在的情况下三层密度成层流体界面内波的一阶渐近解(线性波解)、频散关系及二阶渐近解不仅依赖于各层流体的厚度和密度，也依赖于各层流体的背景流场；界面内波波面位移的二阶Stokes波解不仅描述了界面波之间的二阶非线性相互作用，也描述了背景流与界面波之间的二阶非线性相互作用；当每层流 关键词： 界面波 均匀流 二阶Stokes波解 Kelvin-Helmholtz不稳定性     

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     

二维均匀流与重力短峰波相互作用解析

短峰波和海流广泛分布于海洋之中,但二者的相互作用直到近些年才逐渐受到关注,根据速度势函数理论,推导二维均匀流与重力短峰波的相互作用,区别于之前的研究,推导时不考虑波面的毛细影响,避免了将位置变量(x)与时间变量(t)绑定的假设,使得二阶速度势函数包含了的时间(t)一阶项,从而给出了完整的二维流与短峰波交互作用的二阶解析解,对比结果说明上述考虑对于波流共同作用结果有影响,尤其是在波高较大时,影响更加明显,所得结果,可用于高波浪条件下海洋波浪与流相互作用的计算.     

具有基本流动的两层流体界面和表面孤波

本文研究了具有基本流动的两层流体浅水孤波,利用多重尺度摄动方法求得了两流体界面和表面波所满足的KdV方程和相应单孤波解;对所得结果进行了讨论,并将其应用到海洋温跃层和有剪切流动的均匀密度流体两种常见情形。 关键词：     

环形浅液层内热流体波的可视化实验研究

对外壁加热、内壁冷却、厚度为1.0 mm的环形硅油浅液层内的热毛细对流及其稳定性进行了可视化实验研究,观察到了旋转的螺纹状的热流体波,确定了发生热流体波的临界温差值△Tc=4.8 K,证实了热流体波从两组逐渐演变为一组的发展过程,验证了已有的数值模拟结果.     

有限深两层流体中内孤立波造波实验及其理论模型

将置于大尺度密度分层水槽上下层流体中的两块垂直板反方向平推, 以基于 Miyata-Choi-Camassa (MCC)理论解的内孤立波诱导上下层流体中的层平均水平速度作为其运动速度, 发展了一种振幅可控的双推板内孤立波实验室造波方法. 在此基础上, 针对有限深两层流体中定态内孤立波 Korteweg-de Vries (KdV), 扩展KdV (eKdV), MCC和修改的Kdv (mKdV)理论的适用性条件等问题, 开展了系列实验研究.结果表明, 对以水深为基准定义的非线性参数ε 和色散参数μ, 存在一个临界色散参数μ₀, 当μ < μ₀ 时, KdV理论适用于ε ≤μ 的情况, eKdV理论适用于μ < ε ≤√μ 的情况, 而MCC理论适用于ε > √μ 的情况, 而且当μ ≥μ₀ 时MCC理论也是适用的.结果进一步表明, 当上下层流体深度比并不接近其临界值时, mKdV理论主要适用于内孤立波振幅接近其理论极限振幅的情况, 但这时MCC理论同样适用.本项研究定量地表征了四类内孤立波理论的适用性条件, 为采用何种理论来表征实际海洋中的内孤立波特征提供了理论依据. 关键词： 两层流体 内孤立波 双板造波 临界色散参数     

环形液层内热毛细对流的线性稳定性分析

为了了解液层深度对热毛细对流不稳定性的影响,利用线性稳定性理论分析了内径为20 mm、外径为40 mm、深度为1～20 mm的环形液层内硅油(Pr=6.7)的热毛细对流,重点考察了发生热流体波的临界温差及热流体波的临界周向波数,结果表明,临界温差随液层深度的增加而降低.讨论了浮力对热流体波及其临界条件的影响,并证实了常重力条件下当液层厚度大于5 mm时,热流体波呈静止状态这一现象.     

表面张力-重力短峰波作用的海底边界层速度二阶解

依据最近提出的三阶表面张力-重力短峰波理论,通过求解经典的Prandtl边界层方程,给出海底边界层速度的二阶解析解,为确定海底边界层的质量输运提供了一个必备的先行理论基础.     

低β尘埃等离子体中尘埃-动力学阿尔文孤立波

用三成分的流体模型,研究了尘埃等离子体中的尘埃－动力阿尔文波。导出了描述离子密度变化的非线性的能量积分方程。在小振幅极限下,得到密度的孤立子解,对Ｓａｇｄｅｅｖ势进行了数值研究。结果表明,在不同的参数区域,可以激发具有密度坑或密度隆起的孤立波;随着尘埃密度的增加,密度坑变浅,密度隆起增大。     

伴随均匀流作用的有限水深三阶三色三向表面张力-重力波之完备对称解

着眼于"多色多向"这一典型的海洋表面波传播特征而以"三色三向"加以基本地刻画,并纳入普遍的波-流相互作用机理和丰富多样的表面张力波效应,由此给出了有限水深三阶三色三向波运动系统的一完备对称解.这是对目前业已存在的经典、现代"单色、多色多向波理论"的一次充分包容和集中反映. 关键词： 三色三向波 表面张力-重力波 波-流相互作用 完备对称解     

Third-order Stokes wave solutions for interfacial internalwaves in three-layer dendity-stratified fluid

<正>Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular perturbation method,and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory.As expected,the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves.The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.     

Nonlinear gravitational waves on the surface of viscous fluid: Lagrangian approach

The problems of the asymptotic theory of weakly nonlinear surface waves in viscous fluid are discussed. For standing waves on deep water, the solutions obtained in the first- and second-order approximations in a small parameter—wave steepness—are analyzed. The evolution equation for the amplitude of wave packet envelope is obtained where the inverse Reynolds number is equal to the squared steepness. It is shown that this is a nonlinear Schrödinger equation with linear dissipation.     

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.     

Amplitude equation and pattern selection in Faraday waves

A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude equation is derived from the governing equations. The amplitude equation is of gradient form, and the coefficients of the associated Lyapunov function are computed for regular patterns of various symmetries as a function of a viscous damping parameter gamma. For gamma approximately 1, the selected wave pattern comprises a single standing wave (stripe pattern). For gamma<1, patterns of square symmetry are obtained in the capillary regime (large frequencies). At lower frequencies (the mixed gravity-capillary regime), a sequence of sixfold (hexagonal), eightfold, ...patterns are predicted. For even lower frequencies (gravity waves) a stripe pattern is again selected. Our predictions of the stability regions of the various patterns are in quantitative agreement with recent experiments conducted in large aspect ratio systems.     

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.     

Soliton solutions for a generalized fifth-order KdV equation with t-dependent coefficients

We consider a generalized fifth-order KdV equation with time-dependent coefficients exhibiting higher-degree nonlinear terms. This nonlinear evolution equation describes the interaction between a water wave and a floating ice cover and gravity-capillary waves. By means of the subsidiary ordinary differential equation method, some new exact soliton solutions are derived. Among these solutions, we can find the well known bright and dark solitons with sech and tanh function shapes, and other soliton-like solutions. These solutions may be useful to explain the nonlinear dynamics of waves in an inhomogeneous KdV system supporting high-order dispersive and nonlinear effects.     

Energy spectrum of the ensemble of weakly nonlinear gravity-capillary waves on a fluid surface

We consider nonlinear gravity-capillary waves with the nonlinearity parameter ? ～ 0.1–0.25. For this nonlinearity, time scale separation does not occur and the kinetic wave equation does not hold. An energy cascade in this case is built at the dynamic time scale (D-cascade) and is computed by the increment chain equation method first introduced in [15]. We for the first time compute an analytic expression for the energy spectrum of nonlinear gravity-capillary waves as an explicit function of the ratio of surface tension to the gravity acceleration. We show that its two limits—pure capillary and pure gravity waves on a fluid surface—coincide with the previously obtained results. We also discuss relations of the D-cascade model with a few known models used in the theory of nonlinear waves such as Zakharov’s equation, resonance of modes with nonlinear Stokes-corrected frequencies, and the Benjamin-Feir index. These connections are crucial in understanding and forecasting specifics of the energy transport in a variety of multicomponent wave dynamics, from oceanography to optics, from plasma physics to acoustics.     

Sound generation due to the interaction of surface waves

Two opposite gravity-capillary waves of equal frequency give rise to the formation of a standing wave on the ocean surface and, thus, in the nonlinear approximation, generate a sound wave of twofold frequency with an amplitude proportional to the squared height of the surface wave [1]. This effect, being caused by the nonlinear interaction of opposite surface waves, can give rise to the radiation of sound waves in both ocean and atmosphere [2]. Opposite waves can appear in the ocean as a result of different ocean-atmosphere interactions and, in particular, as a result of the blocking of capillary waves on the slope of a gravity wave.