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.     

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     

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.     

三层密度分层流体毛细重力波二阶Stokes波解

以小振幅波理论为基础,利用摄动方法研究了三层密度分层流体的毛细重力波,给出了三层成层状态下各层流体速度势的二阶渐近解及毛细重力波波面位移的二阶Stokes波解.结果表明:一阶解及二阶解除了依赖于各层流体的厚度及密度,与表面张力也有很重要的关系.     

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     

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.     

A kind of extended Korteweg——de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio $\varepsilon $, represented by the ratio of amplitude to depth, and the dispersion ratio $\mu $, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin {\it et al} in the study of the surface waves when considering the order up to $O(\mu ^2)$. As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin {\it et al} for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.     

线性密度分层流体中半球体运动生成内波的实验研究

在密度线性分布的分层流试验水槽中,对贴近侧壁面的半球体模型运动生成的内波进行了实验研究. 采用多通道电导率阵列,测量分析了拖曳模型产生内波的波形结构、垂向位移场及其相关速度等. 实验结果表明:半球体模型产生的内波可以分为两类,一类是由定常源激发的体积效应内波,另一类是由非定常源激发的尾迹内波,由前者转换为后者的临界内Froude(Fr)数是Fr_s =1.6;与球体模型实验比较,Fr_s约为球体的2/3,转换更迅速,界线更清 关键词： 分层流 半球模型 内波 尾迹     

有限深密度分层流体中运动物体生成内波的一种等效质量源方法

采用一种等效移动质量源来模拟有限深密度分层流体中运动物体生成内波的体积效应和旋涡、湍流尾迹激发源,结合内波本征值问题及Fourier变换等方法,建立了计算运动物体生成内波垂向位移场的一种理论模型,提出了确定移动质量源速度、回转直径及长度的具体方法.利用该理论模型,对一类典型密度分层流体中运动球生成内波的波系与波形结构,以及波高特征等进行了数值模拟与分析,结果与Robey实验结果符合良好,表明了所建立理论模型的合理与有效性. 关键词： 分层流体 内波 等效质量源     

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     

New structures for closed-form wave solutions for the dynamical equations model related to the ion sound and Langmuir waves

This treatise analyzes the coupled nonlinear system of the model for the ion sound and Langmuir waves.The modified(G'/G)-expansion procedure is utilized to raise new closed-form wave solutions.Those solutions are investigated through hyperbolic,trigonometric and rational function.The graphical design makes the dynamics of the equations noticeable.It provides the mathematical foundation in diverse sectors of underwater acoustics,electromagnetic wave propagation,design of specific optoelectronic devices and physics quantum mechanics.Herein,we concluded that the studied approach is advanced,meaningful and significant in implementing many solutions of several nonlinear partial differential equations occurring in applied sciences.     

Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics

The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK) equation. The solutions obtained contain first-order, second-order, and third-order wave solutions. At the critical point,the second-order derivative and Hessian matrix for only one point is investigated, and the lump solution has one maximum value. He's semi-inverse variational principle(SIVP) is also used for the generalized BK equation. Three major cases are studied, based on two different ansatzes using the SIVP. The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below, using a selection of suitable parameter values.This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer, fluid dynamics, etc.     

非线性LC电路方程的显式精确行波解

理论上考察了具有耗散的非线性LC电路中的行波. 借助于作者最近发展的精确求解非线性偏微分方程的扩展的双曲函数方法解析地研究了模拟非线性电路中冲击波的四阶耗散非线性波动方程. 一致地获得了丰富的显式精确解析行波解, 包括精确冲击波解和奇异的行波解, 和三角函数有理形式的周期波解. 关键词： LC电路')" href="#">非线性LC电路 非线性耗散波动方程 冲击波 周期波     

具有Dzyaloshinskii-Moriya相互作用的一维随机量子XY模型中的纠缠特性

研究了一维随机量子XY自旋链中中心两量子位的纠缠特性,在该系统中引入了自旋间的交换耦合杂质、磁杂质和Dzyaloshinskii-Moriya相互作用,并且杂质满足高斯分布关系.通过数值计算,求出了自旋的关联函数和平均磁化强度,给出了Concurrence的解析表达式.结果表明：高斯分布和Dzyaloshinskii-Moriya相互作用对两量子位的纠缠有重要的影响,选择合适的交换耦合、外界磁场和Dzyaloshinskii-Moriya相互作用参数,可以控制和提高中心两量子位的纠缠. 关键词： 纠缠 XY模型')" href="#">随机量子XY模型 高斯分布 Dzyaloshinskii-Moriya相互作用     

Tunneling conductance in quantum wire/insulator/dx2 -y2 + idxy mixed wave superconductor junctions

Using the extended Blonder-Tinkham-Klapwijk (BTK) theory, this paper calculates the tunnelling conductance in quantum wire/insulator/dx2-y2 + idxy mixed wave superconductor (q/I/dx2-y2 + idxy) junctions. That is different from the case in d- and p-wave superconductor junctions. When the angle α between a-axis of the dx2-y2 wave superconductor and the interface normal is π/4, there follows a rather distinctive tunnelling conductance. The zero-bias conductance peak (ZBCP) may or may not appear in the tunnelling conductance. Both the interface potential z and the quasi-particle lifetime factor Γ are smaller, there is no ZBCP. Otherwise, the ZBCP will appear. The position of bias conductance peak (BCP) depends strongly on the amplitude ratio of two components for dx2-y2 + idxy mixed wave. The low and narrow ZBCP may coexist with the BCP in the tunnelling conductance. Using those features in the tunnelling conductance of q/I/dx2-y2 + idxy junctions, it can distinguish dx2-y2 + idxy mixed wave superconductor from d- and p-wave one.     

Evolution of polarization of electromagnetic waves in a plasma with uniformly sheared magnetic field

Summary An analytic solution is found for the evolution of the state of polarization of an electromagnetic wave propagating in a plasma with uniformly sheared magnetic field. It is the generalization of the one found previously for the special case of propagation perpendicular to the magnetic field.     

Solitons and periodic waves for a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics

Under investigation in this paper is a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics. Soliton and one-periodic-wave solutions are obtained via the Hirota bilinear method and Hirota–Riemann method. Magnitude and velocity of the one soliton are derived. Graphs are presented to discuss the solitons and one-periodic waves: the coefficients in the equation can determine the velocity components of the one soliton, but cannot alter the soliton magnitude; the interaction between the two solitons is elastic; the coefficients in the equation can influence the periods and velocities of the periodic waves. Relation between the one-soliton solution and one-periodic wave solution is investigated.     

GdBaCo2O5+δ体系的滞弹性内耗研究

GdBaCo₂O_5+δ体系的低频内耗研究表明：体系中存在一个由额外氧运动引起的弛豫内耗峰；额外氧δ对这个弛豫内耗峰的大小、峰形及峰位有较大影响，反映了额外氧状态随δ而变化.当δ=0.005，体系中额外氧含量很少而接近零时，相应的内耗峰消失；δ达到一定数量后，出现弛豫内耗峰.由δ=0.278，0.407，0.421，0.515样品的弛豫内耗峰分析可得到体系随δ不同存在着三种不同的额外氧形态.此外，δ=0.421及0.515的样品在360K附近存在一个相变内耗峰，它对应着体系中的金属—绝缘体转变. 关键词： 2O_5+δ')" href="#">GdBaCo₂O_5+δ 额外氧 内耗峰     

Interference of dissociating wave packets in the I2 molecule driven by femtosecond laser pulses

The interference between two dissociating wave packets of the I2 molecule driven by femtosecond laser pulses is theoretically studied by using the time-dependent quantum wave packet method.Both the internuclear distanceand velocity-dependent density functions are calculated and discussed.It is demonstrated that the interference pattern is determined by the phase difference and the delay time between two pump pulses.With two identical pulses with a delay time of 305 fs and a FWHM of 20 fs,more interference fringes can be observed,while with two pump pulses with a delay time of 80 fs and a FWHM of 20 fs,only a few interference fringes can be observed.     

Planar and nonplanar ion-acoustic envelope solitary waves in a very dense electron-positron-ion plasma

Ion-acoustic envelope solitary waves in a very dense plasma comprised of the electrons, positrons and ions are investigated. For this purpose, the quantum hydrodynamic model and the Poisson equation are used. A modified nonlinear Schrödinger equation is derived by employing the reductive perturbation method. The effects of the quantum correction and of the positron density on the propagation and stability of the envelope solitary waves are examined. The nonplanar (cylindrical/spherical) geometry gives rise to an instability period. The latter cannot exist for planar case and it affected by the quantum parameters, as well as the positron density. The present investigation is relevant to white dwarfs.