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1.
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.  相似文献   

2.
崔巍  闫在在  木仁 《物理学报》2014,63(14):140301-140301
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.  相似文献   

3.
陈小刚  宋金宝  孙群 《物理学报》2005,54(12):5699-5706
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  相似文献   

4.
庞晶  陈小刚  宋金宝 《物理学报》2007,56(8):4733-4741
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  相似文献   

5.
徐涛  陈勇 《中国物理 B》2016,25(9):90201-090201
We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.  相似文献   

6.
The effect of space- and time-dependent random mass density, velocity, and pressure fields on frequencies and amplitudes of acoustic waves is considered by means of the analytical perturbative method. The analytical results, which are valid for weak fluctuations and long wavelength sound waves, reveal frequency and amplitude alteration, the effect of which depends on the type of random field. In particular, the effect of a random mass density field is to increase wave frequencies. Space-dependent random velocity and pressure fields reduce wave frequencies. While space-dependent random fields attenuate wave amplitudes, their time-dependent counterparts lead to wave amplification. In another example, sound waves that are trapped in the vertical direction but are free to propagate horizontally are affected by a space-dependent random mass density field. This effect depends on the direction along which the field is varying. A random field, which varies along the horizontal direction, does not couple vertically standing modes but increases their frequencies and attenuates amplitudes. These modes are coupled by a random field which depends on the vertical coordinate, but the dispersion relation remains the same as in the case of the deterministic medium.  相似文献   

7.
The influence of random mass density and velocity fields on the frequencies and amplitudes of the sound waves that propagate along a constant gravity field is examined in the limit of weak random fields, small amplitude oscillations and a weakly stratified medium. Using a perturbative method, we derive dispersion relations from which we conclude that the effect of a space-dependent random mass density field is to attenuate sound waves. Frequencies of these waves are higher than in the case of a coherent medium. A time-dependent random mass density field increases frequencies and amplifies the sounds waves. On the other hand, a space-dependent random flow reduces the wave frequencies and attenuates the sound waves. The time-dependent random flow raises the frequencies of the sound waves and amplifies their amplitudes. In the limit of the gravity-free medium the above results are in an agreement with the former findings.  相似文献   

8.
This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller's method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.  相似文献   

9.
小孔衍射和近场散射数值计算的格林函数方法   总被引:1,自引:1,他引:0  
从简谐光波满足的亥姆霍兹方程出发,将由格林定理得到的介质分界面上的积分方程转化为以表面上的光波及其导数为未知量的线性方程组,并对其进行数值求解,实现了光场的数值计算。然后将这一方法应用于亚波长尺度的小孔衍射的光波以及自仿射分形表面产生的随机光场及其在近场区域范围内的传播的计算。在随机表面产生的光场计算中.提出了类比推导夫琅禾费面上散斑场自相关函数的方法产生随机表面,以及计算其导数的傅里叶变换方法。对光场的计算结果表明,在近场范围内,光场随离开表面的距离的增加而迅速变化,其传播特性完全不同于光场在远场范围内的传播特性。  相似文献   

10.
The ratio of amplitudes of waves generated by different interfaces in stratified inhomogeneous liquid is analytically studied. The amplitudes of waves generated by the second interface depend on the initial conditions and can be greater or less than the amplitudes of waves generated by the third interface. The amplitude ratio of the external and internal waves significantly depends on the ratio of liquid densities and layer thicknesses. Substantial effect of the initial conditions is manifested as a variation in the ratio of the amplitudes of external and internal waves and the amplitude ratio of waves generated by different interfaces.  相似文献   

11.
Wang J  Du J  Lu W  Mao H 《Ultrasonics》2006,44(Z1):e941-e945
For an accurate approximation of the effect of a thin layer over a finite substrate, we consider the displacements are continuous across the interface, while the stress components are obtained from derivatives of displacements. As a result, the stress boundary conditions are transformed to a relationship between stresses in the vicinity of the interface of two layers and density of the metal layer. Through this approximation, we eventually have four equations to solve for the surface acoustic wave dispersion relation of the two-layer structure. The approximate and accurate results are compared with good agreement for small thickness of the metal layer. These results are intended for periodic structures with separate solutions for electroded and unelectroded regions, which can be connected by the continuity boundary conditions for the analysis of the complete structure of typical surface acoustic wave resonators.  相似文献   

12.
以耦合非线性薛定谔方程为理论模型,数值研究了两个一阶暗怪波在正常色散单模光纤中的相互作用.基于一阶暗怪波精确解,采用分步傅里叶数值模拟法,从间距、相位差和振幅系数比方面讨论相邻两个一阶暗怪波之间的相互作用.基于二阶暗怪波精确解,讨论了两个一阶暗怪波的非线性相互作用.研究结果表明:同相位情况下,间距参数T1为0、5、20时,相邻两个一阶暗怪波相互作用激发产生“扭结型”暗怪波.相比较于单个暗怪波发生能量的弥散,“扭结型”暗怪波分裂形成多个次暗怪波.反相位情况下,间距参数T1为2、7、12时,相邻两个一阶暗怪波相互作用也可以激发产生“扭结型”暗怪波.并且“扭结型”暗怪波初始激发的空间位置偏离原始单个暗怪波的位置5.振幅系数比越大,该空间位置越接近5.二阶暗怪波可以看作是两个一阶暗怪波的非线性叠加,复合型和三组分型二阶暗怪波与相邻两个一阶暗怪波的相互作用略有相似.  相似文献   

13.
In this paper, based on the Hirota bilinear method and symbolic computation approach, multiple-order rogue waves of (2+1)-dimensional Boussinesq type equation are constructed. The reduced bilinear form of the equation is deduced by the transformation of variables. Three kinds of rogue wave solutions are derived by means of bilinear equation. The maximum and minimum values of the first-order rogue wave solution are given at a specific moment. Furthermore, the second-order and third-order rogue waves are explicitly derived. The dynamic characteristics of three kinds of rogue wave solutions are shown by three-dimensional plot.  相似文献   

14.
徐涛  陈勇  林机 《中国物理 B》2017,26(12):120201-120201
We investigate some novel localized waves on the plane wave background in the coupled cubic–quintic nonlinear Schr o¨dinger(CCQNLS) equations through the generalized Darboux transformation(DT). A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higherorder localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed:(i) the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions;(ii) hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons;(iii) hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α.These results further uncover some striking dynamic structures in the CCQNLS system.  相似文献   

15.
Capillary wave flow in a two-layer fluid with the upper layer moving parallel to the charged interface at a constant velocity is treated within a linear mathematical model. Interaction between waves excited on the free surface of the upper layer and at the interface results not only in classical Kelvin-Helmholtz instability (at low velocities of the upper layer) but also in oscillatory instability of the interface. The instability increment depends on the fluid density ratio, translational velocity, and charge density at the interface.  相似文献   

16.
A new frequency-domain electromagnetics algorithm is developed for simulating curved interfaces between anisotropic dielectrics embedded in a Yee mesh with second-order error in resonant frequencies. The algorithm is systematically derived using the finite integration formulation of Maxwell’s equations on the Yee mesh. Second-order convergence of the error in resonant frequencies is achieved by guaranteeing first-order error on dielectric boundaries and second-order error in bulk (possibly anisotropic) regions. Convergence studies, conducted for an analytically solvable problem and for a photonic crystal of ellipsoids with anisotropic dielectric constant, both show second-order convergence of frequency error; the convergence is sufficiently smooth that Richardson extrapolation yields roughly third-order convergence. The convergence of electric fields near the dielectric interface for the analytic problem is also presented.  相似文献   

17.
We consider the flow being a superposition of random waves and describe the evolution of the spectrum of the passive scalar in the leading (fourth) order with respect to the wave amplitudes. We find that wave turbulence can produce an exponential growth of the passive scalar fluctuations when either both solenoidal and potential components are present in the flow or there are potential waves with the same frequencies but different wave numbers.  相似文献   

18.
<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.  相似文献   

19.
Within the full system of Maxwell's equations this paper investigates the effects of three kinds of transmission conditions at the interfaces between the laminae of a periodic piezoelectric structure on band gaps of Bloch-Floquet waves propagating oblique to the interfaces. The results that are obtained show that under both electrically shorted and magnetically closed transmission conditions Bloch-Floquet waves exist only at acoustic frequencies. The effects of piezoelectricity on Bloch-Floquet wave band structures are studied at such frequencies. It is shown that for periodic crystal structures with laminae made of identical materials the propagation of Bloch-Floquet waves can occur under electrically shorted interface conditions but not under magnetically closed interface conditions.For electrically open interfaces with mechanically smooth contacts the dynamic setting of the problem provides solutions only for photonic crystals. In this case the piezoelectricity has no effect on band gaps.  相似文献   

20.
A theoretical model of the sum-frequency wave field produced by a nonlinear acoustic source with three-frequency pumping is reported. The model allows for the dissipation and diffraction of the Gaussian beam. The sum-frequency wave is represented within the second-order approximation as a superposition of two synchronous copropagating waves with equal frequencies. It is shown that the spatial and amplitude-phase characteristics of the sum-frequency wave are affected not only by the amplitude-phase relations in the pumping spectrum, but also by the diffraction-caused variations in amplitudes and phases of the primary waves. This dependence is most clearly seen under the phase exclusion conditions, when the generation of the sum-frequency wave is actually suppressed (excluded) owing to the appropriate choice of the amplitude and phase pumping spectra. The theoretical results are found to agree well with experimental data. The possible practical applications of the phase exclusion conditions are as follows: inspection of inhomogeneous media, detection of objects near interfaces, reduction of nonlinear attenuation, acoustic measurements, etc.  相似文献   

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