内孤立波沿缓坡地形传播特性的实验研究

以南中国海东北部海域底部缓坡地形为背景, 在大型重力式分层流水槽中模拟了下凹型内孤立波沿缓坡地形传播过程中的浅化、破碎、分裂等现象, 利用分层染色标识方法和多点组合探头阵列技术对内孤立波沿缓坡地形演化特征进行了定性分析和定量测量. 实验表明: 浅化效应使内孤立波传播速度减小, 对大振幅内孤立波具有抑制作用, 对小振幅波具有放大效应; 浅化效应可导致内孤立波的剪切失稳及破碎, 还可导致大振幅内孤立波的分裂. 利用Miles稳定性理论可定性描述内孤立波沿缓坡地形传播时发生不稳定状态的位置, 实验结果与理论分析相符合. 关键词： 分层流 缓坡地形 内孤立波 不稳定性     

具有密度跃层分层流体中回转体激发内波特性实验

在具有连续密度跃层的分层流体中,对长径比为7:1的回转体在迎水和背水运动下激发体积效应与尾迹效应内波特性开展了系列实验.结果表明,体积效应激发内波属于一种相对于回转体定常的多模态Lee波结构,而尾迹效应激发主控内波为相对于回转体非定常的拟Lee波结构,这是一类由湍流尾迹中大尺度相干结构作为移动源激发的内波结构,在Lee波与拟Lee波之间存在一个与长径比近似为线性关系的临界转捩Froude数Fr_c,当FrFr_c 时拟Lee波为主控内波,而且拟Lee波相关速度Froude数近似为一个常数0.8,其无因次峰-峰幅值随Fr的增大近似线性增大,其中Fr为回转体特征直径Froude数.结果还表明,回转体头部与尾部几何形式并不影响其激发内波临界转捩Froude数Fr_c、 拟Lee波相关速度Froude数及其峰-峰幅值变化特性.     

拖曳体激发内波时空特性实验及其理论模型

在具有密度跃层的分层流体中,采用沿水槽中纵剖面对称布置电导率探头阵列的方法,对1个球体和2个不同长径比细长体在拖曳运动下激发内波的时空特性进行了系列实验.结果表明:存在一个与长径比近似为线性关系的临界Froude数Frc,当FrFr_c时,内波相关速度均与物体运动速度一致,体积效应内波为主控内波,内波波高均随拖曳速度增大而先增大后减小,Lee波峰值对应速度随长径比增大而增大;当FrFr_c时,内波相关速度均小于物体运动速度,其相关速度Froude数Fr_(iw)均在0.43—1.18之间的一个条带内变化,尾迹效应内波为主控内波,内波波高均随拖曳速度增大而近似线性增大.此外,从波形结构上看,体积效应内波关于水槽中纵剖面是对称的,而尾迹效应内波关于水槽中纵剖面是不对称的.结合上述实验结果,在已有针对拖曳球产生内波的等效源理论模型基础上,针对体积效应内波,提出了不同长径比模型的等效源移动速度和体积的设置方法;针对尾迹效应内波正对称和反对称这一特性,提出了正对称组合源和反对称组合源理论模型及其参数设置方法.所得计算结果在波高、波形结构和波系分布上与实验结果符合良好,表明了所提出的理论模型及其参数设置方法的合理性和有效性.     

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     

具有能量输入/输出的固体层中孤立波的传播及相互作用特性

首先利用直接微扰方法,确定了孤立波的放大或衰减与孤立波的初始幅度以及介质的结构参数之间的关系.然后利用线性化技术构造出一种四阶精度的差分格式,并对孤立波在细观结构固体层中传播及不同幅度的孤立波的相互作用进行了数值模拟,从而得到在适当条件下细观结构固体层中孤立波传播时可以衰减、放大也可以稳定传播,且相互作用不影响它们这种传播特性.     

Interaction phenomena between lump and solitary wave of a generalized (3+1)-dimensional variable-coefficient nonlinear-wave equation in liquid with gas bubbles

In this paper, a generalized (3+1)-dimensional variable-coefficient nonlinear-wave equation is studied in liquid with gas bubbles. Based on the Hirota's bilinear form and symbolic computation, lump and interaction solutions between lump and solitary wave are obtained,which include a periodic-shape lump solution, a parabolic-shape lump solution, a cubic-shape lump solution, interaction solutions between lump and one solitary wave, and between lump and two solitary waves. The spatial structures called the bright lump wave and the bright-dark lump wave are discussed. Interaction behaviors of two bright-dark lump waves and a periodic-shape bright lump wave are also presented. Their interactions are shown in some 3D plots.     

Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential

For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV－mKdV equation.     

Large-eddy simulation of the generation and propagation of internal solitary waves

A modified large-eddy simulation model,the dynamic coherent eddy model(DCEM)is employed to simulate the generation and propagation of internal solitary waves(ISWs)of both depression and elevation type,with wave amplitudes ranging from small,medium to large scales.The simulation results agree well with the existing experimental data.The generation process of ISWs is successfully captured by the DCEM method.Shear instabilities and diapycnal mixing in the initial wave generation phase are observed.The dissipation rate is not equal at different locations of an ISW.ISW-induced velocity field is analyzed in the present study.The structure of the bottom boundary layer(BBL)of internal wave packets is found to be different from that of a single ISW.A reverse boundary jet instead of a separation bubble exists behind the leading internal wave while separation bubbles appear in other parts of the wave-induced velocity field.The boundary jet flow resulting from the adverse pressure gradients has distinctive dynamics compared with free shear jets.     

Propagation and interaction of ion-acoustic solitary waves in a quantum electron-positron-ion plasma

This paper discusses the existence of ion-acoustic solitary waves and their interaction in a dense quantum electron-positron-ion plasma by using the quantum hydrodynamic equations.The extended Poincar’e-Lighthill-Kuo perturbation method is used to derive the Korteweg-de Vries equations for quantum ion-acoustic solitary waves in this plasma.The effects of the ratio of positrons to ions unperturbation number density p and the quantum diffraction parameter H e (H p) on the newly formed wave during interaction,and the phase shift of the colliding solitary waves are studied.It is found that the interaction between two solitary waves fits linear superposition principle and these plasma parameters have significantly influence on the newly formed wave and phase shift of the colliding solitary waves.The investigations should be useful for understanding the propagation and interaction of ion-acoustic solitary waves in dense astrophysical plasmas (such as white dwarfs) as well as in intense laser-solid matter interaction experiments.     

非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了Burgers方程，得到了其扭结形孤立波的近似解析解，该解非常接近于相应的精确解.结果表明，同伦分析法可用来求解非线性演化方程的孤立波解.同时，也对所用方法进行了一定扩展，得到了Kadomtsev-Petviashvili(KP)方程的钟形孤立子解.经过扩展后的方法能够更方便地用于求解更多非线性演化方程的高精度近似解析解. 关键词： Burgers方程 同伦分析法 KP方程 孤立波解     

一维铁磁链中量子孤波的能级和磁矩

使用Hartree近似和一种简化的准离散多标度方法,研究了具有交换作用和经典磁矩相互作用的一维铁磁链中的量子孤波解. 这种一维铁磁链中不仅存在着运动的量子孤波,也存在着静态的量子孤波(即量子内禀局域模).利用所获得的量子孤波解,进一步研究了量子孤波的能级和由量子孤波所携带的磁矩. 研究表明,量子孤波的能量和磁矩都是量子化的,这些结果为正确理解磁性材料中像磁滞回线的量子台阶等宏观量子特性提供了一条可能的途径.     

高维非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了修正的Kadomtsev-Petviashvili方程, 得到了它的近似孤立波解, 该解与精确解符合得非常好.结果表明，同伦分析法在求解高维非线性演化方程的孤立波解时, 仍然是一种行之有效的方法. 关键词： 同伦分析法 修正的Kadomtsev-Petviashvili方程 孤立波解     

切伦柯夫相互作用中分段式慢波结构与均匀慢波结构的比较研究

分析了切伦柯夫束波相互作用中使用单段慢波结构的缺点。指出在分段式慢波结构中,漂移段及其两端的慢波结构组成一Bragg谐振腔,当漂移段长度合适时,根据渡越时间效应理论,这种结构能减小调制束中电子的速度分散,提高束波转化效率。通过粒子模拟方法,比较了均匀慢波结构与分段式慢波结构中束波相互作用的物理图像,验证了理论分析结果,并说明了后者有束密度群聚充分,束电子速度分散小,产生微波功率高、频谱质量好,最佳工作电流大,输入电功率高等优点。     

Allowable propagation of short pulse laser beam in a plasma channel and electromagnetic solitary waves

Nonparaxial and nonlinear propagation of a short intense laser beam in a parabolic plasma channel is analyzed by means of the variational method and nonlinear dynamics. The beam propagation properties are classified by five kinds of behaviors. In particularly, the electromagnetic solitary wave for finite pulse laser is found beside the other four propagation cases including beam periodically oscillating with defocussing and focusing amplitude, constant spot size, beam catastrophic focusing. It is also found that the laser pulse can be allowed to propagate in the plasma channel only when a certain relation for laser parameters and plasma channel parameters is satisfied. For the solitary wave, it may provide an effective way to obtain ultra-short laser pulse.     

On the study of ion-acoustic solitary waves and double-layers in a drift multicomponent plasma with electron-inertia

Using the pseudopotential method, theoretical investigation has been made on the firstorder Korteweg-deVries ion-acoustic solitons in a multicomponent plasma consisting of warm positive ions, negative ions and isothermal electrons. The effects of electron-inertia and drift motion of the ions on the amplitudes and widths of the solitons have been studied in a plasma having (H⁺, Cl⁻), (H⁺, O⁻), (He⁺, H⁻) and (He⁺, O⁻) ions. Ion-acoustic double-layers have also been investigated for such plasmas. It has been found that drift velocity and electron-inertia have significant contribution on the formation of double-layers in multicomponent plasma     

Gain/loss effect on bright solitary wave in a cigar-shaped attractive condensate in the presence of expulsive parabolic potential

<正>Taking into account both gain/loss and time-dependent atomic scattering length,this paper analytically derives an exact bright solitary wave in a cigar-shaped attractive condensate in the presence of an expulsive parabolic potential. Due to the balance of the scattering length and gain/loss,the bright solitary wave is shown to have constant amplitude. Especially,it is found that the bright solitary wave is accelerated by expulsive force,whose velocity can be modulated by changing the axial and transverse angular frequencies.The results are in good agreement with the experimental observations by Khaykovich et al(2002 Science 296 1290).     

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.     

A hyperbolic function approach to constructing exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice

Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.