流体力学中的强迫孤立波

简要讨论了８０年代发现的以先驱孤立波和非传播孤立波为代表的流体力学中的强迫孤立波．介绍了这些孤立波产生的方法、力学模型、控制方程、研究现状及有待解决的问题．      

考虑表面张力的非传播孤立波

本文考虑了表面张力,用多重尺度法导出了与立方 Schrodinger 方程相类似的非传播孤立波的基本方程,得到了非传播孤立波解。用毛细重力波理论解释了非传播孤立波横向谐振中波峰尖、波谷平的原因。在σ～kh 平面上首次给出了可产生非传播孤立波的二个参数区,但现有的实验点都在区域(1)中。     

二流体系统中界面孤立波的分裂

本文讨论了二流体系统界面上内孤立波的分裂,发现上下层流体密度比对分裂成两个内孤立波的条件没有影响,此时只要孤立波从较深的流体运动到较浅的流体就会发生分裂,但分裂成二个以上孤立波的条件受密度比和上游上下层流体厚度比的影响。     

二流体系统中界面孤立波的分裂

本文讨论了二流体系统界面上内孤立波的分裂,发现上下层流体密度比对分裂成两个内孤立波的条件没有影响,此时只要孤立波从较深的流体运动到较浅的流体就会发生分裂,但分裂成二个以上孤立波的条件受密度比和上游上下层流体厚度比的影响。     

微结构固体中钟型与扭结孤立波的演化

根据Mindlin理论和Murnaghan模型,首先建立了描述耗散、频散及非线性微结构固体中一维纵波传播的一种简单模型.然后利用有限差分方法,数值模拟了微结构效应对钟型与扭结孤立波演化的影响. 结果表明,随着微结构效应的减弱,钟型孤立波的幅度衰减以及非对称特征变得越来越明显;随着微结构效应的增强,扭结孤立波顶部出现的“帽子”状变化以及由此产生的非对称特征变得越来越明显.      

等波高双孤立波直墙爬高的数值模拟

基于RANS方程、VOF方法以及修正的Goring造波方法建立了模拟活塞式推波板运动的二维数值波浪水槽,实现了双孤立波直墙爬高的数值模拟．利用动边界技术模拟造波机推波板的运动,有效地实现了不同波峰间距双孤立波的造波方法．在验证单孤立波直墙爬高的基础上,模拟了不同相对波高、相对波峰间距的等波高双孤立波的直墙爬高过程,给出了波面、速度场及波动能量的变化规律．数值模拟结果表明：对于等波高的双孤立波,当入射波波高较大及两个波峰间距相对较小时,跟随在后孤立波的爬高放大系数小于先导孤立波的爬高放大系数;双孤立波在直墙爬高过程中,波动场的势能时间过程线呈现三峰形态,其中居中的最大势能峰值出现在第二个孤立波与经直墙反射后反向传播的第一个孤立波完全对撞的时刻．     

位移浅水内孤立波

研究两层浅水系统中的内孤立波，该系统由两层常密度不可压缩无黏性水组成。利用Lagrange坐标和Hamilton原理，推导了两层浅水系统的位移浅水内波方程，并进一步导出了两层浅水系统的位移内孤立波解。数值实验表明，位移内孤立波与经典的KdV内孤立波吻合很好，说明Lagrange坐标和Hamilton方法适用于内波分析，可以为构造内波分析的保辛方法提供一种途径。     

细观结构固体层中孤立波的传播及相互作用特性

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二阶精度的稳定差分格式,并对孤立波在细观结构固体层中传播特性进行了数值模拟,特别对细观结构固体层中传播的不同幅度的孤立波的相互作用进行了详细的数值模拟,从而得到在适当条件下细观结构固体层中孤立波传播时即可以衰减、放大又可以稳定传播,且相互作用不影响这种传播特性.     

分层流体中gKdV型孤立波的迎撞

本文采用约化摄动法和PLK方法并通过双参数摄动展开,讨论了分层流体中以推广的Korteweg-de vries方程(gKdV方程)描述的孤立波的迎撞问题,求得了二阶近似解。分析结果表明,gKdV型孤立波碰撞后保持原来的形状不变,在碰撞时最大波幅为两个来碰孤立波的最大波幅的线性叠加。     

孤立波与多个潜水障碍物相互作用的数值研究

本文以完整二维Navier-Stokes方程为控制方程,采用VOF界面跟踪技术和差分方法,数值计算孤立波与多个淹没水下物体相互作用的问题。本文对潜水物体的高度接近水深时,孤立波通过水下孤立直立方柱、两个间距较大的水下直立方柱和两个间距较小的水下直立方柱等三种情况分别进行了计算,给出了波形随时间的演化图,可以看到反射波、前传波和跟随振荡型小波列的生成。对孤立波通过水下孤立直立方柱情形的计算结果,与实验结果和势流理论结果进行了比较。     

INTERNAL SOLITARY WAVE LOADS EXPERIMENTS AND ITS THEORETICAL MODEL FOR A CYLINDRICAL STRUCTURE

在大型重力式密度分层水槽中, 对内孤立波与圆柱型结构的相互作用特性开展了系列实验. 基于两层流体中 内孤立波的KdV,eKdV和MCC理论, 建立了圆柱型结构内孤立波载荷的理论预报模型, 给出了该载荷理论预报模型中3类内孤立波理论的适用性条件.研究表明, 圆柱型结构内孤立波水平载荷包括水平Froude-Krylov力、附加质量力和拖曳力3个部分, 可以由Morison公式计算, 而内孤立波垂向载荷主要为垂向Froude-Krylov力, 可以由内孤立波诱导动压力计算.系列实验结果表明, 附加质量系数可以取为常数1.0, 拖曳力系数与内孤立波诱导速度场的雷诺数之间为指数函数关系, 而且基于理论预报模型的数值结果与系列实验结果吻合.     

On optical Airy beams in integrable and non-integrable systems

The interaction of an accelerating Airy beam and a solitary wave is investigated for integrable and non-integrable equations governing nonlinear optical propagation in various media. For the integrable nonlinear Schrödinger equation, by way of a Bäcklund transformation, we show that no momentum exchange takes place, as the only effect of the interaction is to modulate the amplitude of the solitary wave. The latter result also holds for propagation in anisotropic media with birefringent walkoff and nonlocality, as specifically addressed with reference to uniaxial nematic liquid crystals in the absence of beam curvature. When the wavefront curvature characteristic of accelerating Airy beams is accounted for, both asymptotic and numerical solutions show that a small amount of momentum is initially exchanged, with the solitary wave rapidly settling to a state of constant momentum.     

On some localized waves described by the extended KdV equation

The influence of higher-order nonlinear terms on the shape of solitary waves is studied for mechanical systems governed by a generalization of the 5th order Korteweg–de Vries equation. New localized travelling wave with intrinsic oscillations (not breathers) is shown to arise from arbitrary initial pulse thanks only to the higher-order quadratic nonlinearity, while cubic nonlinearity is responsible for the formation of so-called ‘fat’ solitary wave. To cite this article: A.V. Porubov et al., C. R. Mecanique 333 (2005).     

Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma

The one-dimensional nonlinear dynamical wave interactions in a system of quasineutral two-fluid plasma in a constant magnetic field are investigated.The existence of the travelling wave solutions is discussed.The modulation stability of linear waves and the modulation instability of weakly nonlinear waves are presented.Both suggest that the Korteweg-de Vries(KdV) system is modulationally stable.Besides,the wave interactions including the periodic wave interaction and the solitary wave interaction are captured and presented.It is shown that these interacting waves alternately exchange their energy during propagation.The Fourier spectrum analysis is used to depict the energy transformation between the primary and harmonic waves.It is known that the wave interactions in magnetized plasma play an important role in various processes of heating and energy transportation in space and astrophysical plasma.However,few researchers have considered such magnetohydrodynamic(MHD) wave interactions in plasma.It is expected that this work can provide additional insight into understanding of behaviors of MHD wave interactions.     

Non-propagating solitary waves with the consideration of surface tension

In this paper, the governing equation for the non-propagating solitary waves, similar to the cubic Schrödinger equation, is derived by the multiple scales with the consideration of surface tension. The non-propagating solitary wave solution is given. It is explained by the capillary-gravity wave theory that the crests are sharpened and the troughs are flattened in the transversal harmonic of the non-propagating solitary waves. On σ～kh plane, two parameter regions are obtained in which the non-propagating solitary wave can occur, but all existing experimental parameters are in region 1 (Fig. 1).     

Diffraction of solitary water waves around three-dimensional floating bodies

By using the matched asymptotic expansion method and the idea of edge layer, a mathematic model for describing the interaction between weakly nonlinear shallow-water waves and three-dimensional floating bodies is formed in the paper. As a numerical example, the diffraction of a solitary wave around a vertically floating circular cylinder has been investigated and the results are presented. The present method can further be extended to the study of wave diffraction around floating bodies of general shape. The project is supported by the National Natural Science Foundation of China.     

孤立波激发港口振荡的数值研究

采用Boussinesq数值波浪模型模拟了在孤立波作用下复杂形状港内水体的响应。孤立波在进入港口后会引起港内水体的振荡并被反射,港内波面扰动是一个随时间变化的瞬变波动过程。通过基于连续小波变换的时频分析结果并与现有的理论值进行比较发现,孤立波引起的振荡其主要能量主要集中在港池第一振荡模态上,这为估计复杂形状港口的自振频率提供了一个可行的方法。     

Generation of stable solitary waves by a piston-type wave maker

The focus of present study is on how to generate solitary waves as pure as possible by using a piston type wave maker. A meshless numerical model, which can simulate the trajectories of fluid particles in a wave motion exerted by the wave paddle, is established for the purpose of present study. The present numerical model is verified by the comparison with experimental data before it is employed to the focused problem. Various wave paddle motions are considered. The results show that solitary waves generated by applying Fenton’s solitary solution to the paddle motion proposed by Goring are purer than those generated by other paddle motions.