TWO-DIMENSIONAL ALGEBRAIC SOLITARY WAVE AND ITS VERTICAL STRUCTURE IN STRATIFIED FLUID

IntroductionItis known thatthere exists a special kind of solitary waves—the algebraic solitary waveas the disturbance range is close to the scale of vertical variation of density in thecontinuously stratified fluid.The algebraic solitary wave is governe…     

谈镐生简介

谈镐生教授是我国著名力学家,现任中国科学院学部委员、学位委员,中国科学院力学研究所副所长兼学术委员会主任,中国科技大学力学系主任、研究生院物理数学部副主任,中国力学学会常务理事.由于他早年在空气动力学和湍流理论方面的成就,近年来又...     

QUASI-PERIODIC WAVES AND QUASI-SOLITARY WAVES IN STRATIFIED FLUID OF SLOWLY VARYING DEPTH

The nonlinear waves in a stratified fluid of slowly varying depth are investigated in this paper.The model considered here consists of a two-layer incompressible constant-density inviscid fluid confined by a slightly uneven bottom and a horizontal rigid wall.The Korteweg-de Vries(KdV)equation with varying coefficients is derived with the aid of the reductive perturbation method.By using the method of multiple scales,the approximate solutions of this equation are obtained.It is found that the unevenness of bottom may lead to the generation of socalled quasi-periodic waves and quasi-solitary waves,whose periods,propagation velocities and wave profiles vary slowly.The relations of the period of quasi-periodic waves and of the amplitude,propagation velocity of quasi-solitary waves varying with the depth of fluid are also presented.The models with two horizontal rigid walls or single-layer fluid can be regarded as particular cases of those in this paper.     

SOLITARY WAVES AT THE INTERFACE OF A TWO-LAYER FLUID

In this paper,we discuss the solitary waves at the interface of a two-layer incompressible inviscid fluid confined by two horizontal rigidwalls,taking the effect of surface tension into account.First of all,we establish the basic equations suitable for the model considered,and hence derive the Korteweg-de Vries(KdV)equation satisfied bythe first-order elevation of the interface with the aid of the reduc-tive perturbation method under the approximation of weak dispersion.Itis found that the KdV solitary waves may be convex upward or downward.It depends on whether the signs of the coefficients α and μof the KdVequation are the same or not.Then we examine in detail two criticalcases,in which the nonlinear effect and the dispersion effect cannotbalance under the original approximation.Applying other appropriateapproximations,we obtain the modified KdV equation for the criticalcase of first kind(α=0),and conclude that solitary waves cannot existin the case considered as μ>0,but may still occur as μ<0,be     

前言

第七届全国力学史与方法论研讨会将于2015年7月12～14日在北京召开,本栏刊登的是在本届会议上交流的论文精选。16世纪英国的著名哲学家弗兰西斯·培根曾说:"阅读使人充实,会谈使人敏捷,写作使人精确。······读史使人明智,诗歌使人巧慧,数学使人精细,博物使人深沉,伦理之学使人庄重,逻辑与修辞使人善辩。"20世纪伟大的物理学家爱因斯坦说过:"方法比知识更重要。"这里要强调的是,"读史使人明智"和方法论的重要性。     

怎样告慰钱伟长先生在天之灵？

 这些天来,在上海大学延长校区,已有三万余人前来悼念钱伟长先生;社会上,各方人士以 各种方式在表示对这位科技伟人离世的悲恸. 一位大学校长的辞世在世间引起这样大的震撼, 说明钱伟长先生在人们心目中的崇高地位,说明他的精神感人至深！ 此刻,我想说的是,老校长已经永远地离开了我们,我们怎样告慰他老人家的在天之灵？我 认为,最好的行动是传承他的伟大精神,倾情奉献,实现他的遗愿！什么是钱伟长精神？可 以归纳为6个字：爱国,执着,坦荡. 钱校长是彻底的爱国者,爱国主义是贯穿他漫长人生的红线. 他在人生抉择的六个关口,他 都以爱国主义为准绳毫不犹豫地做了正确的选择. 无论在顺境还是在逆境,他的热爱祖国的 拳拳之心从未改变. ``反右'之后的26年,他承受了各种屈辱和磨难,但报国之情矢志不渝. 1980年代初,国内盛传钱伟长已移居国外,钱先生一笑置之,他说：``我从来没这么想过, 我要是有这个想法,1946年就不会回来. 我是中国人,决不会离开哺育我成长的伟大的祖国. 我的岗位在这里！'有人问起这些年他对所遭受的不公正待遇的想法,他说：``祖国是我们 的母亲,哪有母亲不爱自己的子女的？你能说母亲错打你几下屁股,你就记恨了吗？天下没 这个事情. 我们对祖国对人民的责任感就应当是永恒的. '从中可以看出他热爱祖国的赤子 之心！所以,我们要慰籍老人家的在天之灵,首先要像钱先生那样,成为彻头彻尾彻里彻外 的爱国者.     

Solitary waves at the interface of a two-layer fluid

In this paper, we discuss the solitary waves at the interface of a two-layer incompressible inviscid fluid confined by two horizontal rigid walls, taking the effect of surface tension into account. First of all, we establish the basic equations suitable for the model considered, and hence derive the Korteweg-de Vries (KdV) equation satisfied by the first-order elevation of the interface with the aid of the reductive perturbation method under the approximation of weak dispersion. It is found that the KdV solitary waves may be convex upward or downward. It depends on whether the signs of the coefficients and of the KdV equation are the same or not. Then we examine in detail two critical cases, in which the nonlinear effect and the dispersion effect cannot balance under the original approximation. Applying other appropriate approximations, we obtain the modified KdV equation for the critical case of first kind (=0), and conclude that solitary waves cannot exist in the case considered as >0, but may still occur as <0, being in the form other than that of the KdV solitary wave.As for the critical case of second kind (=0), we deduce the generalized KdV equation, for which a kind of oscillatory solitary waves may occur. In addition, we discuss briefly the near-critical cases. The conclusions in this paper are in good agreement with some classical results which are extended considerably.     

A semi-inverse algorithm in application of computer algebra

ProjectsupportcdbytheNationalNaturalScicnceFoundationofChinaandShanghaiMunicipalNaturaIScicnceF0undationI.Introducti0nCQmputeralgebra(i.e.,symbolic'computation)hasfounditswideapp1icationinscientificcomputationandengineeringana1ysis(cf.Refs.[1~31).Aswaspoi…     

分层流体中运动源生成的内波研究进展

针对两类密度分布模型------连续分层流体和间断分层流体, 综述了在运动潜体生成的Kelvin型和非Kelvin型内尾迹研究方面的现状, 内容侧重于运动源生成内波的解析理论和分层拖曳水槽中内尾迹实验方面的研究成果. 介绍了在连续分层流体中运动源生成的Kelvin型非线性内波的一般方程和在间断分层流体中Kelvin型内波的势流分析的一般方法; 概述了运动源诱生的先锋内孤立子、代数孤立子和平孤立波3类特殊非线性内波的研究进展, 其中运动潜体生成的平孤立内波被作者实验证实是一类极限孤立波, 并首次建立了共轭流动模型予以描述; 综合分析了在密度线性分布流体中潜体运动生成内波的动力学过程多样性特征, 其中包括内尾迹近场和远场的时空结构、不稳定结构、涡旋与湍流耦合结构以及湍流与内波相互作用结构等.      

基于跟车思想的一维元胞自动机交通流模型

提出一个改进的一维元胞自动机模型来模拟周期性边界条件下高速公路上车流运动.基于跟车模型的思想,根据所研究车辆与其前方紧邻车辆之间的间距和相对速度来确定该车的运动,间接地反映了次近邻车辆的影响.通过引入安全间距来描述高速运动车辆接近前方缓行车辆时的减速行为,并利用随机减速概率来反映减速行为中的随机因素.由于安全间距的引入,当减速概率大于零时在较高密度下就出现完全的阻塞相.同时在本模型中采用的是有条件减速,因而可以较好描述交通实测中观察到的现象.在临界密度附近,车流运动处于亚稳态并呈现出滞后现象.由于本模型对于车辆微观运动的合理描述,可以直接用以研究在交通灯控制下城市道路交通中的各种现象.