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。     

浅水孤立波在三维浮体上的绕射

浅水域中非线性水波运动的控制方程通常是经过深度平均的Boussinesq方程。然而,这一方程在浮体近旁或水下障碍物附近不再适用,在这些区域,流动在水深方向的变化不容忽略,本文应用匹配渐近展开法和边缘层(edge layer)思想,建立了浅水弱非线性波与三维浮体相互作用的数学模型,作为算例,求解了浅水孤立波在垂直圆柱形浮体上的绕射.本方法可以推广到波在一般浮体上绕射的情况。     

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．      

三维海洋内孤立波数值水槽造波研究

海洋内孤立波因其分布广泛和携带巨大能量,对于潜艇安全航行影响很大.本文采用有限体积自适应半结构多重网格法求解Navier-Stokes方程,并用VOF方法追踪两层流体界面,应用双推板造波法进行内孤立波数值造波,建立了两层流体中的内孤立波数值水槽.数值模拟结果证实了该数值水槽数值造波的有效性和可靠性,为后续研究打下了基础...     

孤立波与孤立子

简要阐述了孤立波与孤立子发现和研究的历史,并由此可看出力学基础研究的深刻意义.     

分层流体中内孤立波数值造波方法及其应用

海洋内波是发生在密度分层海水中的波动,对潜艇航行的稳定性和悬停性都有重要影响。本文采用有限体积自适应半结构多重网格法求解Navier-Stokes方程,并用VOF(Volume of Fluid)方法追踪两层流体界面,应用双推板造波法进行内孤立波数值造波,对两层流体中的内孤立波数值造波方法进行研究和探讨。数值模拟结果证...     

非传播孤立波和表面张力

讨论关于表面张力的实验与理论分析之间的矛盾．把表面张力的能量当作高阶小量、导出了非传播孤立波的基本方程，得到的解与实验结果相符．     

分层流体中内孤立波在台阶上的反射和透射

基于匹配渐近展开和格林函数的方法,研究了两层流体系统中内孤立波在台阶地形上透射、 反射及其分裂的演化特征. 通过保角变换和求解奇异Fredholm积分方程,获得了反映地形 效应对Boussinesq方程影响的约化边界条件,藉此建立了KdV演化方程的``初值'问题, 根据散射反演理论获得了反射波和透射波的解析表达式. 分析结果表明：上下流体层的厚度 比、密度比以及台阶高度对于反射和透射波振幅及其分裂具有显著的影响. 尤其当上层流体 厚度小于下层厚度时,由于存在临界点,在其附近反射波的幅值随台阶高度的演化由单调增 变为单调减,透射波的幅值由单调减变为单调增;上台阶的反射波与入射波反相,其最大幅 值可达到入射波的数倍;此外,下台阶反射波也可发展为单支孤立波,它区别于单层流体中 反射波仅为衰减的振荡波列.     

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.      

THE EXACT SOLITARY WAVE SOLUTIONS FOR THE KLEIN-GORDON-SCHRDINGER EQUATIONS

The solitary wave solutions for the Klein-Gordon-Schrdinger Equations were obtained by using the homogeneous balance principle. The form of the solutions is more generalized than the result that has been proved by pure theoretical and qualitative method in literature; namely, the form of solutions in literature is a particular case of result of the present paper.     

The diffraction of a solitary wave by a circular cylinder

This paper contributes to the diffraction of a solitary wave by a cylinder, governed by the Boussinesq eq. The Spectrum Method is used to transform 2·D eqs.into a set of 1·D eqs., which is solved by F. D. M. The example given in the paper shows that this method is both accurate and cost effective.     

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.     

Numerical simulation of a solitary wave interaction with submerged multi-bodies

The problems of a solitary wave passing over rectangular cylinders have been analysed. The numerical simulation is based on the full nonlinear two-dimensional Navier-Stokes equations which are solved by the finite difference method. The free surface is dealt with by the Volume of Fluid method (VOF). Results for a solitary wave passing over a single cylinder are compared with the experimental data of Seabra-Santos, Penouard and Temperville^[2] and better agreement is obtained than those obtained from the long wave equation based on the potential flow theory. Results are also given for two cylinders with different gaps. The project supported by the National Natural Science Foundation of China and the Development Foundation of Science and Technology of Shanghai Education Committee and the Royal Society.     

Stability of the Korteweg-de Vries solitary wave solution

ＳＴＡＢＩＬＩＴＹＯＦＴＨＥＫＯＲＴＥＷＥＧ－ＤＥＶＲＩＥＳＳＯＬＩＴＡＲＹＷＡＶＥＳＯＬＵＴＩＯＮＬｕＸｉａｎ－ｑｉｎｇ（吕咸青）（ＳｈａｎｄｏｎｇＥｄｕｃａｔｉｏｎＣｏｌｌｅｇｅ,Ｊｉｎａｎ）（ＲｅｃｅｉｖｅｄＪｕｎｅ１８,１９９３,Ｃｏｍｍｕｎ...     

Comparisons of CIP,compact and CIP‐CSL2 schemes for reproducing internal solitary waves

Six different models were evaluated for reproducing internal solitary waves which occur and propagate in a stratified flow field with a sharp interface. Three stages were used to compute internal solitary waves in a stratified field: (1) first‐phase computation of momentum equations, (2) second‐phase computation of momentum equations, which corresponds to computing the Poisson's equation, and (3) density computation. The six models discussed in this paper consisted of combinations of four different schemes, a three‐point combined compact difference scheme (CCD), a normal central difference scheme (CDS), a cubic‐polynomial interpolation (CIP), and an exactly conservative semi‐Lagrangian scheme (CIP‐CSL2). The residual cutting method was used to solve the Poisson's equation. Three tests were used to confirm the validity of the computations using KdV theory; i.e. the incremental wave speed and amplitude of internal solitary waves, the maximum horizontal velocity and amplitude, and the wave form. In terms of the shape of an internal solitary wave, using CIP for momentum equations was found to provide better performance than CCD. These results suggest one of the most appropriate scheme for reproducing internal solitary waves may be one in which CIP is used for momentum equations and CCD to solve the Poisson's equation. Copyright © 2005 John Wiley & Sons, Ltd.     

Internal waves in a two‐layer system using fully nonlinear internal‐wave equations

In order to understand the nonlinear effect in a two‐layer system, fully nonlinear strongly dispersive internal‐wave equations, based on a variational principle, were proposed in this study. A simple iteration method was used to solve the internal‐wave equations in order to solve the equations stably. The applicability of the proposed numerical computation scheme was confirmed to agree with linear dispersion relation theoretically obtained from variational principle. The proposed computational scheme was also shown to reproduce internal waves including higher‐order nonlinear effect from the analysis of internal solitary waves in a two‐layer system. Furthermore, for the second‐order numerical analysis, the balance of nonlinearity and dispersion was found to be similar to the balance assumed in the KdV theory and the Boussinesq‐type equations. Copyright © 2009 John Wiley & Sons, Ltd.     

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。     

Diffraction of a solitary wave by a thin wedge

The diffraction of a solitary wave by a thin wedge with vertical walls is studied when the incident solitary wave is directed along the wedge axis. The method of multiple scales is extended to this problem and reduces the task to that of solving the two-dimensional KdV equation with proper boundary and initial conditions. The finite-difference numerical procedure is carried out with the fractional step algorithm in which difference schemes are all implicit. Except the maximum run-up at the wall, the results in this paper are found to corroborate the Melville's experiments not only qualitatively but also quantitatively. The maximum run-up of our results agrees well with Funakoshi's numerical one but it is considerably larger than that in Melville's experiment. An important reason for this discrepancy is believed to be the effect of viscous boundary layer on the vertical side wall.     

求解浅水波方程的并行物理信息神经网络算法

双曲守恒律方程是一类比较特殊的偏微分方程,其数值求解方法的研究一直是一个热点问题,一个显著特性是即使初始条件是光滑的,其解也可能会发展成间断。浅水波方程作为非线性双曲守恒律方程,由于间断解的存在,其精确求解存在很大困难。针对浅水波方程数值求解问题,本文基于PINN(Physics informed neural networks)反问题网络结构构造新的网络,构造的网络结构包括两个并行的神经网络,其中一个网络与已知状态数据(熵稳定格式加密求出)相关,另一个网络与方程本身相关。利用已知速度数据结合浅水波方程本身求解未知水深,最终通过一些数值算例验证网络的可行性。结果表明,新的网络结构可用于浅水波方程求解,利用速度数据可以较为精确地推算出水深。