The wave model of mesothermal plasma near wakes and Korteweg-de Vries equation

The stationary two-dimensional (x, z) near wakes behind a flat-based projectile which moves at a constant mesothermal speed (V∞) along a z-axis in a rarefied, fully ionized, plasma is studied using the wave model previously proposed by one of the authors (VCL). One-fluid theory is used to depict the free expansion of ambient plasma into the vacuum produced behind a fast-moving projectile. This nonstationary, one-dimensional (x, t) flow which is approximated by the K-dV equation can be transformed, through substitution, t=z/V∞, into a stationary two-dimensional (x, z) near wake flow seen by an observer moving with the body velocity (V∞). The initial value problem of the K-dV equation in (x, t) variables is solved by a specially devised numerical method. Comparisons of the present numerical solution for the asymptotically small and large times with available analytical solutions are made and found in satisfactory agreements.

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 epsilon, 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 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 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.

Recovery of the solitons using a lattice Boltzmann model

We formulate a lattice Boltzmann model which simulates Korteweg-de Vries equation by using a method of higher moments of lattice Boltzmann equation. Using a series of lattice Boltzmann equations in different time scales and the conservation law in time scale to, we obtain equilibrium distribution function. The numerical examples show that the method can be used to simulate soliton.

Rossby Waves With Linear Topography In Barotropic Fluids

Rossby waves are the most important waves in the atmosphere and ocean, and are parts of a large-scale system in fluid. The theory and observation show that, they satisfy quasi-geostrophic and quasi-static equilibrium approximations. In this paper, solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied. In order to simplify the problem, the topography is taken as a linear function of latitude variable y, then employing a weakly nonlinear method and a perturbation method, a KdV (Korteweg-de Vries) equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived. The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow, and extend the classical geophysical theory of fluid dynamics.

约化摄动法和非线性波远场分析

<正> 一、引言 如所周知,摄动法(特别是奇异摄动法)在研究弱非线性波方面有着广泛的应用[1—5]。其中,近年来发展形成的约化摄动法已经成了分析各种非线性波远场的有力工具[6—8]。 约化摄动法的实质是,对于一般的描述非线性波的复杂方程组,通过适当的坐标变形和摄动展开,在一阶近似下,把方程组约化成较为简单可解的单个非线性方程(例如Burgers方程、Korteweg-de Vries方程、非线性Schrodinger方程等),从而可以分析远离波的相互作用区的远场。

两层流体界面上的孤立波

本文讨论两水平固壁间两层不可压无粘流体界面上的孤立波,计及界面上的表面张力效应.首先建立了适用于这种模型的基本方程组,并在弱色散近似下应用约化摄动法,导得了一阶界面升高所满足的Korteweg-de Vries方程,指出了按该方程系数α和μ的符号的异同,KdV孤立波可能凸向上或凸向下.然后详细讨论了原有近似下非线性效应与色散效应不能平衡的两种临界情形.在采用了适当的近似之后,对第一种临界情形(α=0)得到了修正的KdV方程,并指出,在所考虑的情形中,当μ>0时孤立波不存在,当μ<0时,孤立波仍可能存在,其形式与KdV孤立波不同;对第二种临界情形(μ=0),导得了推广的KdV方程,这时存在振荡型孤立波.文中还对近临界情形作了讨论.本文结果与一些经典结果完全一致,并把它们作了拓广.

The effect of variable currents on internal solitary waves

The effect of variable currents on internal solitary waves is described within the context of a variable coefficient Korteweg-de Vries (KdV) equation, and the approximate slowly varying, solitary-wave solution of this equation. The general theory which leads to the variable coefficient KdV equation is described; a derivation for the special case when the solitary wave and the current are aligned in the same direction is given in the Appendix. Using further simplifications and approximations, a number of analytical expressions are obtained for the variation in the solitary wave amplitude resulting from variable shear in the basic current or from when the basic current is a depth-independent flow which is a simple representation of a geostrophic current, tidal flow or inertial wave.

Rossby waves with linear topography in barotropic fluids

Rossby waves are the most important waves in the atmosphere and ocean, and are parts of a large-scale system in fluid. The theory and observation show that, they satisfy quasi-geostrophic and quasi-static equilibrium approximations. In this paper, solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied. In order to simplify the problem, the topography is taken as a linear function of latitude variable y, then employing a weakly nonlinear method and a perturbation method, a KdV (Korteweg-de Vries) equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived. The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow, and extend the classical geophysical theory of fluid dynamics.

Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea

Large amplitude internal solitary waves (ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean. We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea (19A degrees 35'N, 112A degrees E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors, and an acoustic Doppler current profiler (ADCP). We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories. Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width. Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries (KdV) theory than the first-order KdV model. These results indicate that the northwestern South China Sea (SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.

工业机器人机械手的小脑模型自适应控制

本文为动力学控制工业机器人机械手提出一种综合控制算法。该控制算法,利用小脑模型算术计算机模块模拟机器人机械手的动力学方程并计算实现期望运动所需力矩作为前馈力矩控制项;利用自适应控制器实现反馈控制,以消除由输入扰动和参数变化而引起的机器人机械手运动误差。这种控制方法在时间上是有效的,且很适合于定点实现。控制方法的有效性通过四自由度的直接驱动机器人前两个关节的计算机仿真实验得到验证。

有源电磁扩散场克希霍夫积分偏移

As active electromagnetic method, field data of CSAMT method follow the equation of diffusion. Propagting in solid earth media, diffusion EM signal has strong attenuation and dispersion, otherwise seismic wave shows weak attenuation and dispersion, therefore the resolution power of CSAMT method is not better than seismic reflection method. However, there is consistence and similarity between EM signal and seismic wave in wave equation, we can apply Kirchhoff integral migration technique, a proven one in seismic method in time domain, to carry out seduo-seismic processing for CSAMT signal in frequency domain so that the attenuation and dispersion could be made compensated in some extent, and the resolution power and interpretation precision of active EM wave could be improved. Satisfying passive homogeneous Helmholtz quation, we proceed with Green theorem and combine the active inhomogenous Helmholtz quation, the Kirchhoff integral formula could be derived. Given practical problems, if we only consider the surface integral value, and assume that the intergral value in other interface is zero, combined with Green theorem in uniform half space, the expression could be simplified, and we can obtain frequency-domain Kirchhoff integral formula in surface, which is also called downward continuation of EM field in frequency domain. With image conditions and energy compensation considered, in order to get image conditions in time domain Fourier inverse transformation in frequency domain can be performed, so we can formulate the active Kirchhoff integral migration expression. At first, we construct relative stratified model, with different frequency series taken into account, then we change the distances between transmitter and reciever, the EM response can be obtained. Analyzing the EM properties, we can clarify near and far zone that can instruct us to carry out transmitter layout in practical application. Combined with field data surveyed in far zone, We perform Kirchhoff integral migration and compare the results with model to interpret. Secondly, with far field EM data, we apply TM mode to get EM response of given 2D model, then apply Kirchhoff integral migration on modelling data and interpret the results.