水泵进水池内紊流及涡旋的数值模拟

本文对水泵进水池内三维紊流及涡旋进行数值模拟。文中基于雷诺平均的Ｎ－Ｓ方程和к－ε紊流模型，在具有交错网格系统的贴体座标系中（１），采用ＳＩＭＰＬＥＣ算法计算三维素流，得出了流速场和压力场的分布。进一步预测了涡旋发生的位置并分析其结构，这对研究、改进水泵进水池的结构，避免涡旋发生，提高效率具有重要的实际意义。     

交替行为对螺旋波影响的数值模拟研究

在离散可激发介质Greenberg-Hasting模型中引入交替(alternans)行为,研究了交替行为对螺旋波的影响.数值结果表明:在适当选择参数下,交替对螺旋波有很大影响,例如交替导致螺旋波的形状振荡,形成呼吸螺旋波,交替使螺旋波漫游、漂移,甚至使螺旋波漫游出系统的边界,交替使螺旋波破碎形成小螺旋波、反靶波和时空混沌等,首次在均匀介质中观察到交替导致传导障碍,使螺旋波破碎和消失,并对发生这些现象的机理进行了分析. 关键词： 离散可激发介质 螺旋波 靶波 漫游     

两阶段脉冲控制螺旋波的数值模拟

提出两种两阶段的螺旋波控制方法,第一阶段用正相脉冲力作用快变量,第二阶段用反相脉冲力作用快变量或用正相脉冲力作用慢变量,用修改后的Bär模型进行数值模拟,结果表明:两阶段的脉冲控制方法比单阶段控制方法更有效地控制螺旋波,作用力可以减少到后者力大小的38%~55%.结果建议,可以通过两阶段控制螺旋波的方法改进心脏电除颤.     

圆柱振荡绕流中涡旋运动模式(pattern)的数值模拟

提出并发展的一种基于区域分解思想,综合了解N-S方程的有限差分法及涡法各自优点的新数值方法,计算了各种 Keulegan-Carpenter数下(Kc=2~24)振荡流绕圆柱的流动。系统地研究了振荡流中涡旋运动模式随Kc数变化的规律,模拟了不对称区、单对涡区(或模向区)、双对涡区(或对角区)和三对涡区四种不同的涡旋运动模式。将计算所得的阻力系数C_D、惯性系数C_M与国外近期发表的计算结果进行了比较。     

台风莫拉克(2009)暴雨过程中位势切变形变波作用密度诊断分析和预报应用

在水平风场切变形变的基础上引入物理量——位势切变形变, 把水平风场的垂直分量和切变形变与广义位温的空间梯度结合起来. 该物理量的二阶扰动被定义为波作用密度, 在局地直角坐标系中推导了能够描述中尺度扰动系统发展演变的波作用方程. 对2009年登陆台风莫拉克引发的暴雨过程进行诊断分析, 结果表明, 台风中心区切变形变向涡度的转化显著, 该转化通过纬向风的经向梯度实现. 纬向风速的经向梯度与广义位温垂直梯度的耦合引起位涡和位势切变形变之间的转化, 以至于位势切变形变和位涡的异常值区分别位于台风环流的外侧和内侧. 波作用密度因能够描述水平扰动风场的垂直切变和切变形变以及凝 结潜热函数扰动梯度而与观测降水联系紧密. 相关统计分析表明, 2009年夏季波作用密度与6 h观测降水存在明显滞后相关性, 对未来6 h降水有一定的指示意义. 另外, 波作用密度通量散度和扰动非地转风位涡是影响波作用密度局地变化的主要物理因素. 基于波作用密度与观测降水的良好相关性, 建立了波作用密度暴雨预报方程. 2009年登陆台风"苏迪罗", "天鹅", "莫拉菲"和"巨爵"的暴雨预报个例分析和长时间序列的ETS评分计算表明, 波作用密度对台风暴雨具有较好的预报效果, 其预报降水能力略优于美国全球预报系统(GFS)的直接降水预报. 关键词： 位势切变形变 波作用密度 波作用通量散度 台风暴雨     

热敏神经元网络中螺旋波死亡和破裂的数值模拟

实验发现大脑皮层内出现螺旋波且螺旋波对神经元电信号传递有积极作用.利用细胞网络方法从对大脑皮层观察到的螺旋波进行数值模拟.以包含温度因子的热敏神经元模型在二维空间构造规则网络,研究了神经元膜片温度参数对神经元网络中螺旋波演化影响;定义了一类统计同步因子来刻画温度因子引起螺旋波相变(破裂和死亡)的临界条件.发现在规则网络下,当温度超过一定值后螺旋波会死亡和消失而导致整个网络达到均匀同步;在考虑了弱通道噪声情况下,螺旋波温度超越一定临界值则引起螺旋波的破裂.进一步分析了暂时性发烧昏迷的可能机制在于神经系统某些功能区螺旋波传播电信号的中断.     

耦合复金兹堡-朗道(Ginzburg-Landau)方程中的模螺旋波

以双层耦合复金兹堡-朗道(Ginzburg-Landau)方程系统为时空模型, 研究了其中的模螺旋波, 讨论了这种特殊波动现象的稳定条件和相关影响因素. 模螺旋波与该类时空系统中常见的相螺旋波相比, 其中心不存在缺陷点, 同时仅在其变量的振幅部分(而非相位部分) 表现为螺旋结构. 本文通过数值方法研究了耦合复金兹堡-朗道方程中产生模螺旋波所需要的初始和参数条件.研究表明, 当双层耦合系统的初始斑图之间的差距较大时, 才能够产生模螺旋波; 同时观察到系统在参数不匹配的条件下会发生相螺旋波向模螺旋波的转变.通过对同步函数的计算, 发现该转变过程具有非连续性.     

机械孤波的MATLAB数值模拟及实验研究

针对一种产生机械孤波的多摆耦合系统建立了动力学模型,利用MATLAB进行了数值模拟并搭建装置进行了实验.模拟显示系统存在多种形式的孤波解.在实验中也发现了机械孤波,而且实测孤波速度与驱动强度的依赖关系定性上与数值模拟结果一致.     

Visual Basic模拟演示“波的叠加与干涉”

为了提高波动教学中的实验效果,促进学生对该过程的认识和理解.用计算机以VisualBasic为编程工具,设计"波的叠加"教学辅助软件,模拟演示波的产生和传播,并突出显示在波动中的质点仍在原处做简谐振动以及两列波相遇后发生叠加情况与波的干涉实验.     

B-Z反应中斑图的数值模拟及实验研究

根据B-Z反应的FKN机理得出的二维Tyson模型,用差分方法模拟了靶型波、单螺旋波、双螺旋波的形成过程.通过数值模拟发现螺旋波的组织中心是一个点缺陷,系统所有的动力学行为都受这个缺陷点的影响.在此基础上,在封闭的溴酸盐/硫酸/试亚铁灵的B-Z反应体系中,通过割断靶型波的方法,产生了双螺旋波.同时,也观察到了单螺旋波与螺旋波的破碎.这些实验结果与数值模拟结果一致.将B-Z振荡反应实验引入非线性物理实验教学中,可以扩充时空动力学的实验内容.     

Zonal flow interaction with Rossby waves in the Earth's atmosphere: A numerical simulation

A numerical simulation of the Charney-Obukhov equation modified by the presence of a sheared zonal flow is carried out. The zonal flow is assumed to propagate longitudinally and is sheared along the meridians. It is shown that owing to the nonlinear interaction of the sheared zonal flow with the initially given disturbances the energy of the zonal flow is accumulating into the formations which are broken into several pieces. As a result new solitary vortex structures arise to produce the structural turbulence     

涡旋中双臂形成的物理机制及其演变

利用柱坐标下的流体涡度方程,研究了涡旋中双臂的形成机制问题.结果表明：涡旋中切向波数为2（m=2）的扰动在基本流场中可出现不稳定快速增长,但其增长率受时间限制;扰动可演变为螺旋双臂并向外扩展;扰动发展的物理机制是扰动的速度场对基本涡度场强平流效应所致. 关键词： 旋涡星系 不稳定波动 螺旋云带 台风     

Analytical investigation of Rossby waves in atmospheric dynamics

The (2+1)-dimensional nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane is analyzed by using the classical Lie group approach. Using the group theory, some types of general exact Rossby wave solutions can be obtained whence a special Rossby wave solution is known. Especially, it is found that the only effect of the time-dependent background basic wind on the Rossby waves is the accumulate motion in the zonal direction. Some types of exact explicit similarity Rossby wave solutions with both nonconstant linear and nonlinear shears are also given.     

Propagation and modulational instability of Rossby waves in stratified fluids

Perturbation analysis and scale expansion are used to derive the (2+1)-dimensional coupled nonlinear Schrödinger (CNLS) equations that can describe interactions of two Rossby waves propagating in stratified fluids. The (2+1)-dimensional equations can reflect and describe the wave propagation more intuitively and accurately. The properties of the two waves in the process of propagation can be analyzed by the solution obtained from the equations using the Hirota bilinear method, and the influence factors of modulational instability are analyzed. The results suggest that, when two Rossby waves with slightly different wave numbers propagate in the stratified fluids, the intensity of bright soliton decreases with the increases of dark soliton coefficients. In addition, the size of modulational instable area is related to the amplitude and wave number in y direction.     

Modified KdV equation for magnetized Rossby waves in a zonal flow of the ionospheric E-layer

Nonlinear interaction of magnetized Rossby waves with sheared zonal flow in the Earth's ionospheric E-layer is investigated. It is shown that in case of weak nonlinearity 2D Charney vorticity equation can be reduced to the one-dimensional modified KdV equation.     

(2+1)-dimensional coupled Boussinesq equations for Rossby waves in two-layer cylindrical fluid*

In this paper, the existence and propagation characteristics of Rossby waves in a two-layer cylindrical fluid are studied. Firstly, based on the dimensionless baroclinic quasi-geostrophic vortex equations including exogenous and dissipative, we derive new (2+1)-dimensional coupled Boussinesq equations describing wave propagation in polar coordinates by employing a multiscale analysis and perturbation method. Then, the Lie symmetries and conservation laws of the coupled Boussinesq equations are analyzed. Subsequently, by using the $(G^{\prime} /G)$-expansion method, the exact solutions of the (2+1)-dimensional coupled Boussinesq equations are obtained. Finally, the effects of coupling term coefficients on the propagation characteristics of Rossby waves are analyzed.     

A(2+1)-dimensional nonlinear model for Rossby waves in stratified fluids and its solitary solution

In this paper,we investigate a(2+1)-dimensional nonlinear equation model for Rossby waves in stratified fluids.We derive a forced Zakharov–Kuznetsov(ZK)–Burgers equation from the quasigeostrophic potential vorticity equation with dissipation and topography under the generalized beta effect,and by utilizing temporal and spatial multiple scale transform and the perturbation expansion method.Through the analysis of this model,it is found that the generalized beta effect and basic topography can induce nonlinear waves,and slowly varying topography is an external impact factor for Rossby waves.Additionally,the conservation laws for the mass and energy of solitary waves are analyzed.Eventually,the solitary wave solutions of the forced ZK–Burgers equation are obtained by the simplest equation method as well as the new modified ansatz method.Based on the solitary wave solutions obtained,we discuss the effects of dissipation and slowly varying topography on Rossby solitary waves.     

A new model equation for nonlinear Rossby waves and some of its solutions

In this paper, we investigate the $(2+1)$ dimensional nonlinear Rossby waves under non-traditional approximation. Using the asymptotic methods of multiple scales and weak nonlinear perturbation expansions, we derive a new modified Zakharov–Kuznetsov equation from the barotropic potential vorticity equation with the complete Coriolis parameter, the topography and the dissipation. Based on the new auxiliary equation method, new exact solutions of the new mZK equation are obtained when the dissipation is absent. However, the new auxiliary equation method fails to solve the new mZK equation with the dissipative term. Therefore, the weak nonlinear method and the homotopy perturbation method are developed to solve the obtained new mZK equation. Through numerical simulations, the results show the effects of different parameters on Rossby waves.     

(2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect

In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.