Numerical Experiments and Structural Transformation of NonLinear Evolution in Illposed Systems

Numerical experiments on nonlinear equations of the 1st and 3rdorder derivatives have been carried out through structural analyses in the phase space according to the numerical instability of illposed systems, with changes of initial values and parameters, etc.. The results show that the quantitative instability in an illposed system may reveal reversed transformation in system evolution by structural representation, and confirm A·Dauglas’ theorem that “a nonlinear equation does not satisfy the existence of the initial value in a linear wellposed system”.     

J-TEXT托卡马克高速单色成像系统研制

在J-TEXT托卡马克上研制了一套高速单色成像系统用于研究等离子体杂质行为与磁流体力学(MHD)不稳定性之间的关系.用STRAH代码模拟估算了碳杂质(CV227.09nm,CIII464.7nm)辐射强度.采用光纤耦合方法设计了系统光路结构,光路覆盖高场侧区域0.3a～0.95a(a为小半径),其空间分辨率为1.3cm...     

Structure formation in turbulence as an instability of effective quantum plasma

Structure formation in turbulence can be understood as an instability of “plasma” formed by fluctuations serving as effective particles. These “particles” are quantumlike in the sense that their wavelengths are non-negligible compared to the sizes of background coherent structures. The corresponding “kinetic equation” describes the Wigner matrix of the turbulent field, and the coherent structures serve as collective fields. This formalism is usually applied to manifestly quantumlike or scalar waves. Here, we show how to systematically extend it to more complex systems using compressible Navier–Stokes turbulence as an example. In this case, the fluctuation Hamiltonian is a five-dimensional matrix operator and diverse modulational modes are present. As an illustration, we calculate these modes for a sinusoidal shear flow and find two modulational instabilities. One of them is specific to supersonic flows, and the other one is a Kelvin–Helmholtz-type instability that is a generalization of the known zonostrophic instability. Our calculations are readily extendable to other types of turbulence, for example, magnetohydrodynamic turbulence in plasma.     

高雷诺数下非混相Rayleigh-Taylor不稳定性的格子Boltzmann方法模拟

本文采用相场格子Boltzmann方法研究了竖直微通道内中等Atwoods数流体的单模Rayleigh-Taylor不稳定性问题,系统分析了雷诺数对相界面动力学行为以及扰动在各发展阶段演化规律的影响.数值结果表明高雷诺数条件下,不稳定性界面扰动的增长经历了四个不同的发展阶段,包括线性增长阶段、饱和速度阶段、重加速阶段及混沌混合阶段.在线性增长阶段,我们计算获得的气泡与尖钉振幅符合线性稳定性理论,并且线性增长率随着雷诺数的增加而增大.在第二个阶段,我们观察到气泡与尖钉将以恒定的速度增长,获得的尖钉饱和速度略高于Goncharov经典势能模型的解析解[Phys.Rev.Lett.200288134502],这归因于系统中产生了多个尺度的旋涡,而涡之间的相互作用促进了尖钉的增长.随着横向速度和纵向速度的差异扩大,气泡和尖钉界面演化诱导产生的Kelvin–Helmholtz不稳定性逐渐增强,从而流体混合区域出现许多不同层次的涡结构,加速了气泡与尖钉振幅的演化速度,并在演化后期阶段,导致界面发生多层次卷起、剧烈变形、混沌破裂等行为,最终形成了非常复杂的拓扑结构.此外,我们还统计了演化后期气泡与尖钉的无量纲加速度,发现气泡和尖钉的振幅在后期呈现二次增长规律,其增长率系数分别为0.045与0.233.而在低雷诺条件下,重流体在不稳定性后期以尖钉的形式向下运动而轻流体以气泡的形式向上升起.在整个演化过程中,界面变得足够光滑,气泡与尖钉在后期的演化速度接近于常数,未观察到后期的重加速与混沌混合阶段.     

Capturing the experimental behaviour of a point-absorber WEC by simplified numerical models

The paper presents a wave basin experiment of a direct-driven point-absorber wave energy converter moving in six degrees of freedom. The goal of the work is to study the dynamics and energy absorption of the wave energy converter, and to verify under which conditions numerical models restricted to heave can capture the behaviour of a point-absorber moving in six degrees of freedom. Several regular and irregular long-crested waves and different damping values of the power take-off system have been tested. We collected data in terms of power output, device motion in six degrees of freedom and wave elevation at different points of the wave basin. A single-body numerical model in the frequency domain and a two-body model in the time domain are used in the study. Motion instabilities due to parametric resonance observed during the experiments are discussed and analysis of the buoy motion in terms of the Mathieu instability is also presented. Our results show that the simplified models can reproduce the body dynamics of the studied converter as long as the transverse non-linear instabilities are not excited, which typically is the case in irregular waves. The performance of the more complex time domain model is able to reproduce both the buoy and PTO dynamics, while the simpler frequency domain model can only reproduce the PTO dynamics for specific cases. Finally, we show that the two-body dynamics of the studied wave energy converter affects the power absorption significantly, and that common assumptions in the numerical models, such as stiff mooring line or that the float moves only in heave, may lead to incorrect predictions for certain sea states.     

基于持续同调的边坡土颗粒应力链失稳分析

采用颗粒离散元方法和持续同调理论,研究了内排土场堆叠至不同高度时的边坡稳定性。为便于研究,现采用一水平金属板向下施加压力,代替不同厚度土层的重力荷载,对边坡在竖向荷载作用下的失稳破坏过程进行了颗粒离散元模拟。研究了二维边坡土颗粒速度总矢量、边坡失稳破坏时滑移开裂面的角度以及边坡坡顶y方向的平均速度等宏观响应过程,并构建了自然堆积下边坡堆积体颗粒的法向力链无向网络模型。最后,用持续同调方法对边坡坡顶颗粒接触力链网络的拓扑特征进行分析,获得条码图,建立了岩体结构持续同调特征与失稳演化的关系。本文为研究边坡失稳拓扑识别提供了一种新方法,从而可以有效预测边坡的失稳破坏。     

Shape stability of a gas bubble in a soft solid

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.     

Hydrodynamic instability of premixed flame propagating in narrow planar channel in the presence of gas flow

The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.     

反应扩散系统中短波不稳定性下的时空斑图

利用扩展的三变量布鲁塞尔模型,得到了新的时空斑图,其中包括振荡四边形斑图、调制条纹斑图以及螺旋波斑图.通过对模型进行线性稳定性分析,发现这些时空斑图是由于短波不稳定性所引起的.另外,还研究了系统大小对时空斑图的影响.     

推力轴承瞬态启动油膜热不稳定性的线性分析

以简化推力轴承为对象 ,理论上证明了推力轴承运行时存在热不稳定性 ,采用小扰动分析法得到了油膜温度的扰动方程 ,应用简正模态分析法推导了无量纲热不稳定性准则数以及推力轴承运行的热不稳定性准则 .