轴向剪切流对Z箍缩等离子体瑞利-泰勒不稳定性的抑制

利用理想磁流体力学模型对有轴向剪切流的Z箍缩等离子体不稳定性进行了分析。给出了可压缩模型的色散关系,分别对可压缩及不可压缩模型中轴向剪切流对Z箍缩等离子体瑞利-泰勒不稳定性的抑制作用进行了比较,讨论了可压缩性对含有轴向剪切流系统不稳定性的影响。结果表明,可压缩性能够减缓瑞利-泰勒P凯尔文-亥姆霍兹(RTPKH)模扰动的增长,因而使得轴向剪切流对系统不稳定性的抑制作用表现得更为突出。计算结果还说明,在RT不稳定性线性增长阶段,等离子体温度较低,使用可压缩模型能够更真实地描述系统的状态。     

可压缩与不可压缩流体中Rayleigh Taylor不稳定性的比较

 对比研究了可压缩与不可压缩流体的Rayleigh Taylor不稳定性小扰动阶段的增长速率，其中，压力是密度的任意单值函数，这个函数也即是可压缩流体的状态方程。研究表明：在相同密度分布条件下，可压缩流体的界面扰动增长速率总是比相应的不可压缩流体的界面增长率大，其相对增长率随扰动波长的增加而增大，随两种介质的声速减小而增大，在长波和易压缩流体中，相对增长率可达0.8以上。因此，在某些条件下，流体可压缩性对Rayleigh Taylor不稳定性的影响是不能忽略的。     

Wave Instabilities of a Collisionless Plasma in Fluid Approximation

Wave properties and instabilities in a magnetized, anisotropic, collisionless, rarefied hot plasma in fluid approx‐imation are studied, using the 16‐moments set of the transport equations obtained from the Vlasov equations. These equations differ from the CGL‐MHD fluid model (single fluid equations by Chew, Goldberger, and Low [5,9]) by including two anisotropic heat flux evolution equations, where the fluxes invalidate the double polytropic CGL laws. We derived the general dispersion relation for linear compressible wave modes. Besides the classic incompressible fire hose modes there appear four types of compressible wave modes: two fast and slow mirror modes – strongly modified compared to the CGL model – and two thermal modes. In the presence of initial heat fluxes along the magnetic field the wave properties become different for the waves running forward and backward with respect to the magnetic field. The well known discrepancies between the results of the CGL‐MHD fluid model and the kinetic theory are now removed: i) The mirror slow mode instability criterion is now the same as that in the kinetic theory. ii) Similarly, in kinetic studies there appear two kinds of fire hose instabilities ‐ incompressible and compressible ones. These two instabilities can arise for the same plasma parameters, and the instability of the new compressible oblique fire hose modes can become dominant. The compressible fire hose instability is the result of the resonance coupling of three retrograde modes ‐ two thermal modes and a fast mirror mode. The results can be applied to the theory of solar and stellar coronal and wind models (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Suppression of Rayleigh-Taylor instability by gyroviscosity and sheared axial flow in imploding plasma pinches

The synergistic stabilizing effect of gyroviscosity and sheared axial flow on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible viscid magneto-hydrodynamic equations.The gyroviscosity(or finite Larmor radius) effects are introduced in the momentum equation through an anisotropic ion stress tensor.Dispersion relation with the effect of a density discontinuity is derived.The results indicate that the short-wavelength modes of the Rayleigh-Taylor instability are easily stabilized by the gyroviscosity effects.The long wavelength modes are stabilized by the sufficient sheared axial flow.However,the synergistic effects of the finite Larmor radius and sheared axial flow can heavily mitigate the Rayleigh-Taylor instability.This synergistic effect can compress the Rayleigh-Taylor instability to a narrow wave number region.Even with a sufficient gyroviscosity and large enough flow velocity,the synergistic effect can completely suppressed the Rayleigh-Taylor instability in whole wave number region.     

瑞利-泰勒不稳定性的格子玻耳兹曼模拟

发展了一个不相混两相流体的格子玻耳兹曼模型，模拟瑞利-泰勒不稳定性．模型使用正方格阵并引入了一外力．数值模拟得到了界面扰动的线性和非线性发展图象，并与实验和其它方法的结果进行了比较 关键词：     

Rayleigh-Taylor instability in a spherical configuration: A viscous potential flow approach

In this paper, Rayleigh-Taylor (RT) instability at the spherical interface is analyzed through the potential flow theory of viscous fluids. The linear stability theory is utilized including normal mode procedure. The viscous, incompressible fluids are confined in the spherical shell and the interface distortion is expressed in terms of spherical harmonic functions. We achieve a quadratic equation for the illustration of instability/stability criterion. We also compute the highest growth of perturbations and corresponding mode. The Plane configuration results are recovered when the mode of perturbations is very large. Viscosity is found to stabilize the interface while the Weber number and Reynolds number have destabilizing nature.     

二维可压缩流体Kelvin-Helmholtz不稳定性

利用高精度数值格式,研究了二维可压缩流体中的Kelvin-Helmholtz不稳定性,主要研究了可压缩性对Kelvin-Helmholtz稳定性增长率的影响.模拟定量的给出低Mach和高Mach数两种情况下,初始静压和对流Mach数以及Kelvin-Helmholtz不稳定性线性增长率的关系.模拟结果和自由剪切层以及混合层的实验结果以及理论分析一致.模拟表明,对流Mach数是描述流体可压缩性的合适参数,对流Mach数越小流体越不可压,Kelvin-Helmholtz不稳定性的线性增长率随对流Mach数的增加而减小. 关键词： Kelvin-Helmholtz不稳定性 可压缩流体 Mach数 超音速流体     

The Compressible Viscous Surface-Internal Wave Problem: Stability and Vanishing Surface Tension Limit

This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant pressure. This is a free boundary problem: the interfaces between the fluids and above the upper fluid are free to move. The fluids are acted on by gravity in the bulk, and at the free interfaces we consider both the case of surface tension and the case of no surface forces. We establish a sharp nonlinear global-in-time stability criterion and give the explicit decay rates to the equilibrium. When the upper fluid is heavier than the lower fluid along the equilibrium interface, we characterize the set of surface tension values in which the equilibrium is nonlinearly stable. Remarkably, this set is non-empty, i.e., sufficiently large surface tension can prevent the onset of the Rayleigh-Taylor instability. When the lower fluid is heavier than the upper fluid, we show that the equilibrium is stable for all non-negative surface tensions and we establish the zero surface tension limit.     

Intermediate nonlinear evolution of the Parker instability: formation of convection-induced discontinuities and absence of finite-time singularities

Direct numerical simulations of the line-tied Parker (or magnetic Rayleigh-Taylor) instability, based on the fully compressible ideal magnetohydrodynamic equations, are presented. In the intermediate nonlinear phase, the instability continues to grow exponentially in time and the plasma tends to develop convection-induced discontinuities in the form of shocklike coherent structures. No evidence of finite-time singularities is seen.     

Rayleigh-Taylor instability in variable density swirling flows

Using linear instability theory and nonlinear dynamics, the Rayleigh-Taylor instability of variable density swirling flows is studied. It is found that the flow topology could be predicted, when the instability sets in, using a function χ dependent on density and axial and azimuthal velocities. It is shown that even when the inner axial-flow is heavier than the outer one (a favorable case for the development of the Rayleigh-Taylor instability thanks to the centrifugal force) the instability is not necessarily Rayleigh-Taylor-dominated. It is also shown that when the Rayleigh-Taylor instability develops, it is helical.     

Rayleigh-Taylor不稳定性的Runge-Kutta间断有限元模拟

 采用发展后的间断有限元方法,对Rayleigh-Taylor不稳定性进行了数值模拟。在计算中采用Level-Set方法进行界面追踪,用虚拟流体方法（Ghost Fluid Method,GFM）对界面附近物理量进行等压装配。对两个典型的Rayleigh-Taylor不稳定性算例的数值研究结果表明,采用该方法计算含有接触间断的多介质流体力学问题是有效的,在交界面附近不出现伪振荡,具有较高的分辨率。     

Rayleigh-Taylor instability experiments with precise and arbitrary control of the initial interface shape

In a Rayleigh-Taylor instability a dense fluid sits metastably atop a less dense fluid, a configuration that can be stabilized using a magnetic field gradient when one fluid is highly paramagnetic. On switching off the magnetic field, the instability occurs as the dense fluid falls under gravity. By affixing appropriately shaped magnetically permeable wires to the outside of the cell, one may impose arbitrarily chosen and well-controlled initial perturbations on the interface. This technique is used to examine both the linear and nonlinear growth regimes for which the perturbation amplitudes, growth rates, and nonlinear growth coefficients are obtained.     

A simplified approximate analytical model for Rayleigh–Taylor instability in elastic–plastic solid and viscous fluid with thicknesses

A simplified theoretical model for the linear Rayleigh-Taylor instability of finite thickness elastic-plastic solid constantly accelerated by finite thickness viscous fluid is performed.With the irrotational assumption,it is possible to consider viscosity,surface tension,elasticity or plasticity effects simultaneously.The model considers thicknesses at rigid wall boundary conditions with the velocity potentials,and deals with solid elastic-plastic transition and fluid viscosity based on the velocity continuity and force equilibrium at contact interface.The complete analytical expressions of the amplitude motion equation,the growth rate,and the instability boundary are obtained for arbitrary Atwood number,viscosity,thicknesses of solid and fluid.The thicknesses effects of two materials on the growth rate and the instability boundary are discussed.     

任意不可压多介质流的粒子有限元方法模拟

基于粒子有限元方法(particle finite element method,PFEM),利用细分混合单元的界面识别思想,模拟种类任意多的不可压多介质流问题.对分步算法采用基于有限增量微积分理论的稳定措施,以适应流体特性差异;将混合单元细分为代表单一流体的小单元,进而得到流体间的边界;通过加密边界、控制粒子速度、自动检查穿透来防止粒子穿透外部边界.瑞利-泰勒不稳定性和水柱在空气中倒塌的模拟与已有结果的对比验证了PFEM及界面识别方法的可靠性和准确性.七种流体混合的模拟结果表明PFEM可有效处理任意多种类不相溶流体的混合流动问题.     

Rayleigh-Taylor/gravitational instability in dense magnetoplasmas

The Rayleigh-Taylor instability is investigated in a nonuniform dense quantum magnetoplasma. For this purpose, a quantum hydrodynamical model is used for the electrons whereas the ions are assumed to be cold and classical. The dispersion relation for the Rayleigh-Taylor instability becomes modified with the quantum corrections associated with the Fermi pressure law and the quantum Bohm potential force. Numerically, it is found that the quantum speed and density gradient significantly modify the growth rate of RT instability. In a dense quantum magnetoplasma case, the linear growth rate of RT instability becomes significantly higher than its classical value and the modes are found to be highly localized. The present investigation should be useful in the studies of dense astrophysical magnetoplasmas as well as in laser-produced plasmas.     

Magneto-Rayleigh-Taylor instability in compressible Z-pinch liner plasmas

In this paper, the characteristics of magneto-Rayleigh-Taylor(MRT) instability of liner plasmas in Mag LIF is theoretically investigated. A three-region slab model, based on ideal MHD equations, is used to derive the dispersion relation of MRT instability. The effect of compressibility on the development of MRT instability is specially examined. It is shown that the growth rate of MRT instability in compressible condition is generally lower than that in incompressible condition in the presence of magnetic field. In the case of zero magnetic field, the growth rate in compressible assumption is approximately the same as that in incompressible assumption. Generally, MRT instability in(x, y) plane can be remarkably mitigated due to the presence of magnetic field especially for short-wavelength perturbations. Perturbations may be nearly completely mitigated when the magnetic field is increased to over 1000 T during liner implosions. The feedthrough of MRT instability in liner outer surface on inner surface is also discussed.     

Effect of tangential electric field on the evolution of the Rayleigh-Taylor instability of a dielectric liquid film

The effect of surface ponderomotive forces produced by a uniform tangential electric field on the evolution of the Rayleigh-Taylor instability of an isothermal film of a homogeneous incompressible dielectric liquid coating the lower surface of a horizontal insulating plate is studied in the long-wavelength approximation for the hydrodynamic equations and a simplified system of electrostatics equations. The lower boundary of the liquid is the interface with a stationary gas. It is shown in the framework of the linear theory that during the disruption of the continuous film, ponderomotive forces induce the formation of liquid billows extended along the applied field lines.     

Nonlinear analysis of the Rayleigh-Taylor instability at the charged interface

An asymptotic solution to the problem of analyzing the nonlinear stage of the Rayleigh-Taylor instability at the uniformly charged interface between two (conducting and insulating) immiscible ideal incompressible liquids is derived in the third order of smallness. It is found that the charge expands the range of waves experiencing instability toward shorter waves and decreases the length of the wave with a maximum growth rate. It turns out that the characteristic linear scale of interface deformation, which arises when the heavy liquid flows into the light one, decreases as the charge surface density increases in proportion to the square root of the Tonks-Frenkel parameter characterizing the stability of the interface against the distributed self-charge.     

瑞利-泰勒不稳定问题的光滑粒子法模拟研究

提出了一种适用于模拟多相流的光滑粒子法,该方法对密度方程在交界面处的离散格式进行了修正以适应多相流所涉及的大密度比问题,在不同相粒子之间施加了很小的排斥力以防止粒子穿透交界面,并采用了最新发展的双曲型光滑函数以消除应力不稳定问题.应用该多相流光滑粒子法模拟研究了单模态和多模态瑞利-泰勒不稳定问题.通过与文献中结果的对比研究表明:在模拟瑞利-泰勒不稳定问题时,本文方法的结果明显优于文献中的大部分光滑粒子法模拟结果,与Grenier等(2009 J.Comput.Phys.228 8380)的结果相当,但本文方法比Grenier等的方法简单方便.对于单模态瑞利-泰勒不稳定问题,研究了交界面的形态,涡结构的演化过程以及贯穿深度随时间的变化关系.对于多模态瑞利-泰勒不稳定问题,研究了交界面演化过程中小尺度结构合并成大尺度结构的过程,水平方向的平均密度随高度的变化关系,以及贯穿深度随时间的变化关系.     

Gas flow characteristics of argon inductively coupled plasma and advections of plasma species under incompressible and compressible flows

In this work, incompressible and compressible flows of background gas are characterized in argon inductively coupled plasma by using a fluid model, and the respective influence of the two flows on the plasma properties is specified. In the incompressible flow, only the velocity variable is calculated, while in the compressible flow, both the velocity and density variables are calculated. The compressible flow is more realistic; nevertheless, a comparison of the two types of flow is convenient for people to investigate the respective role of velocity and density variables. The peripheral symmetric profile of metastable density near the chamber sidewall is broken in the incompressible flow. At the compressible flow, the electron density increases and the electron temperature decreases. Meanwhile, the metastable density peak shifts to the dielectric window from the discharge center, besides for the peripheral density profile distortion, similar to the incompressible flow.The velocity profile at incompressible flow is not altered when changing the inlet velocity, whereas clear peak shift of velocity profile from the inlet to the outlet at compressible flow is observed as increasing the gas flow rate. The shift of velocity peak is more obvious at low pressures for it is easy to compress the rarefied gas. The velocity profile variations at compressible flow show people the concrete residing processes of background molecule and plasma species in the chamber at different flow rates. Of more significance is it implied that in the usual linear method that people use to calculate the residence time, one important parameter in the gas flow dynamics, needs to be rectified. The spatial profile of pressure simulated exhibits obvious spatial gradient. This is helpful for experimentalists to understand their gas pressure measurements that are always taken at the chamber outlet. At the end, the work specification and limitations are listed.