Streaming instability of a dusty plasma in the presence of mass and charge variation

We study the effect of the mass and charge dynamics on the collective behaviour of a dusty plasma. It is shown that the finite non-zero streaming velocity of the dust grains leads to a novel coupling of the dust mass fluctuation with other dynamic variables of the plasma and the grains. The mass fluctuations causes a collisionless dissipation and provides an alternate channel for the beam mode instability to occur. Physically the negative energy wave associated with the beam mode couples to the mass fluctuation induced dissipative medium to produce the instability. We conclude that the higher value of the ion mass density to the dust mass density ratio reduces the threshold value for the onset of the instability. Its application in the astrophysical context is discussed.     

Secondary instabilities of interfacial waves due to coupling with a long wave mode in a two-layer Couette flow

We report experiments on the stability of interfacial waves in a two-layer Couette flow. As the shear rate is increased, the periodic wave train arising from the primary instability undergoes a secondary instability which results in wave coalescence or nucleation, after a long transient. This secondary instability crucially involves the coupling with a long wave mode, which corresponds to variations of the mean interface level. These observations are favourably compared to stability results on travelling wave solutions for a set of two coupled equations, one for the envelope of a weakly unstable wave packet, and the other for the marginal long wave mode with zero wave number. A physical mechanism for this instability is proposed, as well as an interpretation for the onset of chaos.     

矩形管内临界爆轰动力学数值分析

 对矩形管内临界爆轰动力学特征进行了数值分析。采用基元反应描述爆轰化学反应过程,采用二阶附加半隐的龙格-库塔法和5阶WENO格式求解二维反应欧拉方程。对于25%氩稀释化学计量比的氢氧预混气体,当管道宽度为30 mm、初温为300 K时,产生临界爆轰的预混气体初压为3.5 kPa。在此临界条件下,获得了临界爆轰胞格结构、沿壁面的速度和峰值压力曲线及流场波系演变特征。着重对比分析了矩形管内临界爆轰与普通爆轰在爆轰波速度、平均速度、胞格宽长比、横波结构、未反应气囊及旋涡结构之间的差异,深入认识了临界爆轰的不稳定性和化学反应动力学特征。     

Instability of a flat horizontal interface between a thin layer of a ferrofluid and a thin layer of a nonmagnetic liquid in the presence of a vertical magnetic field

An asymptotic analysis of the equations and boundary conditions of fluid dynamics is performed, and a nonlinear model is constructed for the onset of the development of Rosensweig instability in a thin horizontal ferrofluid layer at rest covered with a thin layer of a lighter nonmagnetic liquid. The surface of a nonmagnetized slab is the lower boundary of the ferrofluid, and the interface with a gas is the upper boundary of the nonmagnetic liquid. The pressure in the gas is constant. The instability being considered arises upon the application of a rather strong uniform vertical magnetic field. The proposed model involves five dimensionless parameters. The critical magnetization of the initial ferrofluid layer with a flat upper boundary and the threshold wave number are found. The effect of the governing parameters on the instability region and on the wavelength of the fastest growing mode is studied in the linear formulation of the problem.     

Mathematical simulations of the development of the ion hose instability of a relativistic electron beam in a plasma channel with a varying density

The effect of different parameters of a plasma channel with an increasing or a decreasing density on the onset and behavior of the ion hose instability is investigated using the distributed-mass model.     

Convective and absolute Eckhaus instability leading to modulated waves in a finite box

We report an experimental study of the secondary modulational instability of a one-dimensional nonlinear traveling wave in a long bounded channel. Two qualitatively different instability regimes involving fronts of spatiotemporal defects are linked to the convective and absolute nature of the instability. Both transitions appear to be subcritical. The spatiotemporal defects control the global mode structure.     

Effect of the combined thermal and mass concentration gradients on the stability of a chemically reacting fluid in a porous medium

Summary The onset of instability, due to the combined effects of thermal and mass concentration gradients, is investigated in the hydrodynamic stability regime. It is found that the critical Rayleigh number, which determines the onset of instability, increases as the chemical reaction rate constant increases hyperbolically over a wide range of values at both moderate and high permeabilities. In addition, the instability grows with increase in porosity. Previous results show that the critical Rayleigh number rises linearly when only the mass concentration gradient is considered.     

Morphological instability induced by the interaction of a particle with a solid-liquid interface

We show that the interaction of a particle with a directionally solidified interface induces the onset of morphological instability provided that the particle-interface distance falls below a critical value. This instability occurs at pulling velocities that are below the threshold for the onset of the Mullins-Sekerka instability. The expression for the critical distance reveals that this instability is manifested only for certain combinations of the physical and processing parameters. Its occurence is attributed to the reversal of the thermal gradient in the melt ahead of the interface and behind the particle.Received: 3 December 2003, Published online: 19 February 2004PACS: 81.30.Fb Solidification - 81.05.Ni Dispersion-, fiber-, and platelet-reinforced metal-based composites - 81.10.Fq Growth from melts; zone melting and refining     

Oscillations in rapid fracture

Experiments of pure tensile fracture in thin brittle gels reveal a new dynamic oscillatory instability whose onset occurs at a critical velocity, VC=0.87CS, where CS is the shear wave speed. Until VC, crack dynamics are well described by linear elastic fracture mechanics (LEFM). These extreme speeds are obtained by suppression of the microbranching instability, which occurs when sample thicknesses are made comparable to the minimum microbranch width. The wavelength of these sinusoidal oscillations is independent of the sample dimensions, thereby suggesting that these macroscopic effects are due to an intrinsic microscopic scale that is unrelated to LEFM.     

Formation of a spiraling line defect and its meandering transition in a period-2 medium

The instability of a period-1 spiral wave resulting in a period-2 spiral wave with a line defect is investigated for the first time in a laboratory system. At the very onset the transition proceeds by an emergence of a spiraling line defect, "breathing" intermittently while retaining its symmetry of a period-1 spiral wave. With a further change in a control parameter, the line defect undergoes a meandering transition producing a compound tip trajectory, following a dynamic shape transition. The observed transitions have a strong analogy to the phase synchronization transition of two coupled nonlinear oscillators and the meandering transition of a period-1 spiral wave.     

自然循环过冷沸腾流动不稳定性的实验研究

本文以氟里昂作工质，对自然循环过冷沸腾流动不稳定性进行了实验研究．实验过程中发现自然循环系统内可能发生高频脉动和低频脉动二种类型的过冷沸腾流动不稳定性．通过实验研究揭示了这二种类型流动不稳定性的发生机理，证实高频脉动属于声波型脉动，低频脉动属于密度波型脉动．通过实验得出了判断系统稳定性的界限，并使用积分方程无因次分析方法得出了预测密度波型流动不稳定性的经验公式．     

On capillary motion of a viscoelastic liquid with a charged free surface

The structure of the capillary-relaxation motion spectrum in a liquid with a charged free surface has been investigated taking into account the viscosity relaxation effect. On the basis of numerical analysis of the dispersion equation for the wave motion in a viscoelastic incompressible liquid, it is shown that for a given wave number the range of characteristic relaxation times in which relaxation-type wave motion exists is limited and expands with increasing wave number. The growth rate of instability of the charged liquid surface markedly depends on the characteristic relaxation time and increases with its growth; in liquids with elastic properties, the energy dissipation rate of capillary motion is enhanced. At a surface charge density that is supercritical for the onset of Tonks-Frenkel instability, both purely gravitational waves and waves of a relaxational nature exist.     

~4He超流密度分布研究

一种密度泛函理论用来研究当4He超流体流速u超过朗道临界流速vc时的不稳定性。发现有稳定的周期性密度波出现,其振幅正比于(u-vc)1/2,其波矢与旋子波矢一致。同时对纳米管道内氦流体进行了计算。     

Local plasma parameters and integral characteristics of a magnetogasdynamic channel under conditions of ionization instability

Results are presented from an experimental investigation of the onset of ionization instability in a disk-shaped Faraday magnetogasdynamic channel attached to a shock tube. The experiments were carried out in a pure inert gas (xenon) without alkaline additives. A relation is found between the integral plasma characteristics of a nonequilibrium magnetogasdynamic channel and the local parameters of a plasma that is unstable against the ionization instability. Mechanisms for amplifying perturbations and increasing the effective conductivity are revealed. It is concluded that these effects stem mainly from the features of three-body recombination in rare gases.     

Modulation instability of pulsed radiation in an optical waveguide in the presence of the traveling refractive index wave

The conditions for the onset of modulation instability of wave packets in an optical waveguide in the presence of the traveling refractive index wave are investigated. An expression governing the growth rate of a small harmonic perturbation at the early development stage of the modulation instability is obtained. Based on numerical analysis, the behavior of the wave packet at the developed modulation instability stage is studied for different parameters of the waveguide and the refractive index wave.     

Linear stability analysis on the onset of Soret-driven motion in a nanoparticles suspension

The onset of Soret-driven instability in binary mixture heated from above is analysed using the linear stability theory. The horizontal fluid layer placed between two plates is in a thermally stable state but the Soret diffusion can induce buoyancy-driven convection in the case of a negative Soret coefficient. It is well known that convective motion sets in from both boundaries if the Rayleigh number exceeds its critical value. For the case of highly unstable density stratification the buoyancy-driven motion sets in during the transient diffusion stage. The new stability equations are derived and are solved analytically and numerically. Here the stability limits which are related to the onset time of instabilities and wave number are presented as a function of the Rayleigh number, Lewis number and the separation ratio. The present stability criteria are compared with the existing experimental data.     

Gravitational Instability of a Two-Component Viscous Plasma with Finite Conductivity Flowing Through a Porous Medium with Fir Corrections

The gravitational instability of a two component plasma is studied to include the simultaneous effects of collisions, gyroviscosity, finite conductivity, viscosity and porosity of the medium within the framework of two-fluid theory. From linearized equations of the system, using normal mode analysis, the dispersion relations for parallel and perpendicular directions to the magnetic field are derived and discussed. For longitudinal wave propagation it is found that the value of critical JEANS' wave number increases with increasing density and decreasing temperature of the neutral component. For transverse wave propagation the value of critical JEANS' wave number depends on gyroviscosity, ALFVÉN number, ratio of sonic speeds and densities of the two component and porosity of the medium. It is observed that the effect of magnetic field and porosity is suppressed by finite condutivity of the plasma and similarly the effect of gyroviscosity is removed by viscosity from JEANS' expression of instability. For both the directions instability is produced when the velocity perturbations are considered parallel to wave vector. The damping effect is produced due to collisional frequency, permeability of the porous medium and viscosity. The density of the neutral component and porosity of the medium tends to destabilize the system while an increased value of FLR corrections leads the system towards stabilization.     

On the stability of capillary waves on the surface of a space-charged dielectric liquid jet moving in a material medium

We have derived and analyzed the dispersion equation for capillary waves with an arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible dielectric medium. It has been proved that the existence of a tangential jump of the velocity field on the jet surface leads to a periodic Kelvin–Helmholtz- type instability at the interface between the media and plays a destabilizing role. The wavenumber ranges of unstable waves and the instability increments depend on the squared velocity of the relative motion and increase with the velocity. With increasing volume charge density, the critical value of the velocity for the emergence of instability decreases. The reduction of the permittivity of the liquid in the jet or an increase in the permittivity of the medium narrows the regions of instability and leads to an increase in the increments. The wavenumber of the most unstable wave increases in accordance with a power law upon an increase in the volume charge density and velocity of the jet. The variations in the permittivities of the jet and the medium produce opposite effects on the wavenumber of the most unstable wave.     

Sound propagation in a planar channel in the presence of a two-layer flow

Expressions describing the field of a point source in a planar channel with admittance walls enclosing a two-layer nonuniform flow are obtained. The dispersion equation that determines the eigenvalues in a wide range of flow velocities in the layers (including supersonic velocities) is studied. The effect of the admittance of the channel walls on the growth rate of unstable disturbances is considered for different frequencies. It is established that the effect of the admittance of the channel walls on the growth rate of the instability waves decreases with increasing frequency and essentially depends on the type of admittance. It is shown that, in the presence of the admittance, new unstable disturbances are formed with a growth rate that can exceed that of the Kelvin—Helmholtz instability wave.     

Chemical wave propagation with a chemically induced hydrodynamical instability

Propagation of trigger waves in a Belousov-Zhabotinsky (BZ) solution was performed in a capillary slit of parallel glass panes. With an open liquid-air interface, an instability of the upward moving wave fronts was observed up from the middle of the slit. This instability was found to be due to a fluid convection in the upper part of the slit which is generated by diffusion of oxygen through the interface. The explanation for the onset of the convection is based on the fact that oxygen is known to increase the production of bromide in BZ systems.