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     

Kelvin-Helmholtz instability in anisotropic superfluids

Motivated by recent theoretical and experimental interest in the subject, we derive the condition of interfacial Kelvin-Helmholtz instability for a system of two flowing superfluids (one sliding on the other). The tensor structure of superfluid densities in anisotropic superfluids, such as ³He-A and also ³He-B under an external magnetic field, is properly taken into account. The consequences relevant to experiments on the A–B phase boundary in superfluid ³He are discussed.     

Kelvin-Helmholtz instability in a plasma with negative ions

A dispersion relation for low-frequency electrostatic modes in a plasma with negative ions is derived for the case in which a velocity shear Kelvin-Helmholtz instability exists in the positive ion flow along the magnetic field. It is found that the negative ions have, generally, a destabilizing effect, as seen previously for ion-acoustic and electrostatic ion-cyclotron waves. The influence of the negative-ion-to-positive-ion mass mass ratio on the stability is also examined     

Subharmonic suppression of a transverse Kelvin-Helmholtz instability

A plasma density modulation applied at nearly twice the frequency of an unstable mode was observed to produce amplitude suppression exhibiting strong hysteresis.     

On the Kelvin-Helmholtz instability in superfluids

The Kelvin-Helmholtz instability in superfluids is discussed on the basis of the first experimental observation of such an instability at the interface between superfluid ³He-A and superfluid ³He-B (R. Blaauwgeers, V. B. Eltsov, G. Eska et al., cond-mat/0111343). We discuss why the Kelvin-Helmholtz criterion, the Landau critical velocity for nucleation of ripplons, and the free-energy consideration all give different values for the instability threshold.     

Kelvin-Helmholtz instability of miscible ferrofluids

We study the stability of an interface between two inviscid magnetic fluids of different densities flowing parallel to each other in an oscillatory manner. The system is pervaded by a uniform oblique magnetic field distribution. The analysis allows for mass and heat transfer across the interface. A general eigenvalue relation is derived and discussed analytically. The classical stability criterion is found to be substantially modified due to the effect of the oblique magnetic field with mass and heat transfer. Some previous studies are reported for appropriate data choices. The longitudinal magnetic field has a strong stabilizing influence on all wavelengths, which can be used to suppress the destabilizing influence of the mass and heat transfer. We conclude with a discussion of the stability of unsteady shear layers on the basis of the results. The parametric excitation of the surface waves is analyzed by means of the multiple-time-scales method. The transition curves are obtained analytically.     

Kelvin-Helmholtz instability in a rotating ideally conducting inhomogeneous plasma

The Kelvin-Helmholtz instability in sheared magnetohydrodynamic flow of an ideally conducting rotating inhomogeneous compressible plasma is investigated. The asymptotic behaviour inx of the Kelvin-Helmholtz eigenfunctions for the case of finite compressibility in the presence of rotation is discussed and instability condition is derived. In the incompressible limit, a dispersion relation is derived which has been solved numerically and discussed in detail. It is found that the inhomogeneous system is unstable in an incompressible plasma.     

Darrieus–Landau instability and Markstein numbers of premixed flames in a Hele-Shaw cell

Hydrodynamic flame instabilities are studied in a Hele-Shaw burner. By studying the development of perturbations, starting from a 2D Bunsen flame at the top of the burner, growth rates are measured for propane and methane–air mixtures, and compared to theoretical predictions. It is found that the dispersion relation in a Hele-Shaw cell has the same dependence with wavenumber $\sigma =k?k^2$ as the one predicted in tubes. Markstein numbers relative to fresh gases are obtained for propane and methane flames and compared to the literature.     

黏性各向异性磁流体Kelvin-Helmholtz不稳定性:二维数值研究

利用corner transport upwind和constrained transport算法求解非理想磁流体动力学方程组,对匀强平行磁场作用下,黏性各向异性等离子体自由剪切层中的Kelvin-Helmholtz不稳定性进行了数值模拟.从流动结构、涡结构演化、磁场分布、横向磁压力、抗弯磁张力等角度对各向同性和各向异性黏性算例结果进行了讨论,分析了黏性各向异性对Kelvin-Helmholtz不稳定性的影响.结果表明,黏性各向异性比黏性各向同性更利于流动的稳定.其稳定性作用是由于磁感线方向上剪切速率降低导致界面卷起程度和圈数的降低,并使卷起结构中小涡产生增殖、合并,破坏了涡的常规增长,从而导致流动的稳定.黏性各向异性对横向磁压力的影响比对抗弯磁张力更大.     

Shear flow and Kelvin-Helmholtz instability in superfluids

The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with the classic Kelvin-Helmholtz theory when modified for two-fluid hydrodynamics.     

Magnetic reconnection in the two-dimensional Kelvin-Helmholtz instability

Magnetic reconnection in the two-dimensional Kelvin-Helmholtz instability is studied. The flow is modeled by the reduced MHD equations with constant resistivity and viscosity. For super-Alfvénic flow, localized transient reconnection is observed on the Kelvin-Helmholtz time scale (this is not new). We study this transient reconnection and consider the peak reconnection rate which occurs with the initial vortex formation. Over the range of resistivities considered, it is shown that this peak reconnection rate is not a function of resistivity, and is a function of the initial flow shear. Additionally, it is demonstrated that there is a fundamental difference between the evolution of a problem at S = 200 and S = 10,000.     

超声速流体Kelvin-Helmholtz不稳定性速度梯度效应研究

利用加权本质上无振荡（WENO）方法模拟超声速流体Kelvin-Helmholtz（KH）不稳定性,研究速度梯度对KH不稳定性线性增长率和后期非线性演化的影响.模拟发现超声速流体中的速度梯度对KH不稳定性具有较强的致稳作用,给出了包含速度梯度致稳的线性增长率经验公式.数值模拟和经验公式符合得很好.模拟给出了清晰的流场密度等值线,这说明WENO方法模拟超声速流体KH不稳定性具有较好的界面变形捕捉能力.模拟结果表明速度梯度影响KH涡的演化,在给定密度梯度的情况下速度梯度越大KH涡的横向尺度越小. 关键词： Kelvin-Helmholtz不稳定性 超声速流体 速度梯度     

Magnetohydrodynamic Kelvin-Helmholtz instability for finite-thickness fluid layers

We have derived the analytical formulas for the Kelvin-Helmholtz instability (KHI) of two superposed finite-thickness fluid layers with the magnetic field effect into consideration. The linear growth rate of KHI will be reduced when the thickness of the fluid with large density is decreased or the thickness of fluid with small density is increased. When the thickness and the magnetic field act together on the KHI, the effect of thickness is more obvious when the magnetic field intensity is weak. The magnetic field transition layer destabilizes (enforces) the KHI, especially in the case of small thickness of the magnetic field transition layer. When considering the effect of magnetic field, the linear growth rate of KHI always decreases after reaching the maximum with the increase of total thickness. The stronger the magnetic field intensity is, the more obvious the growth rate decreases with the total thickness. Thus, it should be included in applications where the effect of fluid thickness on the KHI cannot be ignored, such as in double-cone ignition scheme for inertial confinement fusion.     

Nonlinear asymptotic calculation of the Kelvin-Helmholtz instability

The problem of periodic capillary-gravitational wave motion on the uniformly charged interface between two ideal immiscible incompressible liquids is solved in the third order of smallness. The lower liquid is assumed to be ideally conducting, while the upper one is a dielectric executing translational motion parallel to the interface with a constant velocity. A nonlinear frequency correction in the resonance form is found. It is shown that the positions of internal nonlinear resonances depend on the sum of the field and Weber parameters, the density ratio of the liquids, and the wave number. When the upper liquid is denser than the lower one, resonances are absent.     

Analog of Kelvin-Helmholtz instability on a free surface of a superfluid liquid

We analyze the analog of the Kelvin-Helmholtz instability on the free surface of a superfluid liquid. This instability is induced by the relative motion of superfluid and normal components of the same liquid along the surface. The instability threshold is found to be independent of the value of viscosity, but turns out to be lower than in the absence of dissipation. The result is similar to that obtained for the interface between two sliding super-fluids (with different mechanisms of dissipation) and confirmed by the first experimental observation of the Kelvin-Helmholtz instability on the interface between ³He-A and ³He-B by Blaauwgeers et al. (cond-mat/0111343).     

Parametric buildup of the instability of a charged flat liquid surface imposed on Kelvin-Helmholtz instability

The instability of capillary gravitational waves that is developed at the charged flat interface between media is studied for the case when the upper medium moves parallel to the interface with a velocity that has constant and time-dependent components. It is shown that the Mathieu-Hill equation, describing the temporal evolution of the capillary wave amplitudes in such a system, has unstable solutions at those values of physical parameters (electric field strength and wind velocity) meeting the conditions for Saint Elmo fire initiation in the atmosphere.     

双界面耦合作用对KH不稳定的影响（英）

研究了含有中间层的流体系统的双界面KH不稳定性。计算发现:由于耦合作用,界面KH不稳定性呈现出不同的增长模式。主要研究了对增长率影响最大的夹层厚度对增长模式的影响,发现厚度小于半个扰动波长时,耦合作用必须考虑。另外发现在特定厚度下,界面不稳定性将出现简并的增长模式。