Finite larmor-radius effects on Rayleigh-Taylor instability of a dusty magnetized plasma

This paper discusses the Rayleigh-Taylor (RT) instability of an infinitely conducting medium having an exponential density distribution which includes the effects of finite ion Larmor-radius (FLR) corrections and suspended particles in the presence of a uniform horizontal magnetic field. The relevant equations of the problem are linearized and from the linearized perturbation equations a dispersion relation is obtained, using appropriate boundary conditions. It has been found that the criterion for the stable density stratification remains uninfluenced by the simultaneous inclusion of the FLR corrections and suspended particles. The stability of the medium has been proved for the case of stable stratification when the FLR corrections are not considered in the analysis. The growth rate of unstable RT modes with increasing relaxation frequency of the suspended particles is evaluated analytically. It has been shown that the presence of suspended particles in the medium suppresses the growth rate of the unstable RT modes, thereby implying a stabilizing influence of the particles on the considered configuration.     

Rayleigh-Taylor instability of a viscous compressible plasma of variable density

A study has been made of the problem of the Rayleigh-Taylor instability of a hydromagnetic plasma of varying density to investigate the influence of the simultaneous presence of the effects of compressibility and viscosity. The solution is shown to be characterized by a variational principle. Based on the variational principle proper solutions have been obtained for a semi-infinite plasma, in which the density has a one-dimensional gradient along the direction of a uniform vertical magnetic field, confined between two planes. Both the viscosity and magnetic field are found to have a stabilizing influence. The effect of compressibility is found to be destabilizing.     

Rayleigh-Taylor instability of two viscous superposed rotating and conducting fluids

Classical R-M and synthetic W-D analysis of V758 Centauri are presented. Two solutions (semi-detached and contact) were found from differential corrections approach. The semi-detached model is physically acceptable since the system is thermally decoupled. The solution for this case and the photometric data are consistent with a B9 primary and A9 secondary components having parameters close to Main-Sequence values. It is suggested that V758 Centauri is a B-type W UMa system at the brokencontact phase predicted by the Thermal Relaxation Oscillations theory.     

Rayleigh-Taylor instability of ionized viscous fluids with FLR-corrections and surface-tension

The problem of Rayleigh-Taylor instability of superposed viscous magnetized fluids through porous medium is investigated in a partially-ionized medium. The fluid has ionized and neutralized particle components interacting with collisions. The effect of surface tension on R-T instability is also included in the present problem. The magnetohydrodynamic equations are modified for finite-Larmor radius corrections which is in the form of tensor. The equations of problem are linearized and using appropriate boundary condition, general dispersion relation is derived for two superposed fluids separated by horizontal boundary. The first part of the dispersion relation gives stable mode and condition is investigated using Hurwitz conditions. The second part of the dispersion relation shows that the growth rate of unstable system is reduced due to FLR corrections, viscosity, and collisional frequency of the neutrals. The role of surface tension on the system is also discussed.     

Finite Larmor radius effects on the Rayleigh-Taylor instability of a rotating plasma of variable density

The Rayleigh-Taylor instability in a rotating plasma of variable density has been investigated to include simultaneously the effects of viscosity and the finiteness of the ion Larmor radius. It is shown that, for a plasma in which the density is stratified along the vertical, the solution is characterized by a variational principle. Making use of this, proper solutions have been otained for a semiinfinite plasma in which the density varies exponentially. The dispersion relation has been solved numerically and it is found that the influence of the effects of both FLR and viscosity is stabilizing. The Coriolis forces are found to have a dual role, stabilizing for small wave numbers and destabilizing for large wave numbers. The range of the small wave numbers, over which the Coriolis forces have a stabilizing influence, is found to increase with Coriolis forces.     

Rayleigh-Taylor instability of rotating fluid in the presence of a vertical magnetic field

The Rayleigh-Taylor instability of two rotating superposed fluids in the presence of a vertical magnetic field has been investigated. It is shown thatn ² is purely real, wheren is the growth rate of a perturbation. In the basis of this fact it is shown that a unique dispersion relation exists if the lighter fluid lies beneath the heavier one. However, if the heavier fluid lies beneath the lighter fluid, then no unique dispersion relation exists. The effect of rotation is to slow down the rate at which potentially unstable stratification departs from the equilibrium position.     

Dissipative structures in the F-region of the equatorial ionosphere generated by Rayleigh-Taylor instability

The non-linear regime of electrostatic perturbations of the equatorial ionospheric F-region generated by Rayleigh-Taylor instability has been discussed, taking into account conductivity along magnetic field lines. A closed non-linear equation has been derived in the stationary limit for the polarization electric field potential. It coincides with the Karman equation of an ideal liquid. To solve the equation, the averaged variational Whitham method has been proposed. Some solutions localized along and across the geomagnetic field, B, as well as quasi-periodic solutions in the transverse direction, have been investigated. Non-linear longitudinal localization of perturbations has been shown to be due to electron-ion collisions.     

Note on the Helmholtz instability in stratified flows with magnetic fields

The nature of the neutral curves for the stability of a Helmholtz velocity profile in a stratified, Boussinesq fluid in the presence of a uniform magnetic field for the cases (1) an infinite fluid (2) a semi-infinite fluid with a rigid boundary is discussed.     

Dissipative-acoustic instability in accretion disks at a nonlinear stage

Nonstationary hydrodynamic models of a viscous accretion disk around a central compact object were constructed. Two different numerical methods (TVD and SPH) are used to study the dynamics of dissipatively unstable acoustic perturbations at the nonlinear stage in terms of the standard α-disk model. The standard disk accretion in the Shakura-Sunyaev model is unstable against acoustic waves for various parameters of the system. If the α parameter, which specifies the level of turbulent viscosity, exceeds α?0.03, then a complex nonstationary system of small-scale weak shock waves is formed. The growth rate of the perturbations is higher in the central disk region. For α?0.2, the relative shock amplitude can exceed 50% of the equilibrium disk parameters. The reflection of waves from the disk boundaries and their nonlinear interaction are important factors that can produce unsteady accretion. The luminosity of such a disk undergoes quasi-periodic oscillations at a level of several percent (?5%) of the equilibrium level.     

Effects of initial velocity on the sinking of ilmenite-bearing cumulates in the early lunar mantle:Insight from the theory of Rayleigh-Taylor instability

The early lunar mantle overturn,associated with the sinking of the dense ilmenite-bearing cumulate(IBC)crystallized at the shallow lunar mantle,provides satisfactory explanations for the origination of high-Ti basalt,the abnormally strong magnetic field between~3.9 and~3.6 Ga and the low-viscosity zone in the deep lunar mantle,but still poses a debate regarding the initial state of IBC in the early lunar mantle.If the sinking of IBC initiated before the end of lunar magma ocean crystallization,the solidified IBC can acquire a greater thickness and a higher initial velocity at the IBC-mantle boundary.The variation of initial velocity can affect the strain rate of IBC and,correspondingly,the dislocation creep components at the shallow lunar mantle.In this work,we analyze the effects of initial velocity on the dynamics of early lunar mantle by using the theory of Rayleigh-Taylor instability.To couple the effects of diffusion creep and dislocation creep for all major minerals in the lunar mantle,we exploit an improved Minimized Power Geometric(IMPG)model and isostress mixing model to characterize the upper limit and lower limit for the viscosity of the lunar mantle comprising four major minerals,i.e.olivine,orthopyroxene,clinopyroxene and ilmenite.The modeling results suggest that a high initial velocity,in any case,can shorten the onset time,tending to promote the early lunar mantle overturn even in a rheologically-strong lunar mantle.The effect of initial velocity on the overturn wavelength shows a strong dependence on the rheological mixing model.For the isostress mixing model,the increase of initial velocity tends to elongate the overturn wavelength.For the IMPG mixing model,the overturn wavelength is insensitive to the variation of initial velocity.As the actual lunar mantle rheology sandwiches between the rheologies predicted by isostress mixing model and IMPG model,it can be anticipated that the increase of initial velocity tends to elongate the overturn wavelength.In consideration of the importance of the initial velocity on the dynamics of early lunar mantle,future investigations should focus on the dynamics of the solid IBC in the solidifying lunar magma ocean.     

Linear and nonlinear cyclotron instability and VLF emissions in the magnetosphere

A theoretical study is made of the whistler mode cyclotron instability both in linear and nonlinear regimes in conjunction with the generation of VLF emissions in the magnetosphere. For the nonlinear treatment, a well-established quasilinear method is used and some physical processes of the cyclotron instability viz. energy conservation, mechanism of instability and frequency change of the excited emissions are clarified. The results are applied to some types of the triggered VLF emissions; whistler triggered emissions and artificially stimulated emissions (ASE). It is found that whistler triggered emissions excited around the upper cutoff frequencies of whistlers may be explained by the whistler mode cyclotron instability by a model distribution function inferred from satellite data. In order to see a nonlinear evolution of the whistler mode cyclotron instability, computer simulations were carried out and it is shown that the change of frequency with time of whistler triggered emissions as well as characteristics of ASE are well explained by resonant nonlinear behaviour of whistler mode cyclotron instability considered in the present paper.     

Rayleigh-Taylor stability in the presence of rotation

The stability of a slab of incompressible fluid with exponentially-increasing density, supported by a semi-infinite homogeneous region and supporting a semi-infinite region of exponentially-decreasing density has been investigated when the whole system rotates uniformly about a vertical axis. The familiar Rayleigh-Taylor stability problems are recovered from the general dispersion relation, both in the presence of rotation and in the absence of rotation.     

Long-term nonlinear behaviour of the magnetorotational instability in a localized model of an accretion disc

For more than a decade, the so-called shearing-box model has been used to study the fundamental local dynamics of accretion discs. This approach has proved to be very useful because it allows high-resolution and long-term studies to be carried out, studies that would not be possible for a global disc.
Localized disc studies have largely focused on examining the rate of enhanced transport of angular momentum, essentially a sum of the Reynolds and Maxwell stresses. The dominant radial–azimuthal component of this stress tensor is, in the classic Shakura–Sunyaev model, expressed as a constant α times the pressure. Previous studies have estimated α based on a modest number of orbital times. Here we use much longer baselines, and perform a cumulative average for α. Great care must be exercised when trying to extract numerical α values from simulations: dissipation scales, computational box aspect ratio, and even numerical algorithms can all affect the result. This study suggests that estimating α becomes more, not less, difficult as computational power increases.     

Flash Code Simulations of Rayleigh-Taylor and Richtmyer-Meshkov Instabilities in Laser-Driven Experiments

We present two- and three-dimensional simulations involving Richtmyer–Meshkov and Rayleigh-Taylor instabilities run with the adaptive mesh refinement code, flash. Variations in the rate of mixing layer growth due to dimensionality, perturbation modes, and simulation resolution are explored. These simulations are designed for detailed comparisons with experiments run on the Omega laser to gain understanding of the mixing processes and to prepare for validation of the Flash code.     

Image processing of radiographs in 3D Rayleigh-Taylor decelerating interface experiments

This paper discusses high-energy-density laboratory astrophysics experiments exploring the Rayleigh-Taylor instability under conditions similar to the blast wave driven, outermost layer in a core-collapse supernova. The planar blast wave is created in an experimental target using the Omega laser. The blast wave crosses an unstable interface with a seed perturbation machined onto it. The perturbation consists of a 3D “egg crate” pattern and, in some cases, an additional longer wavelength mode is added to this 3D, single-mode pattern. The main diagnostic of this experiment is x-ray radiography. This paper explores an image processing technique to improve the identification and characterization of structure in the radiographic data.     

Non-Stationary Rayleigh-Taylor Instabilities in Pulsar Wind Interaction with a Supernova Shell

The Rayleigh-Taylor instability (RTI) plays an important role in the dynamics of several astronomical objects, in particular, in the supernovae (SN) evolution. In the present paper we examine the dynamics of a shell (representing a type II SN remnant) blown-up by a wind emitted by a central pulsar. The shell is accelerated by the pulsar wind and its inner surface experiences the RTI. We develop an analytical approach by using a specific transformation into the coordinate frame co-moving with the SN ejecta. We first derive a non-stationary spherically symmetric solution describing an expansion of a gas shell under the pressure of a central source (pulsar). Then, we analyze its 3D stability with respect to a small perturbation on the inner shell surface. The dispersion relation is derived in the co-moving reference frame. The growth rate of the perturbation is found and its temporal evolution is discussed. We compare our result with the previous published studies and apply it to the Crab nebula evolution.     

The Kelvin-Helmholtz instability on the magnetopause

Conditions for the development of Kelvin-Helmholtz (K-H) waves on the magnetopause have been known for more than 15 years; more recently, spacecraft observations have stimulated further examination of the properties of K-H waves. For amagnetopause with no boundary layer, two different modes of surface waves have been identified and their properties have been investigated for various assumed orientations of magnetic field and flow velocity vectors. The power radiated into the magnetosphere from the velocity shear at the boundary has been estimated. Other calculations have focused on the consequences of finite thickness boundary layers, both uniform and non-uniform. The boundary layer is found to modify the wave modes present at the magnetopause and to yield a criterion for the wavelength of the fastest growing surface waves. The paper concludes by questioning the extent to which the inferences from boundary layer models are model dependent and identifies areas where further work is needed or anticipated.