Assembling Stabilization of the Rayleigh-Taylor Instability by the Effects of Finite Larmor Radius and Sheared Axial Flow

The assembling stabilizing effect of the finite Larmor radius (FLR) and the sheared axial flow (SAF) on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible finite Larmor radius magnetohydrodynamic (MHD) equations. The finite Larmor radius effects are introduced in the momentum equation with the sheared axial flow through an anisotropic ion stress tensor. In this paper a linear mode equation is derived that is valid for arbitrary kL, where k is the wave number and L is the plasma shell thickness. Numerical solutions are presented. The results indicate that the short-wavelength modes of the Rayleigh-Taylor instability are easily stabilized by the individual effect of the finite Larmor radius or the sheared axial flow. The assembling effects of the finite Larmor radius and sheared axial flow can heavily mitigate the Rayleigh-Taylor instability, and the unstable region can be compressed considerably.

Directly driven Rayleigh-Taylor instability of modulated CH targets

Directly driven ablative Rayleigh Taylor （R-T） instability of modulated CH targets was studied using the face- on X-ray radiography on the Shen-Guang II device. We obtained temporal evolution images of the R-T instability perturbation. The RT instability growth factor has been obtained by using the methods of fast Fourier transform and seeking the difference of light intensity between the peak and the valley of the targets. Through comparison with the the theoretical simulation, we found that the experimental data had a good agreement with the theoretical simulation results before 1.8 ns. and was lower than the theoretical simulation results after that.

Sufficient conditions of Rayleigh-Taylor stability and instability in equatorial ionosphere

Rayleigh-Taylor （R-T） instability is known as the fundamental mechanism of equatorial plasma bubbles （EPBs）. However, the sufficient conditions of R-T instability and stability have not yet been derived. In the present paper, the sufficient conditions of R-T stability and instability are preliminarily^derived. Linear equations for small perturbation are first obtained from the electron/ion continuity equations, momentum equations, and the current continuity equation in the equatorial ionosphere. The linear equations can be casted as an eigenvalue equation using a normal mode method. The eigenvalue equation is a variable coefficient linear equation that can be solved using a variational approach. With this approach, the sufficient conditions can be obtained as follows： if the minimum systematic eigenvalue is greater than one, the ionosphere is R-T unstable; while if the maximum systematic eigenvalue is less than one, the ionosphere is R-T stable. An approximate numerical method for obtaining the systematic eigenvalues is introduced, and the R-T stable/unstable areas are calculated. Numerical experiments axe designed to validate the sufficient conditions. The results agree with the derived suf- ficient conditions.

Comparison Between Mitigation Effects of the Finite Larmor Radius and Sheared Axial Flow on Rayleigh-Taylor Instability in Z-Pinch Implosions

A magnetohydrodynamic (MHD) formulation is derived to investigate and compare the mitigation effects of both the sheared axial flow and finite Larmor radius (FLR) on the Rayleigh-Taylor (RT) instability in Z-pinch implosions. The sheared axial flow is introduced into MHD equations in a conventional way and the FLR effect into the equations via /t → -i(w+ik⊥2pi2Ωi,), as proposed in our previous paper [Chin. Phys. Lett. 2002, 19:217] , where k⊥2 pi2 is referred to FLR effect from the general kinetic theory of magnetized plasma. Therefore the linearized continuity and momentum equations for the perturbed mass-density and velocity include both the sheared axial flow and the FLR effect. It is found that the effect of sheared axial flow with a lower peak velocity can mitigate RT instability in the whole wavenumber region and the effect of sheared axial flow with a higher one can mitigate RT instability only in the large wavenumber region (for normalized wavenumber k】2.4); The effect of FLR can mitigate RT instability in the whole wavenumber region and the mitigation effect is stronger than that of the sheared axial flow with a lower peak velocity in the almost whole wavenumber region.

Expansion of Linear Analysis of Rayleigh-Taylor Interface Instability of Metal Materials

The linear analysis of the Rayleigh-Taylor instability in metal material is extended from the perfect plastic constitutive model to the Johnson-Cook and Steinberg-Guinan constitutive model, and from the constant loading to a time-dependent loading. The analysis is applied to two Rayleigh-Taylor instability experiments in aluminum and vanadium with peak pressures of 20 GPa and 90 GPa, and strain rates of 6 × 106 s−1 and 3 × 107 s−1 respectively. When the time-dependent loading and the Steinberg-Guinan constitutive model are used in the linear analysis, the analytic results are in close agreement with experiments quantitatively, which indicates that the method in this paper is applicable to the Rayleigh-Taylor instability in aluminum and vanadium metal materials under high pressure and high strain rate. From these linear analyses, we find that the constitutive models and the loading process are of crucial importance in the linear analysis of the Rayleigh-Taylor instability in metal material, and a better understanding of the Rayleigh-Taylor instability in metals is gained. These results will serve as important references for evolving high-pressure, high-strain-rate experiments and numerical simulations.

Mechanism of the Large Surface Deformation Caused by Rayleigh-Taylor Instability at Large Atwood Number

Studying the dynamical behaviors of the liquid spike formed by Rayleigh-Taylor instability is important to understand the mechanisms of liquid atomization process. In this paper, based on the information on the velocity and pressure fields obtained by the coupled-level-set and volume-of- fluid (CLSVOF) method, we describe how a freed spike can be formed from a liquid layer under falling at a large Atwood number. At the initial stage when the surface deformation is small, the amplitude of the surface deformation increases exponentially. Nonlinear effect becomes dominant when the amplitude of the surface deformation is comparable with the surface wavelength (~0.1λ). The maximum pressure point, which results from the impinging flow at the spike base, is essential to generate a liquid spike. The spike region above the maximum pressure point is dynamically free from the bulk liquid layer below that point. As the descending of the maximum pressure point, the liquid elements enter the freed region and elongate the liquid spike to a finger-like shape.

Effect of surface tension and viscosity on bubble growth of single mode Rayleigh-Taylor instability

Based on the Zufiria theoretical model, a new model regarding the asymptotic bubble velocity for the Rayleigh-Taylor （RT） instability is presented by use of the complex velocity potential proposed by Sohn. The proposed model is an extension of the ordinary Zufiria model and can deal with non-ideal fluids. With the control variable method, the effect of the viscosity and surface tension on the bubble growth rate of the RT instability is studied. The result is consistent with Cao＇s result if we only consider the viscous effect and with Xia＇s result if we only consider the surface tension effect. The asymptotic bubble velocity predicted by the Zufiria model is smaller than that predicted by the Layzer model, and the result from the Zufiria model is much closer to White＇s experimental data.

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.

Surface Expressions of Rayleigh-Taylor Instability in Continental Interiors

Two-dimensional thermal-mechanical numerical models show that Rayleigh-Taylor-type （RT） gravitational removal of high-density lithosphere may produce significant surface deformation （vertical deflection 〉1000 m） in the interior of a continental plate.A reasonable range of crustal strengths and thicknesses,representing a variation from a stable continental interior to a hot orogen with a thick crust,is examined to study crustal deformation and the surface deflection in response to an RT instability.In general,three types of surface deflection are observed during the RT drip event：（1） subsidence and negative topography; （2） uplift and positive topography; （3） subsidence followed by uplift and inverted topography.One key factor that determines the surface expression is the crustal thickness.Models with a thin crust mainly show subsidence and develop a basin.In the thick crust models,surface expressions are more variable,depending on the crustal strength and depth of highdensity anomaly.With weak crust and a deep high-density anomaly,the RT drip is decoupled from the overlying crust,and the surface exhibits uplift or little deflection,as the RT drip induces contraction and thickening of the overlying crust.In contrast,with a strong crust and shallow anomaly,the surface is more strongly coupled with the drip and undergoes subsidence,followed by uplift.

Effects of compressibility on the Rayleigh-Taylor instability in Z-pinch implosions

The effects of compressibility on the Rayleigh-Taylor instability in Z-pinch implosion plasmas are investigated by means of simple slab geometry.The linear mode equation,which includes main steady-state quantities and their gradients,is derived.Numerical solutions are presented.The incompressible fluid result is also obtained.These results indicate that the linear growth rate of the Rayleigh-Taylor instability for the compressible magnetohydrodynamic fluid is far larger than one in the incompressible situation.Therefore,the compressible systems are all more unstable than the incompressible ones.

Nonlinear Evolution of Jet-Like Spikes from the Single-Mode Ablative Rayleigh-Taylor Instability with Preheating

In this research, the nonlinear evolution of jet-like spikes in the single-mode ablative Rayleigh-Taylor instability （ARTI） in the presence of preheating, is studied numerically. It is demonstrated that the preheating plays an essential role in the formation of jet-like spikes in the nonlinear ARTI. The evolution of jet-like spikes in the ARTI with preheating consists of three stages with distinctly different distinguishing features. In the early stage, the preheating contributes to significantly increase the density-gradient scale length and broaden the velocity profile of the ablation surface, where the former can reduce the linear growth of the ARTI and mitigate the growth of its harmonics. In the middle stage, the ablative Kelvin-Helmholtz instability is dramatically suppressed due to the ablation effects. In the late stage, the jet＇s length （i.e. bubble-spike amplitude） is further increased by the bubble acceleration in the highly nonlinear ARTI, resulting eventually in the formation of jet-like spikes.

Rayleigh-Taylor instability of multi-fluid layers in cylindrical geometry

Rayleigh-Taylor instability of three fluid layers with two interfaces in cylindrical geometry is investigated analytically. The growth rates and the amplitudes of perturbation on the two interfaces are obtained. The feedback factor from outer to inner interface is larger than that from inner to outer interface under the same conditions. The growth rate on the initially unstable interface is larger than the corresponding result in planar geometry for low mode perturbation. The two interfaces are decoupled for a larger mode number perturbation. The dependencies of the amplitudes of perturbation on different initial conditions are analyzed. The negative feedback effect from initially stable interface to another unstable interface is observed. In the limit of infinity inner radius and finite shell thickness, the results in planar geometry are recovered.

Coupling between velocity and interface perturbations in cylindrical Rayleigh–Taylor instability

Rayleigh–Taylor instability（RTI） in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear（WN） model. When the initial velocity perturbation is comparable to the interface perturbation, the coupling between them plays a significant role. The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small. The effects of the mode number on the first three harmonics are discussed respectively. The low-mode number perturbation leads to large amplitudes of RTI growth. The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly. When the mode number of the perturbation is large enough,the WN results in planar geometry are recovered.

Viscous Rayleigh-Taylor instability with and without diffusion effect

The approximate but analytical solution of the viscous Rayleigh-Taylor insta- bility （RTI） has been widely used recently in theoretical and numerical investigations due to its clarity. In this paper, a modified analytical solution of the growth rate for the viscous RTI of incompressible fluids is obtained based on an approximate method. Its accuracy is verified numerically to be significantly improved in comparison with the previous one in the whole wave number range for different viscosity ratios and Atwood numbers. Fur- thermore, this solution is expanded for viscous RTI including the concentration-diffusion effect.

Analytical model for Rayleigh-Taylor instability in conical target conduction region

This work builds an isobaric steady-state fluid analytical-physical model of the plasma conduction region in a conical target. The hydrodynamic instability in the double-cone ignition scheme^([21]) for inertial confinement fusion(ICF) proposed by Zhang is studied with the built model. With this idealized model, the relevant parameters, such as density, temperature,and length of the plasma in the conduction region of the conical target under long-pulse conditions are given. The solution of the proposed analytical model dovetails with the trend of the numerical simulation. The model and results in this paper are beneficial for discussing how to attenuate Rayleigh-Taylor instability in ICF processes with conical and spherical targets.

Revisiting the Effects of Compressibility on the Rayleigh-Taylor Instability

The effects of compressibility on the Rayleigh-Taylor instability （RTI） are investigated. It is shown that the controversy over compressibility effects in the previous studies is due to improper comparison, in which the density varying effect obscures the real role of compressibility. After eliminating the density varying effect, it is found that the compressibility destabilizes RTI in both the cases of constant density and exponentially varying density when M 《1. This destabilizing effect is more important at smaller values of the Atwood number AT or greater values of gravity g, and the increment in the growth rate produced by compressibility depends inversely on the pressure p or the ratio of specific heat F.

Linear Rayleigh-Taylor instability analysis of double-shell Kidder's self-similar implosion solution

This paper generalizes the single-shell Kidder＇s self-similar solution to the double-shell one with a discontinuity in density across the interface. An isentropic implosion model is constructed to study the Rayleigh-Taylor instability for the implosion compression. A Godunov-type method in the Lagrangian coordinates is used to compute the one-dimensional Euler equation with the initial and boundary conditions for the double-shell Kidder＇s self-similar solution in spherical geometry. Numerical results are obtained to validate the double-shell implosion model. By programming and using the linear perturbation codes, a linear stability analysis on the Rayleigh-Taylor instability for the double-shell isentropic implosion model is performed. It is found that, when the initial perturbation is concentrated much closer to the interface of the two shells, or when the spherical wave number becomes much smaller, the modal radius of the interface grows much faster, i.e., more unstable. In addition, from the spatial point of view for the compressibility effect on the perturbation evolution, the compressibility of the outer shell has a destabilization effect on the Rayleigh-Taylor instability, while the compressibility of the inner shell has a stabilization effect.

Rayleigh-Taylor Instability in Magnetized Plasma

The Rayleigh-Taylor instability in stratified plasma has been investigated in the presence of combined effect of horizontal and vertical magnetic field. The linear growth rate has been derived for the case where plasma with exponential density distribution is confined between two rigid planes by solving the linear MHD equations into normal mode. Some special cases have been particularized to explain the roles the variables of the problem play;numerical solutions have been made and some stability diagrams are plotted and discussed. The results show that, the growth rate depends on the horizontal and vertical components of magnetic field and also depends on the parameter λ*=λLD ?(λ is constant and LD is the density-scale length). The maximum instability happens at λ*=-0.5 and to get more stability model we select?λ* such that it is different than?λ*=-0.5. The vertical magnetic field component have a greater effect than the horizontal magnetic field component in the case of large wavelength, while in the case of short wavelength, the horizontal magnetic field components have greater effect than the vertical magnetic field component.

Rayleigh-Taylor Instability of Magnetized Plasma through Darcy Porous Medium

Effects of horizontal and vertical magnetic field components on the Rayleigh-Taylor instability of stratified incompressible plasmas layer of variable density through Darcy porous medium are studied. The basic magnetohydrodynamic (MHD) set of equations has been constructed and linearized. Then the linear normalized growth rate is obtained analytically as a function of the physical parameters of the system considered. Numerical calculations have been performed to see the effects of various parameters on the normalized growth rate of Rayleigh-Taylor instability.(For more information,please refer to the PDF.)

External Magnetic Field Effects on the Rayleigh-Taylor Instability in an Inhomogeneous Rotating Quantum Plasma

The effects of external magnetic field effects on the Rayleigh-Taylor instability in an inhomogeneous stratified quantum plasma rotating uniformly are investigated. The external magnetic field is considered in both horizontal and vertical direction. The linear growth rate is derived for the case where a plasma with exponential density distribution is confined between two rigid planes at z=0 and z=h, by solving the linear QMHD equations into normal mode. Some special cases are particularized to explain the roles that play the variables of the problem. The results show that, the presence of both external horizontal and vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration. The maximum stability will happen in the case of wave number parallels to or in the same direction of external horizontal magnetic field.