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.

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.

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.

Rayleigh–Taylor instability of viscoelastic self-rewetting film flowing down a temperature-controlled inclined substrate

Rayleigh–Taylor(RT) instability of gravity-driven viscoelastic self-rewetting film flowing under an inclined substrate uniformly heated or cooled is considered. The surface tension of self-rewetting film is considered as a quadratic function of temperature. The long wave hypothesis is used to derive a nonlinear free surface evolution equation of the thin viscoelastic film. Linear stability analysis shows that for a prescribed the viscoelastic coefficient, substrate cooling products instability,while substrate heating remains stability. Furthermore, we analyze the influence of viscoelastic coefficient on RT instability. Results show that the viscoelastic coefficient reinforces the RT instability whether the substrate is heated or cooled.Moreover, we use the line method to numerically simulate the nonlinear evolution equation and systematically examine the space-time variation of the film free surface. The numerical results illustrate that increasing the viscoelastic coefficient can enhance the disturbance amplitude and wave frequency. This means that the viscoelastic coefficient makes the system unstable, which is consistent with result of the linear stability analysis. In addition, the oscillation tends to accumulate downstream of the inclined substrate when the evolution time is long enough. Finally, the variation of film thickness with related parameters for different viscoelastic coefficients is investigated.

Effect of initial phase on the Rayleigh–Taylor instability of a finite-thickness fluid shell

Rayleigh–Taylor instability(RTI) of finite-thickness shell plays an important role in deep understanding the characteristics of shell deformation and material mixing. The RTI of a finite-thickness fluid layer is studied analytically considering an arbitrary perturbation phase difference on the two interfaces of the shell. The third-order weakly nonlinear(WN) solutions for RTI are derived. It is found the main feature(bubble-spike structure) of the interface is not affected by phase difference. However, the positions of bubble and spike are sensitive to the initial phase difference, especially for a thin shell(kd < 1), which will be detrimental to the integrity of the shell. Furthermore, the larger phase difference results in much more serious RTI growth, significant shell deformation can be obtained in the WN stage for perturbations with large phase difference. Therefore, it should be considered in applications where the interface coupling and perturbation phase effects are important, such as inertial confinement fusion.

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.

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.

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.

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.

Spiky Development at the Interface in Rayleigh-Taylor Instability: Layzer Approximation with Second Harmonic

Layzer’s approximation method for investigation of two fluid interface structures associated with Rayleigh Taylor instability for arbitrary Atwood number is extended with the inclusion of second harmonic mode leaving out the zeroth harmonic one. The modification makes the fluid velocities vanish at infinity and leads to avoidance of the need to make the unphysical assumption of the existence of a time dependent source at infinity. The present analysis shows that for an initial interface perturbation with curvature exceeding , where A is the Atwood number there occurs an almost free fall of the spike with continuously increasing sharpening as it falls. The curvature at the tip of the spike also increases with Atwood number. Certain initial condition may also result in occurrence of finite time singularity as found in case of conformal mapping technique used earlier. However bubble growth rate is not appreciably affected.

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.

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.

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.

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.

Quantum Effects on the Rayleigh-Taylor Instability of Viscoelastic Plasma Model through a Porous Medium

The stability of stratified of incompressible, viscoelastic plasma through a porous medium in the presence of the quantum mechanism is considered. The dispersion relation is obtained using the normal mode technique. The behavior of growth rate with respect to the quantum effect, strain retardation time and stress relaxation time are examined in the presence of porosity of the porous medium, the medium permeability, kinematic viscosity. It is shown that, the presence of quantum term stabilizes a certain wave number band, whereas the system is unstable for all wave numbers in the absence of quantum term. The considered parameters beside the quantum term will bring about more stability on the considered system.

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.