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.

Are cyclones in Jupiter's polar regions modulated by the radially directional Rayleigh–Taylor instability?

The persistence and symmetry of cyclones around the poles of Jupiter are unknown.In the present investigation,inspired by cyclones at the South Pole of the Earth,we propose a mechanism that provides an explanation for this problem.The negative temperature gradient with respect to latitude may play an important role here.This temperature gradient is induced by solar radiation because of the small axial inclination of Jupiter.Our numerical simulations suggest that cyclones in the polar regions of Jupiter may be modulated or controlled by the radially directional Rayleigh–Taylor instability,driven by centrifugal force and the negative temperature gradient along the latitude.

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.

Numerical study on magneto-Rayleigh–Taylor instabilities for thin liner implosions on the primary test stand facility

The thin aluminum liners with an aspect ratio R/?r 1 have been imploded on the primary test stand(PTS) facility,where R is the outer radius of the liner and ?r is the thickness. The x-ray self-emission images present azimuthally correlated perturbations in the liner implosions. The experiments show that at-10 ns before the stagnation, the wavelengths of perturbation are about 0.93 mm and 1.67 mm for the small-radius and large-radius liners, respectively. We have utilized the resistive magnetohydrodynamic code PLUTO to study the development of magneto-Rayleigh–Taylor(MRT) instabilities under experimental conditions. The calculated perturbation amplitudes are consistent with the experimental observations very well. We have found that both mode coupling and long implosion distance are responsible for the more developed instabilities in the large-radius liner implosions.

Interface coupling effects of weakly nonlinear Rayleigh–Taylor instability with double interfaces

Taking the Rayleigh–Taylor instability with double interfaces as the research object,the interface coupling effects in the weakly nonlinear regime are studied numerically.The variation of Atwood numbers on the two interfaces and the variation of the thickness between them are taken into consideration.It is shown that,when the Atwood number on the lower interface is small,the amplitude of perturbation growth on the lower interface is positively related with the Atwood number on the upper interface.However,it is negatively related when the Atwood number on the lower interface is large.The above phenomenon is quantitatively studied using an analytical formula and the underlying physical mechanism is presented.

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.

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.

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.

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.

Cylindrical effects in weakly nonlinear Rayleigh Taylor instability

The classical Rayleigh–Taylor instability（RTI） at the interface between two variable density fluids in the cylindrical geometry is explicitly investigated by the formal perturbation method up to the second order. Two styles of RTI, convergent（i.e., gravity pointing inward） and divergent（i.e., gravity pointing outwards） configurations, compared with RTI in Cartesian geometry, are taken into account. Our explicit results show that the interface function in the cylindrical geometry consists of two parts： oscillatory part similar to the result of the Cartesian geometry, and non-oscillatory one contributing nothing to the result of the Cartesian geometry. The velocity resulting only from the non-oscillatory term is followed with interest in this paper. It is found that both the convergent and the divergent configurations have the same zeroth-order velocity, whose magnitude increases with the Atwood number, while decreases with the initial radius of the interface or mode number. The occurrence of non-oscillation terms is an essential character of the RTI in the cylindrical geometry different from Cartesian one.

Weakly Nonlinear Rayleigh–Taylor Instability in Cylindrically Convergent Geometry

The Rayleigh–Taylor instability（RTI） in cylindrical geometry is investigated analytically through a second-order weakly nonlinear（WN） theory considering the Bell–Plesset（BP） effect. The governing equations for the combined perturbation growth are derived. The WN solutions for an exponentially convergent cylinder are obtained. It is found that the BP and RTI growths are strongly coupled, which results in the bubble-spike asymmetric structure in the WN stage. The large Atwood number leads to the large deformation of the convergent interface. The amplitude of the spike grows faster than that of the bubble especially for large mode number m and large Atwood number A. The averaged interface radius is small for large mode number perturbation due to the mode-coupling effect.

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.

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 at spherical interfaces of incompressible fluids

Rayleigh–Taylor instability（RTI） of three incompressible fluids with two interfaces in spherical geometry is derived analytically. The growth rate on the two interfaces and the perturbation feedthrough coefficients between two spherical interfaces are derived. For low-mode perturbation, the feedthrough effect from outer interface to inner interface is much more severe than the corresponding planar case, while the feedback from inner interface to the outer interface is smaller than that in planar geometry. The low-mode perturbations lead to the pronounced RTI growth on the inner interface of a spherical shell that are larger than the cylindrical and planar results. It is the low-mode perturbation that results in the difference between the RTI growth in spherical and cylindrical geometry. When the mode number of the perturbation is large enough, the results in cylindrical geometry are recovered.

RAYLEIGH–TAYLOR INSTABILITY FOR COMPRESSIBLE ROTATING FLOWS

In this paper, we investigate the Rayleigh-Taylor instability problem for two com- pressible, immiscible, inviscid flows rotating with a constant angular velocity, and evolving with a free interface in the presence of a uniform gravitational field. First we construct the Rayleigh-Taylor steady-state solutions with a denser fluid lying above the free interface with the second fluid, then we turn to an analysis of the equations obtained from linearization around such a steady state. In the presence of uniform rotation, there is no natural varia- tional framework for constructing growing mode solutions to the linearized problem. Using the general method of studying a family of modified variational problems introduced in [1], we construct normal mode solutions that grow exponentially in time with rate like et√c｜ε｜^-1^[1],where ζ is the spatial frequency of the normal mode and the constant c depends on some physical parameters of the two layer fluids. A Fourier synthesis of these normal mode solu-tions allows us to construct solutions that grow arbitrarily quickly in the Sobolev space Hk, and leads to an ill-posedness result for the linearized problem. Moreover, from the analysis we see that rotation diminishes the growth of instability. Using the pathological solutions, we then demonstrate the ill-posedness for the original non-linear problem in some sense.

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.

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.

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.