Growth Of Rayleigh-Taylor Instability Research Articles

Rayleigh-Taylor instability at spherical interfaces of incompressible fluids**Project supported by the National Natural Science Foundation of China (Grant Nos. 11275031, 11475034, 11575033, 11574390, and 11274026) and the National Basic Research Program of China (Grant Nos. 2013CB834100 and 2013CBA01504).

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.

Multiple eigenmodes of the Rayleigh-Taylor instability observed for a fluid interface with smoothly varying density.

In this article, multiple eigen-systems including linear growth rates and eigen-functions have been discovered for the Rayleigh-Taylor instability (RTI) by numerically solving the Sturm-Liouville eigen-value problem in the case of two-dimensional plane geometry. The system called the first mode has the maximal linear growth rate and is just extensively studied in literature. Higher modes have smaller eigen-values, but possess multi-peak eigen-functions which bring on multiple pairs of vortices in the vorticity field. A general fitting expression for the first four eigen-modes is presented. Direct numerical simulations show that high modes lead to appearances of multi-layered spike-bubble pairs, and lots of secondary spikes and bubbles are also generated due to the interactions between internal spikes and bubbles. The present work has potential applications in many research and engineering areas, e.g., in reducing the RTI growth during capsule implosions in inertial confinement fusion.

Flow Stress of beryllium: Attempt for a Bayesian Crossed-data Analysis from Hopkinson Bars to Rayleigh-Taylor Instabilities

In this paper, we demonstrate by a Bayesian approach the incapacity of the Preston-Tonks-Wallace (PTW) strength model to represent, with the same set of parameters, the flow stress of beryllium in both moder-ate and highly dynamic experiments, and suggest hypotheses explaining that limitation. Usual plasticity models such as Johnson-Cook (JC) and PTW are mostly adjusted onto quasi-static and dynamic uni-axial compression data acquired thanks to compression machines and split Hopkinson pressure bars. Nonetheless, they may be used beyond the range of mechanical loading in which they have been fitted. This is the case of the simulations of solid Rayleigh-Taylor instabilities (RTI) driven by high explosives. A recent work of Henry de Frahan et al. noticed the inability of various plasticity models to stand for the growth of beryllium RTI. Amongst them, the PTW model has been particularly examined through four different sets of parameters, each of them largely un-derestimates the growth of the experimental instability. Thus, this work is an attempt, regarding the plastic flow modeling of beryllium, to conciliate uni-axial compression tests (CT) and RTI by means of a crossed Bayesian analysis.

Rayleigh-Taylor instability in accelerated elastic-solid slabs.

We develop the linear theory for the asymptotic growth of the incompressible Rayleigh-Taylor instability of an accelerated solid slab of density ρ_{2}, shear modulus G, and thickness h, placed over a semi-infinite ideal fluid of density ρ_{1}<ρ_{2}. It extends previous results for Atwood number A_{T}=1 [B. J. Plohr and D. H. Sharp, Z. Angew. Math. Phys. 49, 786 (1998)ZAMPA80044-227510.1007/s000330050121] to arbitrary values of A_{T} and unveil the singular feature of an instability threshold below which the slab is stable for any perturbation wavelength. As a consequence, an accelerated elastic-solid slab is stable if ρ_{2}gh/G≤2(1-A_{T})/A_{T}.

Investigating the strength of materials at very high strain rates using electro-magnetically driven expanding cylinders

Most metallic materials exhibit a noticeable strain rate sensitivity in the range of 103–104 s−1 due to changes in dislocation dynamics in this regime. For applications that are sensitive to the material behavior at very high strain rates, there is a true need to measure the material strength at strain rates exceeding 104 s−1 and calibrate a reliable model that accounts for their strain rate hardening.Various experimental methods are reported in the literature for measuring strength at very high strain rates such as explosively driven expanding ring tests (ERT), various plate impact techniques and Rayleigh-Taylor instability growth tests. While the attainable strain rates can be very high, the interpretation of these tests can be somewhat controversial, as coupled effects such as pressure hardening and thermal softening, together with the effects of high strain rates, do not enable a unique determination of the contribution of the high strain rate to the actual measured strength.We present here a new methodology to measure the strength of materials at very high strain rates, up to 7.5⋅104 s−1, using magnetically driven expanding cylinder experiments. We use a pulse current generator (PCG) to apply magnetic forces on hollow cylindrical specimens and measure the expanding motion using velocity interferometery. To investigate the dynamic behavior of the specimens and their strength, we use numerical simulations. 2D hydrodynamic simulations were conducted for the design of the specimens, and 1D MHD simulations for simulating the actual tests. In this work, we present results for nine EM driven OFHC cylinders, reaching strain rates up to 7.5⋅104 s−1. We report a significant strain rate hardening for the OFHC copper and provide a calibrated Modified Johnson Cook (MJC) constitutive model for our data in the regime ranging from 103 s−1 (Kolsky bar tests) up to 105 s−1, from the PCG tests. It is believed that the methodology that is presented here will open the way for very high strain-rate characterization of metallic materials.

The non-linear growth of the magnetic Rayleigh-Taylor instability

This work examines the effect of the embedded magnetic field strength on the non-linear development of the magnetic Rayleigh-Taylor Instability (RTI) (with a field-aligned interface) in an ideal gas close to the incompressible limit in three dimensions. Numerical experiments are conducted in a domain sufficiently large so as to allow the predicted critical modes to develop in a physically realistic manner. The ratio between gravity, which drives the instability in this case (as well as in several of the corresponding observations), and magnetic field strength is taken up to a ratio which accurately reflects that of observed astrophysical plasma, in order to allow comparison between the results of the simulations and the observational data which served as inspiration for this work. This study finds reduced non-linear growth of the rising bubbles of the RTI for stronger magnetic fields, and that this is directly due to the change in magnetic field strength, rather than the indirect effect of altering characteristic length scales with respect to domain size. By examining the growth of the falling spikes, the growth rate appears to be enhanced for the strongest magnetic field strengths, suggesting that rather than affecting the development of the system as a whole, increased magnetic field strengths in fact introduce an asymmetry to the system. Further investigation of this effect also revealed that the greater this asymmetry, the less efficiently the gravitational energy is released. By better understanding the under-studied regime of such a major phenomenon in astrophysics, deeper explanations for observations may be sought, and this work illustrates that the strength of magnetic fields in astrophysical plasmas influences observed RTI in subtle and complex ways.

Linear Growth of Rayleigh–Taylor Instability of Two Finite-Thickness Fluid Layers**Supported by the National Natural Science Foundation of China under Grant Nos 11275031, 11475034, 11575033 and 11274026, and the National Basic Research Program of China under Grant No 2013CB834100.

The linear growth of Rayleigh–Taylor instability (RTI) of two superimposed finite-thickness fluids in a gravitational field is investigated analytically. Coupling evolution equations for perturbation on the upper, middle and lower interfaces of the two stratified fluids are derived. The growth rate of the RTI and the evolution of the amplitudes of perturbation on the three interfaces are obtained by solving the coupling equations. It is found that the finite-thickness fluids reduce the growth rate of perturbation on the middle interface. However, the finite-thickness effect plays an important role in perturbation growth even for the thin layers which will cause more severe RTI growth. Finally, the dependence of the interface position under different initial conditions are discussed in some detail.

Solar effect on the Rayleigh-Taylor instability growth rate as simulated by the NCAR TIEGCM

The TIEGCM (Thermosphere Ionosphere Electrodynamics General Circulation Model) is used to investigate the solar effect on the equatorial ionospheric Rayleigh-Taylor (R-T) instability growth rate, which is responsible for the occurrence of the plasma bubbles. The R-T growth rate is calculated for the solar maximum year 2003 and minimum 2009. The growth rate is strongly dependent on the solar activity. During solar maximum, the pre-reversal enhancement is much stronger leading to higher R-T growth rate. The R-T growth rates from the TIEGCM follow the same solar dependence as the observed occurrence of equatorial plasma bubbles by DMSP satellites. The R-T growth rate also enhances when the day/night terminator is parallel to the magnetic field line near the equator. The R-T growth rate does not correlate well with the solar F10.7 index on a short time scale (~10 days) because the field-line integrated electron content gradient cancels out the positive correlation between the vertical ion drift with the F10.7 index. The TIEGCM result shows the importance of the electron content gradient to the R-T growth rate and the plasma bubble occurrence. The bubble occurrence rates were estimated based on the vertical ion drift simulation results.

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.

Controlling Rayleigh-Taylor Instabilities in Magnetically Driven Solid Metal Shells by Means of a Dynamic Screw Pinch.

Magnetically driven implosions of solid metal shells are an effective vehicle to compress materials to extreme pressures and densities. Rayleigh-Taylor instabilities (RTI) are ubiquitous, yet typically undesired features in all such experiments where solid materials are rapidly accelerated to high velocities. In cylindrical shells ("liners"), the magnetic field driving the implosion can exacerbate the RTI. We suggest an approach to implode solid metal liners enabling a remarkable reduction in the growth of magnetized RTI (MRTI) by employing a magnetic drive with a tilted, dynamic polarization, forming a dynamic screw pinch. Our calculations, based on a self-consistent analytic framework, demonstrate that the cumulative growth of the most deleterious MRTI modes may be reduced by as much as 1 to 2 orders of magnitude. One key application of this technique is to generate increasingly stable, higher-performance implosions of solid metal liners to achieve fusion [M. R. Gomez etal., Phys. Rev. Lett. 113, 155003 (2014)]. We weigh the potentially dramatic benefits of the solid liner dynamic screw pinch against the experimental tradeoffs required to achieve the desired drive field history and identify promising designs for future experimental and computational studies.

Control of fuel target implosion non-uniformity in heavy ion inertial fusion

AbstractIn inertial fusion, one of scientific issues is to reduce an implosion non-uniformity of a spherical fuel target. The implosion non-uniformity is caused by several factors, including the driver beam illumination non-uniformity, the Rayleigh–Taylor instability (RTI) growth, etc. In this paper, we propose a new control method to reduce the implosion non-uniformity; the oscillating implosion acceleration δg(t) is created by pulsating and dephasing heavy-ion beams (HIBs) in heavy-ion inertial fusion (HIF). The δg(t) would reduce the RTI growth effectively. The original concept of the non-uniformity control in inertial fusion was proposed in [Laser Part. Beams (1993) 11, 757–768]. In this paper, it was found that the pulsating and dephasing HIBs illumination provide successfully the controlled δg(t) and that δg(t) induced by the pulsating HIBs reduces well the implosion non-uniformity. Consequently the pulsating HIBs improve a pellet gain remarkably in HIF.

Application of software complex turbo problem solver to rayleigh-taylor instability modeling

The dynamic processes which take place during high-speed impact of two metal plates with different densities are investigated using three-dimensional numerical simulations. It is shown that as a result of the impact the Rayleigh-Taylor instability forms which leads to the formation of three-dimensional ring-shaped structures on the surface of the metal with smaller density. The comparative analysis of the metals interface deformation process with the use of different equations of state is performed. The numerical study is carried out by means of special software complex Turbo Problem Solver developed by the authors. The software complex Turbo Problem Solver implements generalized approach to the construction of hydrodynamic code for various computational fluid dynamics problems. Turbo Problem Solver provides several numerical schemes and software blocks to set initial, boundary conditions and mass forces. The solution of test problem about Rayleigh-Taylor instability growth and development for the case of very rapid density growth is also presented.

A new data processing technique for Rayleigh-Taylor instability growth experiments

Typical face-on experiments for Rayleigh-Taylor instability study involve the time-resolved radiography of an accelerated foil with line-of-sight of the radiography along the direction of motion. The usual method which derives perturbation amplitudes from the face-on images reverses the actual image transmission procedure, so the obtained results will have a large error in the case of large optical depth. In order to improve the accuracy of data processing, a new data processing technique has been developed to process the face-on images. This technique based on convolution theorem, refined solutions of optical depth can be achieved by solving equations. Furthermore, we discuss both techniques for image processing, including the influence of modulation transfer function of imaging system and the backlighter spatial profile. Besides, we use the two methods to the process the experimental results in Shenguang-II laser facility and the comparison shows that the new method effectively improve the accuracy of data processing.

Uniform fuel target implosion in heavy ion inertial fusion

For a steady operation of a fusion power plant the target implosion should be robust against the implosion non-uniformities. In this paper the non-uniformity mitigation mechanisms in the heavy ion beam (HIB) illumination are discussed in heavy ion inertial fusion (HIF). A density valley appears in the energy absorber, and the large-scale density valley also works as a radiation energy confinement layer, which contributes to the radiation energy smoothing for the HIB illumination non-uniformity. The large density-gradient scale, which is typically ∼500μm in HIF targets, also contributes to a reduction of the Rayleigh- Taylor instability growth rate. In HIF a wobbling HIBs illumination would also reduce the Rayleigh-Taylor instability growth and to realize a uniform implosion.

A scheme for reducing deceleration-phase Rayleigh–Taylor growth in inertial confinement fusion implosions

It is demonstrated that the growth of acceleration-phase instabilities in inertial confinement fusion implosions can be controlled, especially in the high-foot implosions [O. A. Hurricane et al., Phys. Plasmas 21, 056314 (2014)] on the National Ignition Facility. However, the excessive growth of the deceleration-phase instabilities can still destroy the hot spot ignition. A scheme is proposed to retard the deceleration-phase Rayleigh–Taylor instability growth by shock collision near the waist of the inner shell surface. Two-dimensional radiation hydrodynamic simulations confirm the improved deceleration-phase hot spot stability properties without sacrificing the fuel compression.

Nighttime thermospheric meridional winds as inferred from ionosonde parameters over Indian region and their plausible effects on plasma irregularities

In this paper, we present nighttime thermospheric meridional winds at Indian low latitude station namely Hyderabad during March–May 2013 derived using (a) h’F method and (b) hpF2 method based on ionosondes. The estimation of meridional winds using h’F method employs the basic principle that the vertical drift at magnetic equator is purely due to ExB drift, while for a station slightly away from magnetic equator, meridional wind also contributes for the vertical drift in addition to diffusion along the field lines. Assuming the EXB drifts are the same at both the locations, the vertical drift contribution is subtracted from the equatorial vertical drifts and then meridional winds are derived, whereas in hpF2 method, winds are derived using the SERVO theory. The winds so derived are compared with HWM07 wind model. The comparison suggests that magnitude of winds derived using h’F method are in better agreement with HWM07 model than hpF2 derived winds where their polarities are better comparable to HWM07 model than hpF2 method. The poor agreement of hpF2 method could be due to uncertainties involved in estimating various ionospheric parameters. Also the winds derived using h’F method showed signatures of the well known phenomenon of Midnight Temperature Maximum (MTM). Based on these results, we suggest that h’F method is better suited for meridional wind estimates over low latitudes than hpF2 method. Accordingly, we further investigated the role of thermospheric meridional winds in equatorial spread F (ESF) occurrence. Our results suggest that equatorward winds along with post sunset height increase could enhance the Rayleigh Taylor (RT) instability growth rate and thereby leading to the generation of ESF/scintillations. The Superposed Epoch Analysis (SEA) technique has been applied to understand the general trend of h’F and meridional winds around the ESF onset time. The study showed reduction in poleward winds, half an hour prior to the onset of ESF. Hence indicating the role of meridional winds in the generation of plasma irregularities/scintillations in addition to post sunset height rise.

Experimental demonstration of laser imprint reduction using underdense foams

Reducing the detrimental effect of the Rayleigh-Taylor (RT) instability on the target performance is a critical challenge. In this purpose, the use of targets coated with low density foams is a promising approach to reduce the laser imprint. This article presents results of ablative RT instability growth measurements, performed on the OMEGA laser facility in direct-drive for plastic foils coated with underdense foams. The laser beam smoothing is explained by the parametric instabilities developing in the foam and reducing the laser imprint on the plastic (CH) foil. The initial perturbation pre-imposed by the means of a specific phase plate was shown to be smoothed using different foam characteristics. Numerical simulations of the laser beam smoothing in the foam and of the RT growth are performed with a suite of paraxial electromagnetic and radiation hydrodynamic codes. They confirmed the foam smoothing effect in the experimental conditions.

Hydrodynamic growth and mix experiments at National Ignition Facility

Hydrodynamic growth and its effects on implosion performance and mix were studied at the National Ignition Facility (NIF). Spherical shells with pre-imposed 2D modulations were used to measure Rayleigh-Taylor (RT) instability growth in the acceleration phase of implosions using in-flight x-ray radiography. In addition, implosion performance and mix have been studied at peak compression using plastic shells filled with tritium gas and imbedding localized CD diagnostic layer in various locations in the ablator. Neutron yield and ion temperature of the DT fusion reactions were used as a measure of shell-gas mix, while neutron yield of the TT fusion reaction was used as a measure of implosion performance. The results have indicated that the low-mode hydrodynamic instabilities due to surface roughness were the primary culprits to yield degradation, with atomic ablator-gas mix playing a secondary role.

Stabilization of Rayleigh–Taylor instability in the presence of viscosity and compressibility: A critical analysis

The stabilization of the Rayleigh–Taylor instability growth rate due to the combined effect of viscosity and compressibility has been studied. A detailed explanation of the observed results has been made from theoretical point of view. The numerical results have been compared qualitatively with those of Plesset and Whipple [Phys. Fluids 17, 1 (1974)] and Bernstein and Book [Phys. Fluids 26, 453 (1983)].

Rayleigh-Taylor instability in non-uniform magnetized rotating strongly coupled viscoelastic fluid

The Rayleigh-Taylor instability (RTI) in an incompressible strongly coupled viscoelastic fluid is investigated considering the effects of inhomogeneous magnetic field, density gradient, and uniform rotation. The generalized hydrodynamic equations have been formulated, and linear dispersion relation is derived taking appropriate density and magnetic field profiles for the considered system. The gravity induced stable and unstable configurations of RTI are analyzed in hydrodynamic and kinetic limits. In the kinetic limit, shear wave modified dispersion relation and the condition of RTI are derived in terms of magnetic-viscoelastic Mach number and viscoelastic Froude number. The criteria of RTI and critical wavenumber for the growth of RTI to be unstable are estimated numerically for white dwarf and inertial confinement fusion target. It is observed that magnetic field, rotation, and viscoelastic effects play a significant role in the suppression of RTI in these systems. The stabilizing influence of magnetic field, rotation, and magnetic-viscoelastic Mach number while the destabilizing influence of viscoelastic Froude on the growth rate of RTI number is observed graphically. The growth rate of RTI decreases faster in kinetic limit as compared to the hydrodynamic limit.