Linear Rayleigh-Taylor Instability Research Articles

Improved analytic modeling of the linear Rayleigh–Taylor instability with plasma transport

The Rayleigh–Taylor (R–T) instability with transport effects has long been studied analytically in the neutral fluid regime. How this picture may differ in plasmas has been given less consideration, however. Leveraging previous numerical simulations with plasma viscosity and diffusion of R–T at a binary plasma interface, we show how plasma transport and kinetic effects alter the linear R–T dispersion relation. Our insight informs a much improved analytical dispersion relation, which better matches the simulation data than previously established models. Additionally, we demonstrate the importance of employing asymptotically correct viscosity coefficients in fluid codes for accurately capturing plasma R–T growth.

Multi-instrumental analysis of the day-to-day variability of equatorial plasma bubbles

This paper presents a multi-instrument observational analysis of the equatorial plasma bubbles (EPBs) variation over the American sector during a geomagnetically quiet time period of 07–10 December 2019. The day-to-day variability of EPBs and their underlying drivers are investigated through coordinately utilizing the Global-scale Observations of Limb and Disk (GOLD) ultraviolet images, the Ionospheric Connection Explorer (ICON) in-situ and remote sensing data, the global navigation satellite system (GNSS) total electron content (TEC) observations, as well as ionosonde measurements. The main results are as follows: 1) The postsunset EPBs’ intensity exhibited a large day-to-day variation in the same UT intervals, which was fairly noticeable in the evening of December 07, yet considerably suppressed on December 08 and 09, and then dramatically revived and enhanced on December 10. 2) The postsunset linear Rayleigh-Taylor instability growth rate exhibited a different variation pattern. It had a relatively modest peak value on December 07 and 08, yet a larger peak value on December 09 and 10. There was a 2-h time lag of the growth rate peak time in the evening of December 09 from other nights. This analysis did not show an exact one-to-one relationship between the peak growth rate and the observed EPBs intensity. 3) The EPBs’ day-to-day variation has a better agreement with that of traveling ionospheric disturbances and atmospheric gravity waves signatures, which exhibited relatively strong wavelike perturbations preceding/accompanying the observed EPBs on December 07 and 10 yet relatively weak fluctuations on December 08 and 09. These coordinate observations indicate that the initial wavelike seeding perturbations associated with AGWs, together with the catalyzing factor of the instability growth rate, collectively played important roles to modulate the day-to-day variation of EPBs. A strong seeding perturbation could effectively compensate for a moderate strength of Rayleigh-Taylor instability growth rate and therefore their combined effect could facilitate EPB development. Lacking proper seeding perturbations would make it a more inefficient process for the development of EPBs, especially with a delayed peak value of Rayleigh-Taylor instability growth rate.

Linear Rayleigh-Taylor instability for compressible viscoelastic fluids

<abstract><p>In this paper, we consider the linear Rayleigh-Taylor instability of an equilibrium state of 3D gravity-driven compressible viscoelastic fluid with the elasticity coefficient $ \kappa $ is less than a critical number $ \kappa_{c} $ in a moving horizontal periodic domain. We first construct the maximal growing mode solutions to the linearized equations by studying a family of modified variational problems, and then we prove an estimate for arbitrary solutions to the linearized equations.</p></abstract>

Two-fluid simulations of Rayleigh-Taylor instability in a magnetized solar prominence thread

Solar prominences are formed by partially ionized plasma with inter-particle collision frequencies, which generally warrant magnetohydrodynamic treatment. In this work, we explore the dynamical impacts and observable signatures of two-fluid effects in the parameter regimes when ion-neutral collisions do not fully couple the neutral and charged fluids. We performed 2.5D two-fluid (charge – neutrals) simulations of the Rayleigh-Taylor instability (RTI) at a smoothly changing interface between a solar prominence thread and the corona. The purpose of this study is to deepen our understanding of the RTI and the effects of partial ionization on the development of the RTI using nonlinear two-fluid numerical simulations. Our two-fluid model takes into account viscosity, thermal conductivity, and collisional interaction between neutrals and charge: ionization or recombination, energy and momentum transfer, and frictional heating. In this paper, we explore the sensitivity of the RTI dynamics to the prominence equilibrium configuration, including the impact of the magnetic field strength and shear supporting the prominence thread, and the amount of prominence mass-loading. We show that at small scales, a realistically smooth prominence-corona interface leads to qualitatively different linear RTI evolution than that which is expected for a discontinuous interface, while magnetic field shear has the stabilizing effect of reducing the growth rate or eliminating the instability. In the nonlinear phase, we observe that in the presence of field shear the development of the instability leads to formation of coherent and interacting 2.5D magnetic structures, which, in turn, can lead to substantial plasma flow across magnetic field lines and associated decoupling of the fluid velocities of charged particles and neutrals.

A simplified approximate analytical model for Rayleigh–Taylor instability in elastic–plastic solid and viscous fluid with thicknesses* *Project supported by of the Science Challenge Project of China (Grant No. TZ2018001).

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.

Rayleigh–Taylor instability at spherical interfaces between viscous fluids: The fluid/fluid interface

Through the computation of the most-unstable modes, we perform a systematic analysis of the linear Rayleigh–Taylor instability at a spherical interface separating two different homogeneous regions of incompressible viscous fluids under the action of a radially directed acceleration over the entire parameter space. Using the growth rate as the dependent variable, the parameter space is spanned by the spherical harmonic degree n and three dimensionless variables: the Atwood number A, the viscosity ratio s, and the dimensionless variable B=(aRρ22/μ22)1/3R, where aR, ρ2, and μ2 are the local radial acceleration at the interface and the density and viscosity of the denser overlying fluid, respectively. To understand the effect of the various parameters on the instability behavior and to identify similarities and differences between the planar and spherical configurations, we compare the most-unstable growth rates αP* (planar) and αS* (spherical) under homologous driving conditions. For all A, when s ≪ 1, the planar configuration is more unstable than the spherical (αP*>αS*) within the interval 0 < B < ∞. However, as s increases to O(1), there is a region for small values of B where αS*>αP*, whereas for larger values of B, αP*>αS* once again. When s ∼ 2, the maximum of αS* for the n = 1 mode is greater than αS* for any other mode (n ≥ 2). For s∼O(10), αS*>αP* for all A within 0 < B < ∞. We find that the instability behavior between the planar and spherical systems departs from each other for s ≳ 2 and diverges considerably for s ≫ 1. In the limit when s → ∞, the planar configuration reduces to the trivial solution αP*≡0 for all B and A, whereas αS* has a non-zero limiting value for the n = 1 mode but vanishes for all the other modes (n ≥ 2). We derive an equation for αS* in this limit and obtain closed form solutions for the maximum of αS* and the value of B at which this occurs. Finally, we compare the most-unstable growth rates between the exact dispersion relation and three different approximations to highlight their strengths and weaknesses.

The rotating Rayleigh-Taylor instability in a strongly coupled dusty plasma

The linear Rayleigh-Taylor instability (RTI) in a uniformly rotating strongly coupled dusty plasma (SCDP) is investigated both analytically and numerically. The influence of the Coriolis force on the dust particles is considered mainly owing to the drag force of the magnetized ions. The dispersion relation is analytically derived using appropriate boundary conditions and velocity profile. The dispersion characteristics are analyzed in the strongly coupled (kinetic) limit, and it is observed that the criterion of linear RTI is modified due to the presence of rotation and shear velocity comprising strong correlation effects. It is found that in the presence of intermediate magnetic field in SCDP, dust cloud rotation and strong correlation effects altogether stabilize the growth rate of linear RTI. The analytical growth rate of RTI shows a good agreement with the growth rate calculated numerically.

Linear Rayleigh-Taylor instability in an accelerated Newtonian fluid with finite width.

The linear theory of Rayleigh-Taylor instability is developed for the case of a viscous fluid layer accelerated by a semi-infinite viscous fluid, considering that the top interface is a free surface. Effects of the surface tensions at both interfaces are taken into account. When viscous effects dominate on surface tensions, an interplay of two mechanisms determines opposite behaviors of the instability growth rate with the thickness of the heavy layer for an Atwood number A_{T}=1 and for sufficiently small values of A_{T}. In the former case, viscosity is a less effective stabilizing mechanism for the thinnest layers. However, the finite thickness of the heavy layer enhances its viscous effects that, in general, prevail on the viscous effects of the semi-infinite medium.

Finite-thickness effects on the Rayleigh-Taylor instability in accelerated elastic solids.

A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes into account the finite transit time of the elastic waves across the slab thickness. For Atwood number A_{T}=1, the asymptotic growth rate is found to be in excellent agreement with the exact solution [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998)10.1007/s000330050121], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.

On effects of viscosity and magnetic fields on the largest growth rate of linear Rayleigh–Taylor instability

In this article, we investigate the effect of viscosity on the largest growth rate in the linear Rayleigh–Taylor (RT) instability of a three-dimensional nonhomogeneous incompressible viscous flow in a bounded domain. By adapting a modified variational approach and careful analysis, we show that the largest growth rate in linear RT instability tends to zero as the viscosity coefficient goes to infinity. Moreover, the largest growth rate increasingly converges to one of the corresponding inviscid fluids as the viscosity coefficient goes to zero. Applying these analysis techniques to the corresponding viscous magnetohydrodynamic fluids, we can also show that the largest growth rate in linear magnetic RT instability tends to zero as the strength of horizontal (or vertical) magnetic field increasingly goes to a critical value.

Observation of Rayleigh-Taylor-instability evolution in a plasma with magnetic and viscous effects.

We present time-resolved observations of Rayleigh-Taylor-instability (RTI) evolution at the interface between an unmagnetized plasma jet colliding with a stagnated, magnetized plasma. The observed instability growth time (∼10 μs) is consistent with the estimated linear RTI growth rate calculated using experimentally inferred values of density (∼10(14) cm(-3)) and deceleration (∼10(9) m/s(2)). The observed mode wavelength (≳1 cm) nearly doubles within a linear growth time. Theoretical estimates of magnetic and viscous stabilization and idealized magnetohydrodynamic simulations including a physical viscosity model both suggest that the observed instability evolution is subject to magnetic and/or viscous effects.

Hydrodynamic instability of elastic-plastic solid plates at the early stage of acceleration.

A model is presented for the linear Rayleigh-Taylor instability taking place at the early stage of acceleration of an elastic-plastic solid, when the shock wave is still running into the solid and is driven by a time varying pressure on the interface. When the the shock is formed sufficiently close to the interface, this stage is considered to follow a previous initial phase controlled by the Ritchmyer-Meshkov instability that settles new initial conditions. The model reproduces the behavior of the instability observed in former numerical simulation results and provides a relatively simpler physical picture than the currently existing one for this stage of the instability evolution.

Rayleigh Taylor instability of two superposed compressible fluids in un-magnetized plasma

The linear Rayleigh Taylor instability of two superposed compressible Newtonian fluids is discussed with the effect of surface tension which can play important roles in space plasma. As in both the superposed Newtonian fluids, the system is stable for potentially stable case and unstable for potentially unstable case in the present problem also. The equations of the problem are solved by normal mode method and a dispersion relation is obtained for such a system. The behaviour of growth rate is examined in the presence of surface tension and it is found that the surface tension has stabilizing influence on the Rayleigh Taylor instability of two superposed compressible fluids. Numerical analysis is performed to show the effect of sound velocity and surface tension on the growth rate of Rayleigh Taylor instability. It is found that both parameters have stabilizing influence on the growth rate of Rayleigh Taylor instability.

Rayleigh-Taylor instability in partially ionized compressible plasmas: One fluid approach

We study the modification of the classical criterion for the linear onset and growth rate of the Rayleigh-Taylor instability (RTI) in a partially ionized (PI) plasma in the one-fluid description, considering a generalized induction equation. The governing linear equations and appropriate boundary conditions, including gravitational terms, are derived and applied to the case of the RTI in a single interface between two partially ionized plasmas. The boundary conditions lead to an equation for the frequencies in which some of them have positive complex parts, marking the appearance of the RTI. We study the ambipolar term alone first, extending the result to the full induction equation later. We find that the configuration is always unstable because of the presence of a neutral species. In the classical stability regime the growth rate is small, since the collisions prevent the neutral fluid to fully develop the RTI. For parameters in the classical instability regime the growth rate is lowered, but for the considered theoretical values of the collision frequencies and diffusion coefficients for solar prominences the differences with the compressible MHD case are small. We conclude that PI modifies some aspects of the linear RTI instability, since it takes into account that neutrals do not feel the stabilizing effect of the magnetic field. For the set of parameters representative for solar prominences, our model gives the resulting timescale comparable with observed lifetimes of RTI plumes.

Linear study of Rayleigh-Taylor instability in a diffusive quantum plasma

The linear Rayleigh-Taylor (RT) instability in an incompressible quantum plasma is investigated on the basis of quantum magnetohydrodynamic model. It is shown that the occurrence of RT instability depends on density-temperature inhomogeneity (characteristic lengths) on one hand, and the system layer size on the other. It is also observed that the combined effects of external magnetic field, diffusivity, and quantum pressure significantly modify the dispersion properties of system in both the parallel and perpendicular directions. For any case, the imaginary and real parts of dispersion relation are presented and the possibility and conditions for the instability growth rate are discussed.

Modeling hydrodynamic instabilities of double ablation fronts in inertial confinement fusion

A linear Rayleigh-Taylor instability theory of double ablation (DA) fronts is developed for direct-drive inertial confinement fusion. Two approaches are discussed: an analytical discontinuity model for the radiation dominated regime of very steep DA front structure, and a numerical self-consistent model that covers more general hydrodynamic profiles behaviours. Dispersion relation results are compared to 2D simulations.

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 of two superposed magnetized viscous fluids with suspended dust particles

The linear Rayleigh-Taylor instability of two superposed incompressible magnetized fluids is investigated incorporating the effects of suspended dust particles and viscosity. The basic magnetohydrodynamic set of equations have been constructed and linearized. The dispersion relation for 2-D and 3-D perturbations is obtained by applying the appropriate boundary conditions. The condition of Rayleigh-Taylor instability is investigated for potentially stable and unstable modes, which depends upon magnetic field, viscosity and suspended dust particles. The stability of the system is discussed by applying the Routh-Hurwitz criterion. It is found that the Alfven mode comes into the dispersion relation for perturbations in x, y-directions and in only x-direction, while it does not come into y-directional perturbation. The stable configuration is found to remain stable even in the presence of suspended dust particles. Numerical calculations have been performed to see the effects of various parameters on the growth rate of Rayleigh-Taylor instability. It is found that magnetic field and relaxation frequency of suspended dust particles both have destabilizing influence on the growth rate of Rayleigh-Taylor instability. The effects of kinematic viscosity and mass concentration of dust particles are found to have stabilized the growth rate of linear Rayleigh-Taylor instability.

Formation of fingers around the edges of a drop hitting a metal plate with high velocity

Water droplets (0.55 or 1.3 mm diameter) were photographed as they impinged on a stainless steel surface. The droplet impact velocity (10–50 m s−1) and the average roughness (0.03 or 0.23 μm) of the test surfaces were varied. The stainless steel substrate was mounted on the end of a rotating arm, giving linear velocities of up to 50 m s−1. Different stages of droplet impact were photographed by synchronizing the ejection of a single droplet with the position of the rotating arm and triggering of a camera. Finger-shape perturbations were observed around the edges of spreading droplets. The maximum diameter to which a droplet spread and the number of fingers formed around it were measured. The size and number of fingers increased with impact velocity and droplet diameter. At sufficiently high velocities, the tips of these fingers detached, producing satellite droplets. By increasing surface roughness, both the number of fingers and the maximum extent of spreading were decreased. At high impact velocities the spreading liquid film became so thin that it ruptured in several places. A mathematical model, based on linear Rayleigh–Taylor instability theory, was used to predict the wavelength of the fastest growing perturbation around a spreading droplet. The corresponding wavenumber agreed reasonably well with the number of fingers around the droplet.

Flow-curvature effect on linear Rayleigh–Taylor instability in magnetized plasmas

The effect of sheared poloidal flow on the linear Rayleigh–Taylor (RT) instability of magnetized plasma is reexamined. In the weak curvature flow limit (V⊥0″≪1) the linear RT mode stabilization effect is recovered. In the strong flow curvature limit (V⊥0″≫1) it is shown that the RT mode may not stabilize.