The Rayleigh-Taylor Instability of Transition Layer
A. Tavakoli, D. D. Tskhakaya
发现了Rayleigh方程的新的对称性类型，在小Atwood数下，得到了光滑变化密度分布的解析解。结果表明，具有有限宽度的过渡层可以经历某种分层。
New types of symmetry for the Rayleigh equation are found. For small Atwood number, an analytic solution is obtained for a smoothly varying density profile. It is shown that a transition layer with a finite width can undergo some kind of stratification.
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Combined effect of viscosity and vorticity on single mode Rayleigh -Taylor instability bubble growth
本文研究了粘性和涡量的联合作用对单模Rayleigh -Taylor不稳定性气泡增长速率的影响。它示出的效果，粘度上的运动的较轻的流体与涡内积累的气泡由于质量烧蚀可能是这样的，以减少净粘性阻力的气泡施加的上层较重的流体，因为前者上升通过它。
The effects of velocity shear on the unstable modes driven by the effective gravity (Rayleigh-Taylor and interchange) and resistive drift wave instabilities for inhomogeneous equilibrium fluid/plasma density are analyzed for the localized eigenmode problems. It is shown that the effect of the velocity shear drastically depends on the type of instability. Whereas the velocity shear can significantly suppress both Rayleigh-Taylor and interchange instabilities, it has only a week impact on the growth rate of the resistive drift wave. This is directly related to the physical nature of these instab…
Ablative Rayleigh-Taylor instability growth was investigated to elucidate the fundamental physics of thermal conduction suppression in a magnetic field. Experiments found that unstable modulation growth is faster in an external magnetic field. This result was reproduced by a magnetohydrodynamic simulation based on a Braginskii model of electron thermal transport. An external magnetic field reduces the electron thermal conduction across the magnetic field lines because the Larmor radius of the thermal electrons in the field is much shorter than the temperature scale length. Thermal conduction s…
Observation of Self-Similarity in the Magnetic Fields Generated by the Ablative Nonlinear Rayleigh-Taylor Instability
研究利用超快质子射线照相术测量激光加速平面靶中特定扰动产生的磁场，发现其蜂窝状磁场结构有自相似行为，结果与气泡竞争和合并模型相符，揭示了相关磁场结构与瑞利 - 泰勒气泡及尖峰增长的联系。
Magnetic field generation by the Rayleigh-Taylor instability in laser-driven planar plastic targets
研究利用超快质子射线照相术，在激光驱动平面塑料靶中测量瑞利-泰勒不稳定性产生的磁场，通过特定激光脉冲照射引发靶调制并放大，实验数据与二维磁流体动力学模拟预测相符。
Development of Richtmyer-Meshkov and Rayleigh-Taylor Instability in presence of magnetic field
从天体物理到惯性约束聚变（ICF），流体不稳定性（如Rayleigh-Taylor、Richtmyer-Meshkov和Kelvin-Helmholtz不稳定性）可以发生在广泛的物理现象中。在存在横向磁场时，R-M和R-T不稳定性随磁压和流体动压的方向而被抑制或增强。同样，如果两种流体都是导电的，则两种流体的界面可能振荡。而在线性情况下，磁场对磁感应强度没有影响。
Stabilizing transverse ablative Rayleigh Taylor like instability by using elliptically polarized laser pulses in the hole-boring radiation pressure acceleration regime
结果表明，在打孔辐射压力加速区，椭圆偏振激光可以很好地稳定横向类Rayleigh Taylor不稳定性。激光的$\bm{J}\times\bm{B}$效应将使局域电子热化，并支持离子的横向扩散机制，导致短波长扰动的稳定化，这与初始约束聚变研究中的烧蚀Rayleigh Taylor不稳定性非常相似。在给定激光强度和等离子体密度的条件下，从理论模型中得到了合适的偏振比范围。二维粒子模拟结果证实了椭圆偏振激光驱动离子束的稳定机制，与圆偏振激光驱动离子束相比，椭圆偏振激光驱动的离子束更集中、更强。
Observed transition from Richtmyer-Meshkov jet formation through feedout oscillations to Rayleigh-Taylor instability in a laser target
本文报道了激光驱动冲击波在塑料靶自由波纹后表面触发的流体动力学扰动演化的实验研究。在亚兆巴冲击压力下，在非加速靶中观察到表现出Richtmyer-Meshkov型不稳定性发展的平面射流。当冲击压力超过1毫巴时，观察到振荡的波纹膨胀波，随后是后表面扰动到烧蚀前沿的“馈出”和瑞利-泰勒不稳定性的发展，这打破了加速的目标。
Magnetized laser-produced plasmas are central to many novel laboratory astrophysics and inertial confinement fusion studies, as well as in industrial applications. Here we provide the first complete description of the three-dimensional dynamics of a laser-driven plasma plume expanding in a 20 T transverse magnetic field. The plasma is collimated by the magnetic field into a slender, rapidly elongating slab, whose plasma-vacuum interface is unstable to the growth of the "classical", fluid-like magnetized Rayleigh-Taylor instability.
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 ($\sim 10$~$μ$s) is consistent with the estimated linear RTI growth rate calculated using experimentally inferred values of density ($\sim 10^{14}$~cm$^{-3}$) and deceleration ($\sim 10^9$~m/s$^2$). The observed mode wavelength ($\gtrsim 1$~cm) nearly doubles within a linear growth time. Theoretical estimates of magnetic and viscous stabilization and idealized magnetohydrodyn…
The Rayleigh-Taylor instability develops when fluids are accelerated counter to their density gradients; intense interfacial fluid mixing ensues with time. The Rayleigh-Taylor mixing controls a broad range of processes in fluids, plasmas, materials, at astrophysical and at atomic scales. In this perspective paper we briefly review theoretical and experimental approaches, and apply theory and experiment to investigate order and disorder in Rayleigh-Taylor flows. The theory finds that properties of heterogeneous anisotropic accelerated Rayleigh-Taylor mixing depart from those of homogeneous isot…
Effects of Mass Diffusion on Rayleigh-Taylor Instability Under A Large Gravity
针对惯性约束聚变中Rayleigh-Taylor不稳定性增长率解析预测与实验模拟不符的问题，通过线性近似求解Rayleigh方程，研究大重力下质量扩散和指数密度分布的抑制效应，揭示了密度抑制因子随扰动波数的非单调变化规律。
Suppression of transverse ablative Rayleigh-Taylor-like instability in the hole-boring radiation pressure acceleration by using elliptically polarized laser pulses
结果表明，利用椭圆偏振激光可以抑制打孔辐射压加速中的横向类瑞利-泰勒（RT）不稳定性。EP激光器的适度${J}\times{B}$加热将使局部电子热化，这导致离子的横向扩散，抑制RT不稳定性的短波长扰动。对于给定的激光强度和等离子体密度，解析地得到了一个合适的偏振比条件。二维粒子模拟结果证实了这一观点，表明EP激光驱动的离子束比圆偏振激光驱动的离子束更集中、更强。
Spiky development at the interface in Rayleigh-Taylor instability: Layzer approximation with second harmonic
本文将Layzer近似方法推广到任意Atwood数的Rayleigh Taylor不稳定性的两个流体界面结构的研究中，只考虑了二次谐波模，而忽略了零次谐波模。该修正使得流体速度在无穷远处为零，从而避免了对无穷远处存在时间相关源的非物理假设。本文的分析表明，对于曲率超过1/（2sqrt{A}）的初始界面扰动，其中$A$是Atwood数，出现了几乎自由降落的尖峰，随着它的下落，尖峰的尖锐程度不断增加。尖峰尖端的曲率也随着Atwood数的增加而增加。某些初始条件也可能导致有限时间奇异性的出现，如在以前使用的保角映射技术的情况下发现的。然而，泡沫的增长速度并没有受到明显的影响。
Nonlinear evolution of the ablative Rayleigh-Taylor instability with preheating
数值研究了预热条件下单模烧蚀瑞利-泰勒不稳定性的演化。研究发现，不稳定性的演化强烈依赖于烧蚀前沿界面前的预热长度$L$。对于弱预热（$L/L_{\rm SH}\leq f_0$，其中$L_{\rm SH}$是Spitzer-Harm长度，$f_0\sim 20$是临界值），线性生长速率具有尖锐的最大值，并生成二次尖峰-气泡结构。这种生长结构与主尖峰气泡的相互作用导致后者破裂。然而，对于强预热（$L/L_{\rm SH}>20$），线性增长率没有尖锐的最大值，也不会产生二次尖峰气泡。相反，主尖峰气泡演变成一个细长的射流。这些结果被解释的不稳定性产生的谐波模式的演变和相互作用。
The growth rate of the non-linear ablative Rayleigh-Taylor (RT) instability is enhanced by magnetic fields self-generated by the Biermann battery mechanism; a scaling for this effect with perturbation height and wavelength is proposed and validated with extended-magnetohydrodynamic simulations. The magnetic flux generation rate around a single RT spike is found to scale with the spike height. The Hall Parameter, which quantifies electron magnetization, is found to be strongly enhanced for short wavelength spikes due to Nernst compression of the magnetic field at the spike tip. The impact of th…
The magnetic-Rayleigh--Taylor (MRT) instability is a ubiquitous phenomenon that occurs in magnetically-driven Z-pinch implosions. It is important to understand this instability since it can decrease the performance of such implosions. In this work, I present a theoretical model for the weakly nonlinear MRT instability. I obtain such model by asymptotically expanding an action principle, whose Lagrangian leads to the fully nonlinear MRT equations. After introducing a suitable choice of coordinates, I show that the theory can be cast as a Hamiltonian system, whose Hamiltonian is calculated up to…
Rayleigh-Taylor interfacial mixing has critical importance in a broad range of processes in nature and technology. In most instances Rayleigh-Taylor dynamics is induced by variable acceleration, whereas the bulk of existing studies is focused on the cases of constant and impulsive accelerations referred respectively as classical Rayleigh-Taylor and classical Richtmyer-Meshkov dynamics. In this work we consider Rayleigh-Taylor mixing induced by variable acceleration with power-law dependence on the spatial coordinate in the acceleration direction. We apply group theory and momentum model to fin…
Self-generated magnetic field in three-dimensional ablative Rayleigh-Taylor instability
研究了三维烧蚀瑞利-泰勒不稳定性中的自生磁场，发现3D比2D产生更强磁场，Nernst效应放大磁场，且磁场在3D中主要加速尖刺增长而非气泡。
We consider the long-standing problem of Rayleigh-Taylor instability with variable acceleration, and focus on the early-time dynamics of an interface separating incompressible ideal fluids of different densities subject to an acceleration being a power-law function of time for a spatially extended threedimensional flow periodic in the plane normal to the acceleration with symmetry group p6mm. By employing group theory and scaling analysis, we discover two distinct sub-regimes of the early time dynamics depending on the exponent of the acceleration power-law. The time-scale and the early-time d…
The magneto-Rayleigh-Taylor (MRT) instability has been investigated in great detail in previous work using magnetohydrodynamic and kinetic models for low-beta plasmas. The work presented here extends previous studies of this instability to regimes where finite-Larmor-Radius (FLR) effects may be important. Comparisons of the MRT instability are made using a 5-moment and a 10-moment two-fluid model, the two fluids being ions and electrons. The 5-moment model includes Hall stabilization whereas the 10-moment model includes Hall and FLR stabilization. Results are presented for these two models usi…
We give theoretical analyses of the Magneto-Rayleigh-Taylor instability driven by a rotating magnetic field. Both slab and liner configurations with finite thicknesses are dealt with in the WKB and the non-WKB approximations. Results show that instabilities for all modes (combinations of wave vectors) are alleviated. We further discuss the potential application of the alternant/nested configurations of a theta and a Z pinch to the Theta-Z Liner Inertia Fusion (Theta-Z-LIF) concept.
Electric field-driven Rayleigh-Taylor-like instability in binary complex plasma
本研究通过分子动力学模拟揭示了电场驱动下二元复等离子体中Rayleigh-Taylor类不稳定的形成机制及影响因素。
Role of nonlocal heat transport on the laser ablative Rayleigh-Taylor instability
本研究首次自洽通过理论与辐射流体模拟研究非局域热输运下的激光烧蚀瑞利-泰勒不稳定性，发现非局域热流可稳定烧蚀锋面、抑制短波长扰动增长，且效应随激光强度增强，为惯性约束聚变靶设计提供参考。
Rayleigh-Taylor and Buoyancy-driven instabilities are very common instabilities for an inhomogeneous medium. We examine here how these instabilities grow for incompressible viscoelastic fluids like a strongly coupled dusty plasma by using incompressible generalized hydrodynamic (i-GHD) fluid model. Since the dust particles are pretty massive, the gravitational attraction of earth has a significant role in its dynamics. In this paper the acceleration due to gravity g and the role of strong coupling in the context of gravitationally stratified dusty plasma fluid have been considered. We find tha…
Effect of magnetic field on temporal development of Rayleigh-Taylor instability induced interfacial nonlinear structure
研究了磁场对两流体界面结构引起的Rayleigh-Taylor不稳定性非线性增长率的影响。假设磁场平行于两个流体界面的平面，并沿垂直于波矢量的方向作用。如果磁场仅限于界面的任一侧，则生长速率可能被抑制（可能几乎消失）或被增强，这取决于界面上的磁压力是否与不稳定性驱动压差g（ρh - ρl）y相反或沿相同方向作用。如果在两个流体界面的两侧都存在磁场，则在分离表面周期性地波动的意义上也可以发生稳定化，此时由于两侧上的磁压力而产生的力在相反的方向上作用。这一结果不同于经典线性理论的预言，即当波矢垂直于磁场方向时，平行于表面的磁场对生长速率没有影响。
Rayleigh-Taylor instability (RTI) has critical importance for a broad range of processes in nature and technology, from supernovae to plasma fusion. In most instances RTI is driven by variable acceleration whereas the bulk of existing studies have considered constant acceleration. This work focuses on RTI driven by acceleration with power-law time-dependence, and applies group theory to solve the classical problem. For early time dynamics, we find dependence of RTI growth-rate on acceleration parameters and initial conditions. For late time dynamics, we directly link interface dynamics to inte…
In this research, the height, curvature and velocity of the bubble tip in Rayleigh-Taylor instability at arbitrary Atwood number with horizontal magnetic field are investigated. To support the earlier simulation and experimental results, the vorticity generation inside the bubble is introduced. It is found that, in early nonlinear stage, the temporal evolution of the bubble tip parameters depend essentially on the strength and initial perturbation of the magnetic field, although the asymptotic nature coincides with the non magnetic case. The model proposed here agrees with the previous linear,…
For years, astrophysicists, plasma fusion and fluid physicists have puzzled over Rayleigh-Taylor turbulent mixing layers. In particular, strong discrepancies in the growth rates have been observed between experiments and numerical simulations. Although two phenomenological mechanisms (mode-coupling and mode-competition) have brought some insight on these differences, convincing theoretical arguments are missing to explain the observed values. In this paper, we provide an analytical expression of the growth rate compatible with both mechanisms and is valide for a self-similar, low Atwood Raylei…
We report a novel measurement of the late time self-similar growth constant $α_B$ of the Rayleigh-Taylor instability (RTI) from controlled initial perturbations. To this end, we have developed a laser-driven experiment, fielded on the National Ignition Facility (NIF), to explore deeply non-linear, multimode hydrodynamic growth of a planar interface. The measured value is $α_B=0.038\pm 0.008$, which is consistent with previously reported 2D simulations and closer to previously reported 3D simulations. This resolved the known discrepancy between experiments and simulations of RTI.
Invariants, symmetries and scaling of Rayleigh-Taylor turbulent mixing
本文将Kolmogorov理论关于湍流动力学对称性的思想推广到由Rayleigh-Taylor不稳定性引起的非定常湍流混合的不变量、标度和谱分析。动量损失率的时间和尺度不变性导致尺度之间的非耗散动量传递，速度和雷诺数的幂律尺度依赖性和不同于Kolmogorov的谱，并设置粘性和耗散尺度。与各向同性湍流相比，湍流混合表现出更多的有序性。流动规则化的机制进行了讨论。
Rayleigh-Taylor turbulence is nothing like Kolmogorov turbulence in the self similar regime
近几年来，描述瑞利-泰勒（RT）混合层湍流谱的数值模拟和实验越来越多。在最近的研究中报道的结果允许排除湍流{ \it la Kolmogorov}作为作用于自相似RT湍流混合层的机制。一个不同的机制，这符合数值和实验结果，并涉及RT流到其他浮力流。
Intuitive calculation of the relativistic Rayleigh-Taylor instability linear growth rate
Rayleigh-Taylor不稳定性是从天体物理到惯性约束聚变等许多物理学领域中的一个关键过程。它通常是分析推导线性化流体方程，但背后的物理不稳定性并不总是清楚。最近的工作，这种不稳定性允许一个非常直观的理解的现象，并直接计算的线性增长率。在这封信中，它表明，同样的推理允许一个直接推导的相对论性的线性增长率的不可压缩流体的表达。
Laser-Driven Rayleigh-Taylor Instability: Plasmonics Effects and Three-Dimensional Structures
高强度激光的辐射压力驱动密集靶加速，导致相互作用面产生起伏的瑞利-泰勒不稳定性。使用一个简单的模型，它示出了由正弦纹波引起的辐射压力的自洽调制的影响实质上的波矢谱的RTI依赖于激光偏振。当纹波周期接近激光波长时，局部场的等离子体激元增强设定了主导RTI尺度。通过三维模拟研究了非线性演化，结果表明形成了具有“墙纸”对称性的稳定结构。
Rayleigh-Taylor (RT) mixing has critical importance for a broad range of process in nature and technology, from supernovae and plasma fusion to oil recovery and nano-fabrication. In most instances, RT flows are driven by variable acceleration, whereas the bulk of existing studies have considered only constant and impulsive accelerations. By analyzing symmetries of RT dynamics for certain patterns of variable acceleration, we discover a special class of self-similar solutions and identify their scaling, correlations and spectra. We find that dynamics of RT mixing can vary from super-ballistic t…
Particle acceleration by magnetic Rayleigh-Taylor instability: mechanism for flares in black-hole accretion flows
本研究针对黑洞吸积流耀发的粒子加速机制问题，通过PIC模拟探究相对论无碰撞等离子体的磁瑞利-泰勒不稳定性，发现羽状结构生长合并驱动磁重联可实现高效粒子加速，能解释Sgr A*的吸积流耀发。
Rayleigh--Taylor turbulence in two dimensions
Chertkov [Phys. Rev. Lett. { \bf 91} 115001（2003）]。通过直接数值模拟，我们证实了在二维空间/时间的理论预测，并探讨了故障的唯象描述，由于折射率的影响。我们发现，小尺度的速度和温度的统计遵循Bolgiano-Obukhov标度。在全球可观的水平上，我们表明，随时间变化的努塞尔数和雷诺数的瑞利数的平方根的规模。这些结果指出的结论，瑞利-泰勒湍流在二维和三维，由于没有边界，提供了一个自然的物理实现的Kraichnan缩放制度迄今为止与难以捉摸的“热对流的最终状态”。
Rayleigh Taylor Instability in Multiple Finite-Thickness Fluid Layers
本文提出通用传递矩阵方法分析密度与黏度空间变化流体中的瑞利-泰勒不稳定性，并结合无黏流和无加速度近似获得不同极限下的解析解。
Nonlinear asymptotic bubble growth in single-mode spherical Rayleigh-Taylor instability
针对球形几何中单模态瑞利-泰勒不稳定性气泡的非线性增长，构建了适用于任意阿特伍德数及会聚、发散重力构型的解析模型，揭示了球形几何对气泡增长的不同影响，其预测与数值模拟吻合良好。
This work focuses on Rayleigh-Taylor instability (RTI)driven by acceleration with power-law time-dependence. We review the existing theoretical approaches, apply the group theory approach to solve this long-standing problem, and yield the unified framework for the scale-dependent dynamics of Rayleigh-Taylor (RT) bubbles and RT spikes. For the early-time linear dynamics we provide the dependence of RTI evolution on the acceleration parameters and the initial conditions. For the late-time nonlinear dynamics, we find a continuous family of asymptotic solutions, directly link the interface velocit…
3-D extended-MHD simulations of the magnetized ablative Rayleigh-Taylor instability are presented for the first time. Previous 2-D simulations claiming perturbation suppression by magnetic tension are shown to be misleading, as they do not include the most unstable dimension. For perturbation modes along the applied field direction, the magnetic field simultaneously reduces ablative stabilization and adds magnetic tension stabilization; the stabilizing term is found to dominate for applied fields >5T, with both effects increasing in importance at short wavelengths. For modes perpendicular to t…
Tracing Rayleigh-Taylor instability from measured periodic modulation in laser driven proton beams
本研究通过实验观察到激光加速质子束能谱中的周期性调制，结合理论模型和二维粒子模拟，证实其源于横向类Rayleigh-Taylor不稳定性引起的电子密度调制，为诊断该不稳定性演化提供了新工具。
Non-stationary Rayleigh-Taylor instability in supernovae ejecta
Rayleigh-Taylor不稳定性在许多天体的动力学，特别是超新星演化中起着重要的作用。在本文中，我们发展了一种分析方法，研究了球形膨胀的SN喷出物的稳定性分析，通过使用一个特殊的变换，在共同移动的坐标系。本文首先研究了中心源压力作用下气体壳层的非定常球膨胀。然后，我们分析了它的稳定性相对于一个非径向，非球对称扰动的外壳。我们考虑的情况下，多方常数的SN壳是$γ=5/3$，我们研究的任意壳扰动的演变。导出了色散关系。发现扰动的增长率，并讨论其时空演化。稳定域取决于喷出物壳的厚度，它的加速度，和扰动波长。
We report on results of high resolution two fluid non-linear simulations of the Rayleigh Taylor Instability (RTI) at the interface between a solar prominence and the corona. These follow results reported earlier by Popescu Braileanu et al. (2021a,b) on linear and early non-linear RTI dynamics in this environment. The simulations use a two fluid model that includes collisions between neutrals and charges, including ionization/recombination, energy and momentum transfer, and frictional heating. High resolution 2.5D magnetized RTI simulations with the magnetic field dominantly normal to and sligh…
Effect of viscosity and surface tension on the growth of Rayleigh -Taylor instability and Richtmyer-Meshkov instability induced two fluid inter-facial nonlinear structure
研究了粘性阻力和表面张力对Rayleigh -Taylor不稳定性和Richtmyer-Meshkov不稳定性引起的非线性双流体界面结构的影响，粘性和表面张力对流体不稳定性起重要作用。可以看出，气泡高度的尖端的终端增长率的抑制的大小仅取决于通过其气泡上升和界面的表面张力的上部（较密）流体的粘性系数。但关于尖峰，它表明，在无粘流体尖峰不保持终端，但接近自由降落作为阿特伍德数A的增加。在这方面存在定性的协议与模拟结果也与一些早期的理论结果。粘度可明显地降低自由降落速度，并且随着粘度的增加，趋于使其终止。从描述尖峰时间发展的相关非线性方程的数值积分获得的结果支持上述观察。
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