Lattice Boltzmann study of three-dimensional immiscible Rayleigh–Taylor instability in turbulent mixing stage

In this paper, we numerically studied the late-time evolutional mechanism of three-dimensional (3D) single-mode immiscible Rayleigh–Taylor instability (RTI) by using an improved lattice Boltzmann multiphase method implemented on graphics processing units. The influences of extensive dimensionless Reynolds numbers and Atwood numbers on phase interfacial dynamics, spike and bubble growth were investigated in details. The longtime numerical experiments indicate that the development of 3D singlemode RTI with a high Reynolds number can be summarized into four different stages: linear growth stage, saturated velocity growth stage, reacceleration stage and turbulent mixing stage. A series of complex interfacial structures with large topological changes can be observed at the turbulent mixing stage, which always preserve the symmetries with respect to the middle axis for a low Atwood number, and the lines of symmetry within spike and bubble are broken as the Atwood number is increased. Five statistical methods for computing the spike and bubble growth rates were then analyzed to reveal the growth law of 3D single-mode RTI in turbulent mixing stage. It is found that the spike late-time growth rate shows an overall increase with the Atwood number, while the bubble growth rate experiences a slight decrease with the Atwood number at first and then basically maintains a steady value of around 0.1. When the Reynolds number decreases, the later stages cannot be reached gradually and the evolution of phase interface presents a laminar flow state.     

Measurements of Rayleigh–Taylor instability growth of laser-shocked iron–silicon alloy

The Rayleigh–Taylor (RT) instability of liquid iron alloys is important for understanding the core formation mechanism in the Earth. Here we first report the measurement of RT instability growth for a liquid iron–silicon (Fe–Si) alloy, which is one of the major candidate for the material of the Earth’s core, using a high power laser. We optimized the measurement setup and analytical technique to observe the growth of perturbation on an Fe–Si sample surface. The growth of perturbation amplitude on the Fe–Si alloy under high pressure and temperature was successfully observed using in situ X-ray radiography. The growth rate of the RT instability for the Fe–Si alloy on about 1000?GPa was estimated to be 0.3 ns^?1.     

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.     

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.     

Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation

High-fidelity large eddy simulation (LES) of a low-Atwood number (A = 0.05) Rayleigh–Taylor mixing layer is performed using the 10th-order compact difference code Miranda. An initial multimode perturbation spectrum is specified in Fourier space as a function of mesh resolution such that a database of results is obtained in which each successive level of increased grid resolution corresponds approximately to one additional doubling of the mixing layer width, or generation. The database is then analysed to determine approximate requirements for self-similarity, and a new metric is proposed to quantify how far a given simulation is from the limit of self-similarity. It is determined that mixing layer growth reaches a high degree of self-similarity after approximately 4.5 generations. Statistical convergence errors and boundary effects at late time, however, make it impossible to draw similar conclusions regarding the self-similar growth of more sensitive turbulence parameters. Finally, self-similar turbulence profiles from the LES database are compared with one-dimensional simulations using the k-L-a and BHR-2 Reynolds-averaged Navier–Stokes models. The k-L-a model, which is calibrated to reproduce a quadratic turbulence kinetic energy profile for a self-similar mixing layer, is found to be in better agreement with the LES than BHR-2 results.     

Quantum effects on the Rayleigh–Taylor instability of stratified plasma in the presence of suspended particles

The effects of quantum correction on the Rayleigh–Taylor instability (RTI) in stratified plasma layer have been investigated in the presence of suspended particles. A general dispersion relation is obtained from the linearized set of quantum hydrodynamic (QHD) equations. Two particular cases of suspended particle parameters (f ^? and α ₀) with and without quantum corrections are analysed. The condition of RTI is derived while the stability of the system is discussed by applying Routh–Hurwitz (RH) criterion in the polynomial equation. The results show that, in the absence of quantum term, the relaxation frequency of the suspended particles has a destabilizing effect, while the mass concentration of the suspended particles has a stabilizing effect on the growth rates of RTI. In the presence of the quantum term, the relaxation frequency of the suspended particle yields to the stability behaviour on the growth rates of RTI.     

Nonlinear Rayleigh–Taylor instability of the cylindrical fluid flow with mass and heat transfer

The nonlinear Rayleigh–Taylor stability of the cylindrical interface between the vapour and liquid phases of a fluid is studied. The phases enclosed between two cylindrical surfaces coaxial with mass and heat transfer is derived from nonlinear Ginzburg–Landau equation. The F-expansion method is used to get exact solutions for a nonlinear Ginzburg–Landau equation. The region of solutions is displayed graphically.     

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.     

Application of the continuum surface force model to the Rayleigh — Taylor instability problem

The surface tension effect is introduced according to the continuum model for the surface tension force. A smooth variation of the mollified function of the volume fraction (the color function) across the interface between immiscible fluids occurs due to the convolution of the original color function with the smooth kernel function. The polynomial eighth-degree kernel formulated for plane two-dimensional flows bounded by solid walls or symmetry planes is tested for the Rayleigh — Taylor instability problem.     

Vibrational energy flow models for the Rayleigh–Love and Rayleigh–Bishop rods

Energy Flow Analysis (EFA) has been developed to predict the vibrational energy density of the system structures in the medium-to-high frequency range. The elementary longitudinal wave theory is often used to describe the longitudinal vibration of a slender rod. However, for relatively large diameter rods or high frequency ranges, the elementary longitudinal wave theory is inaccurate because the lateral motions are not taken into account. In this paper, vibrational energy flow models are developed to analyze the longitudinally vibrating Rayleigh–Love rod considering the effect of lateral inertia, and the Rayleigh–Bishop rod considering the effect not only of the lateral inertia but also of the shear stiffness. The derived energy governing equations are second-order differential equations which predict the time and space averaged energy density and active intensity distributions in a rod. To verify the accuracy of the developed energy flow models, various numerical analyses are performed for a rod and coupled rods. Also, the EFA results for the Rayleigh–Love and Rayleigh–Bishop rods are compared with the analytical solutions for these models, the traditional energy flow solutions, and the analytical solutions for the classical rod.     

Experimental study of initial condition dependence on turbulent mixing in shock-accelerated Richtmyer–Meshkov fluid layers

Experimental evidence is needed to verify the hypothesis that the memory of initial conditions is retained at late times in variable density flows. If true, this presents an opportunity to “design” and “control” late-time turbulence, with an improved understanding in the prediction of inertial confinement fusion and other general fluid mixing processes. In this communication, an experimental and theoretical study on the effects of initial condition parameters, namely, the amplitude δ₀ and wavenumber κ₀ , where λ₀ is the initial wavelength) of perturbations, on late-time turbulence and mixing in shock-driven Richtmyer–Meshkov (R-M) unstable fluid layers in a 2D plane is presented. Single and multi-mode membrane-free initial conditions in the form of a gas curtain having a light-heavy-light configuration (air-SF₆-air) with an Atwood number of A= 0.57 were used in our experiments. A planar shock wave with a shock Mach number M= 1.21 drives the R-M instability, and the evolution of this instability after incident shock is captured using high resolution simultaneous planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV) diagnostics. Time evolution of statistics such as amplitude of the mixing layer, 2D turbulent kinetic energy, Reynolds number, rms of velocity fluctuations, probability density functions, and density-specific volume correlation were observed to quantify the amount of mixing and understand the nature of turbulence in this flow. Based on these results, it was found that the R-M mixing layer is asymmetric and non-Boussinesq. There is a correlation between initial condition parameters and large-scale, and small-scale mixing at late times, indicating an initial condition dependence on R-M mixing.     

Phase Effects of Long-Wavelength Rayleigh–Taylor Instability on the Thin Shell

Taking the long-wavelength Rayleigh-Taylor instability(RTI) on the thin shell of inertial confinement fusion as the research object,a linear analytical model is presented to study the phase effects that are caused by the phase difference of single-mode perturbations on the two interfaces.Its accuracy is tested by numerical simulations.By analyzing the characteristic of this model,it is found that the phase difference does not change the basic RTI structure(only one spike and one bubble in a peri...     

Simulation of the Weakly Nonlinear Rayleigh–Taylor Instability in Spherical Geometry

The Rayleigh-Taylor instability at the weakly nonlinear(WN) stage in spherical geometry is studied by numerical simulation.The mode coupling processes are revealed.The results are consistent with the WN model based on parameter expansion,while higher order effects are found to be non-negligible.For Legendre mode perturbation Pn(cos B),the nonlinear saturation amplitude(NS A) of the fundamental mode decreases with the mode number n.When n is large,the spherical NSA is lower than the corresponding...     

Changes in the state of polarization of partially coherent flat-topped beam in turbulent atmosphere for different source conditions

The polarization states, i.e. the size, the shape and the orientation of the polarization ellipse of partially coherent flat-topped (PCFT) beams passing through atmospheric turbulence are studied in detail. The effects are studied of different source conditions on the polarization states of a PCFT beam propagating through atmospheric turbulence. Based on the unified theory of the polarization states for random electromagnetic beams, we have established the detailed formula for calculating the change of the polarization states of such beams. The polarization states behavior of PCFT beams passing through atmospheric turbulence for any arbitrary order of a flat-topped beam “N” under different source conditions were investigated.     

A simplified approximate analytical model for Rayleigh–Taylor instability in elastic–plastic solid and viscous fluid with thicknesses

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.     

On the Orthocomplementation of State–Property–Systems of Contextual Systems

We adopt an operational approach to quantum mechanics in which a physical system is defined by the mathematical structure of its set of states and properties. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter which corresponds with the number N of possible outcomes in an experiment. In the case N=2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical, i.e. the experiments are deterministic and its set of properties is a Boolean lattice. For intermediate situations the change of state due to measurement is neither ‘maximal’ (i.e. quantum) nor ‘zero’ (i.e. classical). We show that two of the axioms used in Piron’s representation theorem for quantum mechanics are violated, namely the covering law and weak modularity. Next, we discuss a modified version of the model for which it is even impossible to define an orthocomplementation on the set of properties. Another interesting feature for the intermediate situations of this model is that the probability of a state transition in general not only depends on the two states involved, but also on the measurement context which induces the state transition.     

The dynamics of the k–ϵ mix model toward its self-similar Rayleigh–Taylor solution

We propose an analysis of the non-linear system of partial differential equations for the k–? model expressing the evolution of a turbulent mixing zone induced by the Rayleigh–Taylor instability. The method developed in this work is based on dynamical system theory. Our objective is to prove the global stability of the self-similar solution and at the same time to investigate the dynamics of transient phases. In fact, it is possible to show the existence of a central manifold allowing to reduce the dimension of the problem to a set of two ordinary differential equations.We establish that this simplified non-linear system globally converges toward a fixed point representing the self-similar solution by application of the Poincaré–Bendixson theorem. In addition, we shed light on the existence of a second fixed point which influences the trajectories in the phase space and leads to a non-physical enhanced growth rate in some cases explicitly detailed.     

Algebraic Bethe ansatz for the Zamolodchikov–Fateev and Izergin–Korepin models with open boundary conditions

We have considered the Zamolodchikov–Fateev and the Izergin–Korepin models with diagonal reflection boundaries. In each case the eigenspectrum of the transfer matrix is determined by application of the algebraic Bethe ansatz.