Single-mode Rayleigh-Taylor Instability Research Articles

Inferring the Magnetic Field from the Rayleigh–Taylor Instability

By extending the potential approach of Layzer and Goncharov to the magnetohydrodynamics equations, we find the nonlinear solutions to the single-mode Rayleigh–Taylor instability subjected to uniform magnetic fields at various inclinations. This allows us to derive the analytical prediction of the terminal bubble and spike velocities at arbitrary Atwood numbers, which are assessed against various 2D and 3D direct numerical simulations. Contrary to the linear phase, where the magnetic field inhibits or delays the instability, the growth rate may be enhanced in the nonlinear regime, exhibiting velocities faster than the Alfvén speed. This sheds light on the importance of the nondimensional number expressing the competition between the magnetic and buoyancy effects. Conversely, we show how the orientation and the intensity of the magnetic field can be simply inferred from these solutions.

Lagrangian investigation of the interface dynamics in single-mode Rayleigh–Taylor instability

We apply Lagrangian particle tracking to the two-dimensional single-mode Rayleigh–Taylor (RT) instability to study the dynamical evolution of fluid interface. At the onset of the nonlinear RT stage, we select three ensembles of tracer particles located at the bubble tip, at the spike tip, and inside the spiral of the mushroom structure, which cover most of the interfacial region as the instability develops. Conditional statistics performed on the three sets of particles and over different RT evolution stages, such as the trajectory curvature, velocity, and acceleration, reveals the temporal and spatial flow patterns characterizing the single-mode RT growth. The probability density functions of tracer particle velocity and trajectory curvature exhibit scalings compatible with local flow topology, such as the swirling motion of the spiral particles. Large-scale anisotropy of RT interfacial flows, measured by the ratio of horizontal to vertical kinetic energy, also varies for different particle ensembles arising from the differing evolution patterns of the particle acceleration. In addition, we provide direct evidence to connect the RT bubble re-acceleration to its interaction with the transported fluid from the spike side, due to the shear driven Kelvin–Helmholtz instability. Furthermore, we reveal that the secondary RT instability inside the spiral, which destabilizes the spiraling motion and induces complex flow structures, is generated by the centrifugal acceleration.

Compressible Rayleigh–Taylor instability subject to isochoric initial background state

The effect of compressibility on the single-mode Rayleigh–Taylor instability is examined using two (2D) and three-dimensional (3D) direct numerical simulations. To isolate compressibility from background stratification effects, this work employs a constant density profile on each side of the interface. The numerical simulations are performed at various Reynolds numbers using the gas kinetic method for static Mach numbers up to M = 0.4. The most important finding is that compressibility acting in isolation enhances the instability and perturbations grows faster with increasing Mach number, unlike previous results with background isothermal state, which show suppression of the instability at higher static Mach numbers. In addition, compressibility is also shown to increase the bubble-spike asymmetry. While the instability grows faster for the 3D case, the findings are qualitatively similar in 2D and 3D. The dynamical reasons underlying the effect of compressibility are elucidated by examining the evolution of vorticity and turbulent kinetic energy transport equations.

A decoupled mechanism of interface growth in single-mode hydrodynamic instabilities

One of the most significant issues in hydrodynamic interfacial instabilities is the growth rate of the interfacial perturbations, which plays an important role in both scientific research (e.g. supernova explosion) and engineering applications (e.g. inertial confinement fusion). Yet the underlying mechanisms of such flow phenomena remain unclear or controversial. In this paper the decoupled mechanisms of two effects are found to dominate the interface growth of the single-mode Rayleigh–Taylor instability (RTI) and Richtmyer–Meshkov instability (RMI) via Layzer's potential-flow model. One is the inertial effect induced by the interfacial density gradient and the acceleration, and the other is the frontal distortion effect stemming from interface shape evolution. The former determines the dominant features of interface evolution, while the latter influences the local concavity and convexity of growth rate such as the overshoot phenomenon. These two effects can be approximated as a linearly decoupled analytical solution if their nonlinear interaction term is neglected. With the decoupled solution, the theoretical growth rates agree well with high-fidelity numerical simulation results. The present result indicates that the long-time evolution of fluid interface in both RTI and RMI at all density ratios can be accurately predicted if both inertia and frontal distortion effects are taken into account. Furthermore, the strong dependence of instability evolution on initial amplitude is quantified based on the effects of decoupling, which sheds light on the physical origin of the overshoot phenomenon.

An investigation of the multi-mode Richtmyer-Meshkov instability at a gas/HE interface using Pagosa

In this work, we present a hydrocode Pagosa and explore the Richtmyer-Meshkov Instability (RMI) at an air/high explosive (HE) interface for the first time that is important but has not received much attention yet in the high explosive safety field. Thus, the presented Pagosa can be expected to predict the whole deflagration-to-detonation transition (DDT) process in future. In Pagosa, spatial discretization is implemented on cubic staggered grids by computing different variables at the vertex and the cell center, respectively, a special operator-splitting technique is employed to reduce the computational cost, and an artificial viscosity is added to handle the discontinuous shock waves in our simulations. To quantitatively evaluate the capability of Pagosa to solve these kinds of instabilities, the single mode Rayleigh-Taylor instability (RTI) and the multimode RMI at an air/SF 6 interface are first performed, respectively. The Pagosa results are compared with the related numerical solutions in the existing references and the experimental result. Moreover, a theoretical derivation of growth of RTI is also provided based on our numerical method. Subsequently, we explore the multi-mode RMI at an air/HE interface as well as the effects of several factors using Pagosa. Numerical results show that Pagosa is a powerful toolset to generate the right structures and the amplitude of RTI and RMI at an air/SF 6 interface. The solid HE can be penetrated by a strong shock wave and forms RMI deformations. The RMI at an air/HE interface behaves very different than at an air/SF 6 interface, periodic, decreased oscillation is observed due to material character, and is very sensitive to the initial simulation settings, that is, a tiny change in physical quantities will lead to a remarkable RMI structure, which is also observed in a shock bubble interaction [41] . The findings in this work are significant, and will present a new insight for the high explosive field. • An enhanced model Pagosa is presented with some special techniques. • Pagosa's capability to accurately capture the RTI at an air/SF 6 interface. • Pagosa's ability to accurately predict the RMI at an air/SF 6 interface. • The RMI at an air/HE interface is different from that at an air/SF 6 interface. • Effects of several factors on RMI at an air/HE interface.

Interface models for three-dimensional Rayleigh–Taylor instability

We derive interface models for three-dimensional Rayleigh–Taylor instability (RTI), making use of a novel asymptotic expansion in the non-locality of the fluid flow. These interface models are derived for the purpose of studying universal features associated with RTI such as the Froude number in single-mode RTI, the predicted quadratic growth of the interface amplitude under multi-mode random perturbations, the optimal (viscous) mixing rates induced by the RTI and the self-similarity of horizontally averaged density profiles and the remarkable stabilization of the mixing layer growth rate which arises for the three-fluid two-interface heavy–light–heavy configuration, in which the addition of a third fluid bulk slows the growth of the mixing layer to a linear rate. Our interface models can capture the formation of small-scale structures induced by severe interface roll-up, reproduce experimental data in a number of different regimes and study the effects of multiple interface interactions even as the interface separation distance becomes exceedingly small. Compared with traditional numerical schemes used to study such phenomena, our models provide a computational speed-up of at least two orders of magnitude.

Numerical Simulation of Single-Mode 3D Rayleigh-Taylor Instability

Rayleigh-Taylor instability (RTI) is analyzed theoretically by Taylor, and 2-dimensional experimental results are obtained by Lewis in 1950. Over the 72 years, several experiments and theories are developed with the shock-driven Ritchmyer-Meshkov instability (RMI) and the shear-driven Kelvin-Helmholtz instability (KHI). Here, we emphasize the single-mode Rayleigh-Taylor instability (RTI) mixing simulation with a surface area in 3 dimensions. The simulation uses concentration equations and nonzero transport. We observed chaotic interface behavior even for this single-mode simulation, in the sense that the interface appears to have an area proportional to Δ x − 1 , with respect to its mesh (non)convergence (i.e., rate of divergence) properties.

Effect of collisions with a second fluid on the temporal development of nonlinear, single-mode, Rayleigh-Taylor instability.

Goncharov's [Phys. Rev. Lett. 88, 134502 (2002)0031-900710.1103/PhysRevLett.88.134502] nonlinear model of a single-mode Rayleigh-Taylor instability (RTI) is investigated for a partially ionized plasma in a predominantly neutral background. Terminal bubble and spike velocities are derived from the nonlinear equationsin the case where the RTI dynamics is dominated by collisions between neutrals and ions. Direct numerical simulations are used to justify the use of Goncharov's model in this regime and observe its limitations.

Numerical investigation on the influence of different physical factors on the interface evolution in 3D RTI using CLSVOF method

The three-dimensional (3D) Rayleigh–Taylor instability (RTI) problem is numerically investigated using the coupled level set and volume of fluid (CLSVOF) method. The CLSVOF method combines the level set and volume of fluid methods to ensure good mass conservation performance, enabling the curvature of the interface captured by numerical simulations to be accurately calculated. A classical single-mode RTI (with only one “mushroom” generated under the initial setting) is adopted for numerical verification, and the shape of the interface and the penetration depth with respect to time are determined. Based on this initial two-dimensional single-mode RTI problem, the influence of factors such as the surface tension, density ratio, Reynolds number, and viscosity ratio on the 3D effects caused by the velocity gradient on both sides of the interface are thoroughly analyzed. This analysis allows us to obtain the basic laws governing the influence of different physical factors on the 3D effects of the RTI.

Effect of surface tension on late-time growth of high-Reynolds-number Rayleigh-Taylor instability

In this paper, we numerically investigate the late-time growth of high-Reynolds-number single-mode Rayleigh-Taylor instability in a long pipe by using an advanced phase-field lattice Boltzmann multiphase method. We mainly analyze the influence of surface tension on interfacial dynamic behavior and the development of the bubble front and spike front. The numerical experiments indicate that increasing surface tension can significantly reduce the complexity of formed interfacial structure and also prevents the breakup of phase interfaces. The interface patterns in the instability process cannot always preserve the symmetric property under the extremely small surface tension, but they do maintain the symmetries with respect to the middle line as the surface tension is increased. We also report that the bubble amplitude first increases then decreases with the surface tension. There are no obvious differences between the curves of spike amplitudes for low surface tensions. However, when the surface tension increases to a critical value, it can slow down the spike growth significantly. When the surface tension is lower than the critical value, the development of the high-Reynolds-number Rayleigh-Taylor instability can be divided into four different stages, i.e. the linear growth, saturated velocity growth, reacceleration, and chaotic mixing. The bubble and spike velocities at the second stage show good agreement with those from the modified potential flow theory that takes the surface tension effect into account. After that, the bubble front and spike front are accelerated due to the formation of Kelvin-Helmholtz vortices in the interfacial region. At the late time, the bubble velocity and spike velocity become unstable and slightly fluctuate over time. To determine the nature of the late-time growth, we also measure the bubble and spike normalized accelerations at various interfacial tensions and Atwood numbers. It is found that both the spike and bubble growth rates first increase then decrease with the surface tension in general. Finally, we deduce a theoretical formula for the critical surface tension, below which the Rayleigh-Taylor instability takes place and above which tension it does not occur. It is shown that the critical surface tension increases with the Atwood number and also the numerical predictions by the lattice Boltzmann method are also in accord well with the theoretical results.

Rayleigh-Taylor Instability: A Status Review of Experimental Designs and Measurement Diagnostics

Abstract The focus of experiments and the sophistication of diagnostics employed in Rayleigh-Taylor instability (RTI) induced mixing studies have evolved considerably over the past seven decades. The first theoretical analysis by Taylor and the two-dimensional experimental results by Lewis on RTI in 1950 examined single-mode RTI using conventional imaging techniques. Over the next 70 years, several experimental designs have been used to creating an RTI unstable interface between two materials of different densities. These early experiments though innovative, were arduous to diagnose and provided little information on the internal, turbulent structure and initial conditions of the RT mixing layer. Coupled with the availability of high-fidelity diagnostics, the experiments designed and developed in the last three decades allow detailed measurements of various turbulence statistics that have allowed broadly to validate and verify late-time nonlinear models and mix-models for buoyancy-driven flows. Besides, they have provided valuable insights to solve several long-standing disagreements in the field. This review serves as an opportunity to discuss the understanding of the RTI problem and highlight valuable insights gained into the RTI driven mixing process with a focus on low to high Atwood number (>0.1) experiments.

Analytical model of nonlinear evolution of single-mode Rayleigh–Taylor instability in cylindrical geometry

Abstract

Bubble dynamics of Rayleigh–Taylor flow

A flow of semi-bounded Rayleigh–Taylor instability (SB-RTI) is constructed and simulated to understand the bubble dynamics of the multi-mode Rayleigh–Taylor mixing (MM-RTM). SB-RTI is similar to the well-known single-mode Rayleigh–Taylor instability (SM-RTI), and it acts as a bridge from SM-RTI to MM-RTM. This idea is inspired by Meshkov’s recent experimental observation on the structure of the mixing zone of MM-RTM [E. E. Meshkov, J. Exp. Theor. Phys. 126, 126–131 (2018)]. We suppose that the bubble mixing zone consists of two parts, namely, the turbulent mixing zone at the center and the laminar-like mixing zone nearby the edge. For the latter, the bubble fronts are situated in an environment similar to that of SM-RTI bubbles in the potential flow stage, but with a much looser environment between neighboring bubbles. Therefore, a semi-bounded initial perturbation is designed to produce a bubble environment similar to that in MM-RTM. A non-dimensional potential speed of FrpSB≈0.63 is obtained in SB-RTI, which is larger than that of FrpSM=0.56 in SM-RTI. Combining this knowledge and the widely reported quadratic growth coefficient of αb ≈ 0.025 in the short-wavelength MM-RTM, we derive β ≡ D(t)/hb(t) ≈ (1 + A)/4. This relation is consistent with the MM-RTM simulations from Dimonte et al. [Phys. Fluids 16, 1668–1693 (2004)]. The current three-dimensional and previous two-dimensional results [Zhou et al., Phys. Rev. E 97, 033108 (2018)] support a united mechanism of bubble dynamics in short-wavelength MM-RTM.

Pure single-mode Rayleigh-Taylor instability for arbitrary Atwood numbers

The validity of theoretical investigation on Rayleigh-Taylor instability (RTI) with nonlinearity is quite important, especially for the simplest and the commonest case of a pure single-mode RTI, while its previous explicit solution in weakly nonlinear scheme is found to have several defections. In this paper, this RTI is strictly solved by the method of the potential functions up to the third order at the weakly nonlinear stage for arbitrary Atwood numbers. It is found that the potential solution includes terms of both the stimulating and inhibiting RTI, while the terms of the decreasing RTI are omitted in the classical solution of the weakly nonlinear scheme, resulting in a big difference between these two results. For the pure single-mode cosine perturbation, comparisons among the classical result, the present potential result and numerical simulations, in which the two dimensional Euler equations are used, are carefully performed. Our result is in a better agreement with the numerical simulations than the classical one before the saturation time. To avoid the tedious expressions and improve a larger valid range of the solution, the method of the Taylor expansion is employed and the velocities of the bubble and spike are, respectively, obtained. Comparisons between the improved and the simulation results show that the improved theory can better predict the evolution of the interface from the linear to weakly nonlinear, even to later of the nonlinear stages.

Effects of compressibility and Atwood number on the single-mode Rayleigh-Taylor instability

In order to study the effect of compressibility on Rayleigh-Taylor (RT) instability, we numerically simulated the late-time evolution of two-dimensional single-mode RT instability for isothermal background stratification with different isothermal Mach numbers and Atwood numbers (At) using a high-order central compact finite difference scheme. It is found that the initial density stratification caused by compressibility plays a stabilizing role, while the expansion-compression effect of flow plays a destabilizing role. For the case of small Atwood number, the density difference between the two sides of the interface is small, and the density distribution of the upper and lower layers is nearly symmetrical. The initial density stratification plays a dominant role, and the expansion-compression effect has little influence. With the increase in the Atwood number, the stabilization effect of initial density stratification decreases, and the instability caused by the expansion-compression effect becomes more significant. The flow structures of bubbles and spikes are quite different at medium Atwood number. The effect of compressibility on the bubble velocity is strong at large At. The bubble height is approximately a quadratic function of time at potential flow growth stage. The average bubble acceleration is nearly proportional to the square of Mach number at At = 0.9.

Lattice Boltzmann method simulations of the immiscible Rayleigh-Taylor instability with high Reynolds numbers

In this paper, an advanced phase-field lattice Boltzmann method based on the multiple-relaxation-time collision model is used to simulate the immiscible single-mode Rayleigh-Taylor instability with a moderate Atwoods number in a long tube, and we systematically analyze the effect of the Reynolds number on the interfacial dynamics and the late-time development stages of interface disturbance. The highest Reynolds number in the current simulation reaches up to 10000. The numerical results show that the Reynolds number significantly affects the development of the instability. For high Reynolds numbers, the instability undergoes a sequence of different growth stages, which include the linear growth, saturated velocity growth, reacceleration, and chaotic mixing stages. In the linear growth stage, the developments of the bubble and spike conform to the classical linear growth theory, and it is shown that the growth rate increases with the Reynolds number. In the second stage, the bubble and spike evolve with the constant velocities, and the numerical prediction for spike velocity is found to be slightly larger than the solution of the potential flow theory proposed by Goncharov [<i>Phys. Rev. Lett.</i> 2002 <b>88 </b> 134502], which can be attributed to the formation of vortices in the proximity of the spike tip. In addition, it is found that increasing the Reynolds number reduces the bubble saturated velocity, which then is smaller than the solution of the potential model. The nonlinear evolutions of the bubble and spike induce the Kelvin–Helmholtz instability, producing many vortex structures with different scales. Due to the interactions among the vortices, the instability eventually enters into the chaotic mixing stage, where the interfaces undergo the roll-up at multiple layers, sharp deformation, and chaotic breakup, forming a very complicated topology structure. Furthermore, we also measured the bubble and spike accelerations and find that the dimensionless values fluctuates around the constants of 0.045 and 0.233, indicating a mean quadratic growth. And for low Reynolds numbers, the heavy fluid will fall down in the form of the spike, and the interface in the whole process becomes very smooth without the appearances of the roll-up and vortices. The late-time evolutional stages such as the reacceleration and chaotic mixing cannot also be observed.

Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity

Growth of the single-fluid single-mode Rayleigh–Taylor instability (RTI) is revisited in 2D and 3D using fully compressible high-resolution simulations. We conduct a systematic analysis of the effects of perturbation Reynolds number (Rep) and Atwood number (A) on RTI’s late-time growth. Contrary to the common belief that single-mode RTI reaches a terminal bubble velocity, we show that the bubble re-accelerates when Rep is sufficiently large, consistent with Ramaparabhu et al. (2006) and Wei and Livescu (2012). However, unlike in Ramaparabhu et al. (2006), we find that for a sufficiently high Rep, the bubble’s late-time acceleration is persistent and does not vanish. Analysis of vorticity dynamics shows a clear correlation between vortices inside the bubble and re-acceleration. Due to symmetry around the bubble and spike (vertical) axes, the self-propagation velocity of vortices points in the vertical direction. If viscosity is sufficiently small, the vortices persist long enough to enter the bubble tip and accelerate the bubble (Wei and Livescu, 2012). A similar effect has also been observed in ablative RTI (Betti and Sanz, 2006). As the spike growth increases relative to that of the bubble at higher A, vorticity production shifts downward, away from the centerline and towards the spike tip. We modify the Betti–Sanz model for bubble velocity by introducing a vorticity efficiency factor η=0.45 to accurately account for re-acceleration caused by vorticity in the bubble tip. It had been previously suggested that vorticity generation and the associated bubble re-acceleration are suppressed at high A. However, we present evidence that if the large Rep limit is taken first, bubble re-acceleration is still possible. Our results also show that re-acceleration is much easier to occur in 3D than 2D, requiring smaller Rep thresholds.

Numerical investigation of interface capturing method by the Rayleigh-Taylor instability, dambreak and solitary wave problems

Free surface simulation always plays an important role among the problems in ship and ocean engineering. In the research described herein, an interface capturing method, combined with the level set (LS) and volume of fluid (VOF) method (CLSVOF), was developed and verified detailedly on the basis of the Rayleigh-Taylor instability (RTI), dambreak and solitary wave problems numerically in two-dimensional (2D) situation. According to CLSVOF approach, the LS function but not the VOF function can estimate the interface normal vector in the reconstruction procedure of interface. The numerical solver was first verified by solving the single-mode RTI. After that, the shape of the interface, the evolution process of vortices and the relationship between penetration depth and time were obtained. Simultaneously, this article separately discussed the effects of surface tension, density ratio and viscosity ratio on the RTI. Next, for the multi-mode RTI, the complicate interface evolution process was finely simulated to verify the mass conservation property during simulation. Eventually, this paper shows dambreak and solitary wave problems to demonstrate that CLSVOF solver is capable of handling a large density difference situation, as well as wave profile evolution in ocean engineering application.

Direct numerical simulations of multi-mode immiscible Rayleigh-Taylor instability with high Reynolds numbers

In this paper, we conduct the high-resolution direct numerical simulations of multimode immiscible Rayleigh-Taylor instability (RTI) with a low Atwood number (At = 0.1) using an improved phase field lattice Boltzmann method. The effect of the Reynolds number on the evolutional interfacial dynamics and bubble/spike amplitudes is first investigated by considering its wide range, from 100 up to a high value of 30 000. The numerical results show that, for sufficiently large Reynolds numbers, a sequence of distinguishing stages in the immiscible RTI can be observed, which includes the linear growth, saturated velocity growth, and chaotic development stages. At the late stage, the RTI induces a complex topology structure of the interface and a mass of dissociative drops can be significantly observed in the system. The accelerations of the bubble and spike front are also measured, and it is reported that their normalized values at the late time are, respectively, approximate to the constant values of around 0.025 and 0.027, exhibiting a terminally quadratic growth. As the Reynolds number is reduced to small ones, the multiple disturbances of the RTI are found to merge into a larger one at the initial stage. Then, the evolutional interfaces display the patterns familiar from the single-mode RTI. The phase interfaces in the whole process become very smooth without the appearance of the breakup phenomenon, and the spike and bubble velocities at the late time approach constant values. Furthermore, we also analyze the effects of the initial conditions in terms of the perturbation wavelength and amplitude, and it is found that the instability undergoes a faster growth at the intermediate stage for a larger wavelength, while the late-time bubble and spike growth rates are insensitive to the changes of the initially perturbed wavelength and amplitude.

Effect of viscosity on two-dimensional single-mode Rayleigh-Taylor instability during and after the reacceleration stage

In this paper, two-dimensional (2D) single-mode Rayleigh-Taylor instability with a low Atwood number (A = 0.15) at different Reynolds (Re) numbers (100 ≤ Re ≤ 10 000) is simulated, and the evolution of the bubble velocity and the bubble vorticity at different viscosities (or equivalently Re) after the quasisteady stage is investigated in detail. Special attention is paid for flows with a medium Reynolds number (200 ≲ Re ≲ 1000), and two new findings are summarized as follows: (1) At the reacceleration stage, we found that the vorticity near the bubble head is linearly inhibited by the viscosity. Based on this discovery, the dimensionless relationship between the vorticity intensity, viscosity, and time is formulated. (2) After the reacceleration stage, we found a new deceleration-acceleration stage, in which the bubble velocity is decelerated and accelerated repeatedly. This stage occurs because the vorticity near the bubble head is first decreased due to the inhibition of viscosity and then increased again when a pair of new Kelvin-Helmholtz instability-induced vortices approaches the bubble head. Consequently, the bubble velocity decelerates and accelerates correspondingly.