Classical Rayleigh-Taylor Instability Research Articles

A fast dynamic smooth adaptive meshing scheme with applications to compressible flow

We develop a fast-running smooth adaptive meshing (SAM) algorithm for dynamic curvilinear mesh generation, which is based on a fast solution strategy of the time-dependent Monge-Ampère (MA) equation, det⁡∇ψ(x,t)=G∘ψ(x,t). The novelty of our approach is a new so-called perturbation formulation of MA, which constructs the solution map ψ via composition of a sequence of near-identity deformations of a reference mesh. Then, we formulate a new version of the deformation method [21] that results in a simple, fast, and high-order accurate numerical scheme and a dynamic SAM algorithm that is of optimal complexity when applied to time-dependent mesh generation for solutions to hyperbolic systems such as the Euler equations of gas dynamics. We perform a series of challenging 2D and 3D mesh generation experiments for grids with large deformations, and demonstrate that SAM is able to produce smooth meshes comparable to state-of-the-art solvers [22,18], while running approximately 200 times faster. The SAM algorithm is then coupled to a simple Arbitrary Lagrangian Eulerian (ALE) scheme for 2D gas dynamics. Specifically, we implement the C-method [64,65] and develop a new ALE interface tracking algorithm for contact discontinuities. We perform numerical experiments for both the Noh implosion problem as well as a classical Rayleigh-Taylor instability problem. Results confirm that low-resolution simulations using our SAM-ALE algorithm compare favorably with high-resolution uniform mesh runs.

Richardson and Reynolds number effects on the near field of buoyant plumes: flow statistics and fluxes

The near-field characteristics of highly buoyant plumes, commonly referred to as lazy plumes, remain relatively poorly understood across a range of flow conditions, particularly compared with our understanding of far-field characteristics. Here, we perform fully resolved three-dimensional numerical simulations of round helium plumes to characterize the effects of different inlet Richardson, ${Ri}_0$ , and Reynolds, ${Re}_0$ , numbers on first- and second-order statistical moments as well as average vertical fluxes in the near field. For sufficiently high ${Re}_0$ at a particular ${Ri}_0$ , heavy air can penetrate the core of the plume, reminiscent of spikes in the classical Rayleigh–Taylor instability. In the most turbulent simulation, this penetration becomes so strong that a recirculation zone forms along the centreline of the plume. Vertical fluxes are found to scale linearly with vertical distance from the plume inlet, consistent with experimental and numerical observations (Jiang & Luo, Flow Turbul. Combust., vol. 64, 2000, pp. 43–69; Kaye & Hunt, Intl J. Heat Fluid Flow, vol. 30, 2009, pp. 1099–1105). We analytically derive this linear scaling from the governing equations by making a radial entrainment hypothesis whereby ambient fluid is entrained, on average, only in the radial direction at a finite distance from the inlet. Through this derivation, we identify physical mechanisms that can cause these relationships to remain only approximately valid for the present simulations. Lastly, we identify near-field power-law scaling relations for the flux magnitudes based on ${Ri}_0$ , and also examine vertical profiles of the non-dimensional Richardson number flux. Ultimately, insights from the present simulations are used to define near-, intermediate- and far-field regions in buoyant plumes.

Effect of ablation on the nonlinear spike growth for the single-mode ablative Rayleigh–Taylor instability

The effect of ablation on the nonlinear spike growth of single-mode ablative Rayleigh–Taylor instability (RTI) is studied by two-dimensional numerical simulations. It is shown that the ablation can reduce the quasi-constant velocity and significantly suppress the reacceleration of the spike in the nonlinear phase. It is also shown that the spike growth can affect the ablation-generated vorticity inside the bubble, which further affects the nonlinear bubble acceleration. The vorticity evolution is found to be correlated with the mixing width (i.e., the sum of the bubble and spike growths) for a given wave number and ablation velocity. By considering the effects of mass ablation and vorticity, an analytical model for the nonlinear bubble and spike growth of single-mode ablative RTI is developed in this study. It is found that the nonlinear growth of the mixing width, induced by the single mode, is dominated by the bubble growth for small-scale ablative RTI, whereas it is dominated by the spike growth for classical RTI.

Kinetic interpretation of the classical Rayleigh-Taylor instability.

Rayleigh-Taylor (RT) instabilities are prevalent in many physical regimes ranging from astrophysical to laboratory plasmas and have primarily been studied using fluid models, the majority of which have been ideal fluid models. This work presents a five-dimensional (two spatial dimensions, three velocity space dimensions) simulation using the continuum-kinetic model to study the effect of the collisional mean free path and transport on the instability growth. The continuum-kinetic model provides noise-free access to the full particle distribution function permitting a detailed investigation of the role of kinetic physics in hydrodynamic phenomena such as the RT instability. For long mean free path, there is no RT instability growth, but as collisionality increases, particles relax towards the Maxwellian velocity distribution, and the kinetic simulations reproduce the fluid simulation results. An important and novel contribution of this work is in the intermediate collisional cases that are not accessible with traditional fluid models and require kinetic modeling. Simulations of intermediate collisional cases show that the RT instability evolution is significantly altered compared to the highly collisional fluidlike cases. Specifically, the growth rate of the intermediate collisionality RT instability is lower than the high collisionality case while also producing a significantly more diffused interface. The higher moments of the distribution function play a more significant role relative to inertial terms for intermediate collisionality during the evolution of the RT instability interface. Particle energy flux is calculated from moments of the distribution and shows that transport is significantly altered in the intermediate collisional case and deviates much more so from the high collisionality limit of the fluid regime.

The early-time dynamics of Rayleigh-Taylor mixing with a premixed layer

The early-time dynamics of Rayleigh-Taylor instability with a premixed density gradient layer was investigated by three-dimensional implicit large eddy simulation. Compared with the classic Rayleigh-Taylor instability, it was found that the mixing layer undergoes an inactive stage when the mixing width of the layer is nearly unchanged. The development of hydrodynamic instability with a premixed layer was studied. Energy transfer and vortex generation at the early time show that span-wise vortices predominate at this stage. Afterwards, initial conditions including the parameters of initial perturbations and the mixing width of premixed layer were investigated in detail. In our study, it was found that the amplitude of initial perturbations and the width of premixed layer are important for determining the characteristic time scale of the inactive stage while the wave number has less effect. The influence of initial conditions on the early-time dynamics of mixing layer was also analysed.

Extended computation of the viscous Rayleigh-Taylor instability in a horizontally confined flow.

In this article, the classical Rayleigh-Taylor instability is extended to situations where the fluid is completely confined, in both the vertical and horizontal directions. This article starts with the two-dimensional (2D) viscous periodic case with finite height where the effect of adding surface tension to the interface is analyzed. This problem is simulated from a dual perspective: first, the linear stability analysis obtained when the Navier-Stokes equations are linearized and regularized in terms of density and viscosity; and second, looking at the weakly compressible version of a multiphase smoothed particle hydrodynamics (WCSPH) method. The evolution and growth rates of the different fluid variables during the linear regime of the SPH simulation are compared to the computation of the eigenvalues and eigenfunctions of the viscous version of the Rayleigh-Taylor stability (VRTI) analysis with and without surface tension. The most unstable mode, which has the maximal linear growth rate obtained with both approaches, as well as other less unstable modes with more complex structures are reported. The classical horizontally periodic (VRTI) case is now adapted to the case where two additional left and right walls are included in the problem, representing the cases where a two-phase flow is confined in a accelerated tank. This 2D case where no periodic assumptions are allowed is also solved using both techniques with tanks of different sizes and a wide range of Atwood numbers. The agreement with the linear stability analysis obtained by a Lagrangian method such as multiphase WCSPH is remarkable.

Numerical investigations of Rayleigh–Taylor instability with a density gradient layer

The Rayleigh-Taylor instability (RTI) with a density gradient layer was investigated by implicit large eddy simulations (ILES) in a framework of three dimensional compressible multiphase flow with the single fluid approximation. The simulations are firstly initialized by multi-mode random perturbations in classic RTI and the associated case with a premixed layer. It is found that the late time behaviours of the turbulent mixing layer in classic and premixed cases are similar although an initial premixed layer slows down the growth of the turbulent mixing layer significantly. A variety of flow quantities for different cases are compared and studied at different time. In addition, the turbulent mixing caused by RTI with a single-mode dominated perturbation is investigated in classic and premixed cases. Different stages are identified for the time evolution of turbulent mixing layer. The dynamics of bubble-spike structures at early time, and the production and transfer of turbulent kinetic energy at late time are expatiated. Typical quantities of turbulent mixing are also summarized. It is found that there is an inactive stage before the fast growth of bubble-spike structures with an initial premixed layer and the spectra need more time to adjust until the flow turns to a self-similar regime.

Nonlinear bubble competition of the multimode ablative Rayleigh–Taylor instability and applications to inertial confinement fusion

The self-similar nonlinear evolution of the multimode ablative Rayleigh–Taylor instability (RTI) and the ablation-generated vorticity effect are studied for a range of initial conditions. We show that, unlike classical RTI, the nonlinear multimode bubble-front evolution remains in the bubble competition regime due to ablation-generated vorticity, which accelerates the bubbles, thereby preventing a transition into the bubble-merger regime. We develop an analytical bubble competition model to describe the linear and nonlinear stages of ablative RTI. We show that vorticity inside the multimode bubbles is most significant at small scales with large initial perturbation. Since these small scales persist in the bubble competition regime, the self-similar growth coefficient αb can be enhanced by up to 30% relative to ablative bubble competition without vorticity effects. We use the ablative bubble competition model to explain the hydrodynamic stability boundary observed in OMEGA low-adiabat implosion experiments.

Multi-mode hydrodynamic evolution of perturbations seeded by isolated surface defects

Inherently multi-mode evolution of isolated defects, such as straight grooves and axisymmetric dots on planar laser targets, is studied theoretically. The development of perturbations is considered for a propagating rippled shock front, a material interface subject to the classical Richtmyer–Meshkov instability (RMI), a rippled rarefaction wave produced by the feedout process, an ablation front subject to the ablative RMI, and a thin fluid layer subject to the classical Rayleigh–Taylor instability (RTI). For the small-amplitude regime, we have established specific characteristics of the perturbation evolution initiated with such defects, scaling, and conservation laws governing it. The main features of the nonlinear growth of the classical and ablative RTI starting from isolated defects are the lateral expansion of the bubbles and the oblique with respect to the direction of the acceleration, ejection of spikes. It results in filling up the void left from the bubble growth by the laterally converging spike material. This effect, first discovered in simulations by Dahlburg et al. [Phys. Fluids B 5, 571 (1993)], and very recently observed by Zulick et al. [Phys. Rev. Lett. 125, 055001 (2020)], is captured by the appropriate modification of the Ott–Basko thin-layer classical RTI theory for arbitrary defect profiles. Predictions for novel hydrodynamic experiments on multi-mode hydrodynamic perturbation evolution are presented.

Evolution of Rayleigh-Taylor instability under interface discontinuous acceleration induced by radiation.

Rayleigh-Taylor instability (RTI) under radiation background is commonly found in both engineering applications and natural phenomena. In the optically thin and incompressible limit, the corresponding problem can be simplified as an interface discontinuous acceleration (IDA) RTI problem, but to date has only been studied in the linear stage. In this paper, the entire IDA-RTI evolution was studied numerically and theoretically, particularly for the stages beyond the linear stage. The results show that the IDA-RTI problem is equivalent to the classical RTI with the effective acceleration g_{eff}^{*} that is introduced in this work. Moreover, our studies further show that IDA-RTI can occur if and only if g_{eff}^{*}>0 (from heavy fluid to light fluid). This criterion means that IDA-RTI can occur when (i) heavy fluid supports (or accelerates) the light fluid or (ii) the two fluids have the same density, in contrast to the classical RTI problem. Moreover, the quasisteady bubble and spike velocities are theoretically predicted with quantitative accuracy, showing good agreement with the results of numerical simulations in a wide range of density ratios and acceleration configurations.

A study of bubble growth in the compressible Rayleigh–Taylor and Richtmyer–Meshkov instabilities

Within the framework of modified Layzer-type potential flow theory [V. N. Goncharov, “Analytical model of nonlinear, single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers,” Phys. Rev. Lett. 88, 134502 (2002)], we study bubble growth in compressible Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities. It is known from adiabatic equations that the density ρ and adiabatic index γ are compressibility-related factors for a given static pressure p. Here, we introduce a dynamically varying stagnation point pressure P̃=p±12ρ̃η̇02, which relates time-varying quantities, such as fluid density ρ̃, pressure P̃, and bubble tip velocity η̇0, and then, we analytically derive the governing equations for time evolution of bubbles in the RT and RM instabilities of compressible fluids. For the RT instability, the upper fluid adiabatic index γu and density ρu increase the bubble amplitude and velocity, but they decrease the bubble curvature radius at the early stage, while the lower fluid adiabatic index γl and density ρl have opposite effects on those of γu and ρu, which is consistent with recent results. For the RM instability, γu and ρu decrease the bubble amplitude and velocity, but they increase the bubble curvature radius at the early stage; however, γl and ρl have opposite effects on those of γu and ρu. Moreover, we find a good agreement between our three-dimensional results of the RM bubble amplitude and recent numerical simulations.

Interaction of an accelerating layer with a cloud: formation of tails and cumulative jets

ABSTRACT We consider the penetration of spherical dense cloud into a planar layer of gas that is in gravitational equilibrium in a constant field of gravity with acceleration W. We take into account the compressibility of the medium in contrast to the classical problem of a drop falling on the surface of an incompressible fluid. Our goal is to study the formation of cumulative jets in relation to the conditions on the borders of H ii regions. We determine those features of motion that would distinguish jet streams from inhomogeneities of a different origin. Our simulation has shown that cumulative jets may arise in the presence of an acceleration layer W. The gas in jet moves in the direction opposite to the initial velocity Vc. At the same time, there are both a cumulative jet and tails, teardrop-shaped condensations, caused, respectively, by gas inflow in the wake behind the cloud and the classical Rayleigh–Taylor instability. We assume the model, according to which the H ii RCW 82 region formed in an initially homogeneous cloud. In framework of this model, we estimated the characteristic time of a cumulative jet formation ts ≈ 0.15 Myr. This is less than the present age of the H ii RCW 82 region, which is about 0.4 Myr. From the obtained estimates, it follows that the conditions at the periphery of the H ii RCW 82 region are favourable for the manifestation of cumulative effects on scales of ∼1.4 × 1017 cm, which are significantly smaller than the layer thickness.

A multiscale model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities

We develop a novel multiscale model of interface motion for the Rayleigh-Taylor instability (RTI) and Richtmyer-Meshkov instability (RMI) for two-dimensional, inviscid, compressible flows with vorticity, which yields a fast-running numerical algorithm that produces both qualitatively and quantitatively similar results to a resolved gas dynamics code, while running approximately two orders of magnitude (in time) faster. Our multiscale model is founded upon a new compressible-incompressible decomposition of the velocity field u=v+w. The incompressible component w of the velocity is also irrotational and is solved using a new asymptotic model of the Birkhoff-Rott singular integral formulation of the incompressible Euler equations, which reduces the problem to one spatial dimension. This asymptotic model, called the higher-order z-model, is derived using small nonlocality in the asymptotic parameter, allows for interface turn-over and roll-up, and yields a significant simplification for the equation describing the evolution of the amplitude of vorticity. This incompressible component w of the velocity controls the small scale structures of the interface and can be solved efficiently on fine grids. Meanwhile, the compressible component of the velocity v remains continuous near contact discontinuities and can be computed on relatively coarse grids, while receiving subgrid scale information from w. We first validate the incompressible higher-order z-model by comparison with classical RTI experiments as well as full point vortex simulations. We then consider both the RTI and the RMI problems for our multiscale model of compressible flow with vorticity, and show excellent agreement with our high-resolution gas dynamics solutions.

Mode-coupling branches in single-mode classical Rayleigh-Taylor instability for arbitrary Atwood numbers

Abstract In this research, the effect of the mode-coupling branches/channels on harmonic amplitudes in single-mode classical Rayleigh-Taylor instability for arbitrary Atwood numbers in the weakly nonlinear stage is investigated by employing the tracking technology of the mode coupling up to the fifth order. When the effect of the mode-coupling channels is not taken into account (i.e., this effect is automatically merged in the derivation process), our results are the same as the first five-order results from the prediction of previous literatures within the framework of tenth-order perturbation theory (Liu et al., 2012). In the progress of the mode coupling, the tracking technology of the channel parameters equal to constant 1 is used and all the mode-coupling channels are distinctly extracted. It is found that the nth-harmonic amplitude with mth order mainly depends on f m , n factor. However, this factor comes from different mode-coupling branches which are either constant or variable with Atwood numbers A. For the channels with A, they can either strengthen or inhibit the growth of the relevant harmonic. For some channels, they are closed all the time for some fixed A.

From ICF to laboratory astrophysics: ablative and classical Rayleigh–Taylor instability experiments in turbulent-like regimes

Rayleigh–Taylor instability (RTI) occurs whenever fluids of different densities are accelerated against the density gradient, as is the case for the target ablator in ICF implosions. The advent of megajoule class lasers, like the National Ignition Facility (NIF) or Laser Mégajoule, offers novel opportunities to study turbulent mixing flows in high energy density plasmas for fundamental hydrodynamics or laboratory astrophysics experiments. Here, we review different RTI experiments, performed either at the ablation front or at a classical embedded interface. A two-dimensional bubble-merger, bubble-competition regime was evidenced for the first time at the ablation front in indirect-drive on the NIF thanks to an unprecedented long x-ray drive. Similarly, a novel large-area, planar platform enables the capabilities to perform long duration direct drive hydrodynamics experiments on NIF. Starting from imprinted seeds, a three-dimensional bubble-merger regime was also observed in direct-drive, as larger bubbles overtook and merged with smaller bubbles. In the astrophysical context, RTI also plays a role in supernova (SN) explosions, either of Type Ia or II. We report on experiments performed on the LULI2000 facility studying RTI in scaled laboratory conditions relevant for the physics of young SN remnants. Using a light CH foam as a deceleration medium, we measured, for the first time, the RTI mixing zone by PW transverse radiography.

Surface Tension Effect on Harmonics of Rayleigh-Taylor Instability

Using the method of the parameter expansion up to the third order, explicitly investigates surface tension effect on harmonics at weakly nonlinear stage in Rayleigh-Taylor instability (RTI) for arbitrary Atwood numbers and compares the results with those of classical RTI within the framework of the third-order weakly nonlinear theory. It is found that surface tension strongly reduces the linear growth rate of time, resulting in mild growth of the amplitude of the fundamental mode, and changes amplitudes of the second and third harmonics, as is expressed as a tension factor coupling in amplitudes of the harmonics. On the one hand, surface tension can either decrease or increase the space amplitude; on the other hand, surface tension can also change their phases for some conditions which are explicitly determined.

Prediction of two-dimensional dripping onset of a liquid film under an inclined plane

Falling films flowing down a vertical plane are unstable due to inertial effects. This instability, first studied by Kapitza in 1948, is always of convective nature. Films flowing underneath an inclined plane are additionally destabilized by gravity as in the classical Rayleigh–Taylor instability for an horizontal plane. In such a situation, the instability can be of absolute nature if the plane is sufficiently inclined from the vertical. Thus, the unstable falling film exhibits an absolute/convective transition, as it has been shown recently using first a lubrication equation, and then a set of equations which include inertia and second-order viscous terms, referred to as the Weighted Residual Integral Boundary Layer (WRIBL) model. Experimental observations suggest that the absolute/convective transition corresponds roughly to the limit of dripping. This study investigates numerically the dripping limit by comparing stationary waves of the WRIBL model to numerical solutions of the Navier–Stokes equations. It is shown that this limit can be characterized by two alternative arguments: i) a secondary instability of stationary solutions of the model, or a loss of stationary solutions if the full expression of the interface curvature is used, and ii) a critical value of the area enclosed in a wave period that provides a sufficient mass for dripping.

Improved thin layer model of classical Rayleigh-Taylor instability for the deformation of interface

The thin shell (layer) configuration is adopted in inertial-confinement fusion (ICF) implosions. The weakly nonlinear deformation of the thin shell significantly influences the performances of implosion acceleration and fusion ignition, which is an important issue for the study of ICF physics. Based on the thin layer model of Ott (Ott E 1972 Phys. Rev. Lett. 29 1429), an improved thin layer model is proposed to describe the deformation and nonlinear evolution of the perturbed interface induced by the Rayleigh-Taylor instability (RTI). Differential equations describing motion are obtained by analyzing the forces of fluid elements (i.e., Newton's second law), which are then solved by numerical method. Then the position of the perturbed interface with an initial perturbation can be obtained. The linear growth rate obtained from our thin layer approximation agrees with that from the classical RTI. For fixed Atwood number (wave number), the total amplitudes of the bubble and spike obtained from the improved thin layer model agree with those from the three-order weakly nonlinear model. In addition, we compare the deformation and evolution of the layer from our model with results of the numerical simulation. In the linear regime, the amplitudes of the bubble and spike obtained from our model agree with those from the numerical simulation. And the evolution of the perturbed interface obtained from the improved thin layer model is consistent with that from the numerical simulation. In the nonlinear regime, the evolution trends of the total amplitude of the bubble and spike for both the improved thin layer model and numerical results are the same. However, the amplitude of the bubble is obviously greater than that of the spike in the later stage of the perturbation. This is because of some shortcomings in the improved thin layer model. The first shortcoming is that ignoring the dynamical pressure in the pressure difference. In fact, the shear velocity of the fluids plays an important role in the nonlinear regime of the perturbation. The second shortcoming is that the surface area of the upper interface equals the lower interface in the whole perturbation process of the present model. Thus, the present model can be used to describe the nonlinear evolution of the perturbed interface before the mushroom structure. Finally, it is worth noting that the improved thin layer model can be used to describe the deformation and nonlinear evolution of a thin layer for arbitrary Atwood number with a perturbation of large initial amplitude and arbitrary distribution. The initial perturbations of the triangular and rectangular waves are also discussed.

Three-dimensional Rayleigh–Taylor instability under a unidirectional curved substrate

We investigate the Rayleigh–Taylor instability of a thin liquid film coated on the inside of a cylinder whose axis is orthogonal to gravity. We are interested in the effects of geometry on the instability, and contrast our results with the classical case of a thin film coated under a flat substrate. In our problem, gravity is the destabilizing force at the origin of the instability, but also yields the progressive drainage and stretching of the coating along the cylinder’s wall. We find that this flow stabilizes the film, which is asymptotically stable to infinitesimal perturbations. However, the short-time algebraic growth that these perturbations can achieve promotes the formation of different patterns, whose nature depends on the Bond number that prescribes the relative magnitude of gravity and capillary forces. Our experiments indicate that a transverse instability arises and persists over time for moderate Bond numbers. The liquid accumulates in equally spaced rivulets whose dominant wavelength corresponds to the most amplified mode of the classical Rayleigh–Taylor instability. The formation of rivulets allows for a faster drainage of the liquid from top to bottom when compared to a uniform drainage. For higher Bond numbers, a two-dimensional stretched lattice of droplets is found to form on the top part of the cylinder. Rivulets and the lattice of droplets are inherently three-dimensional phenomena and therefore require a careful three-dimensional analysis. We found that the transition between the two types of pattern may be rationalized by a linear optimal transient growth analysis and nonlinear numerical simulations.

Nonlinear saturation of Rayleigh-Taylor instability in a finite-thickness fluid layer

Nonlinear amplitude saturation (NAS) of the fundamental mode of Rayleigh–Taylor instability (RTI) in a finite-thickness incompressible fluid layer is investigated analytically by considering high-order corrections (HOCs) up to the ninth order. The results of classical RTI [Liu et al., Phys. Plasmas 19, 042705 (2012)] can be recovered for the normalized fluid thickness kd→∞. It is found that the NAS of the fundamental mode on the lower and upper interfaces is clearly larger than its third-order counterpart [Wang et al., Phys. Plasmas 21, 122710 (2014)] when the HOCs are considered, especially for the lower (linearly unstable) interface. Furthermore, the NAS on both interfaces exhibits the trend of convergence with increasing order of corrections.