This issue of Laser and Particle Beams contains 27 contributed articles based on presentations given at the eighth International Workshop on the Physics of Compressible Turbulent Mixing (IWPCTM) (see http://www.llnl.gov/IWPCTM), held at the California Institute of Technology, Pasadena, California from December 9 to 14, 2001, and organized jointly by the Lawrence Livermore National Laboratory (LLNL) and the California Institute of Technology. This conference is the eighth in a biennial series of conferences on the general subject of experimental, numerical, and theoretical studies of compressible turbulent mixing, initiated by LLNL in the late 1980s. Previous conferences were held in Princeton, New Jersey (1988), Pleasanton, California (1989), Royaumont, France (1991), Cambridge, United Kingdom (1993), Stony Brook, New York (1995), Marseille, France (1997), and St. Petersburg, Russia (1999). The ninth IWPCTM is to be held at the University of Cambridge in 2004.

Directed energy and turbulence structure are shown to be crucial in understanding the growth of self-similar Rayleigh–Taylor and incompressible Richtmyer–Meshkov turbulent mixing zones. Averaging over the mixing zone is used to analyze the response of a modified k–ε model and a turbulent two-fluid model. Three different transport regimes are then identified by considering self-similar variable acceleration RT flows (SSVARTs), which appear as promising reference flows for model testing.

An accurate turbulent mixing model for gravitationally induced instabilities with arbitrarily variable accelerations has been developed to capture the following physical aspects: (1) directed transport, (2) correct buoyancy forces, (3) turbulence diffusion, and (4) geometrical aspects. We present the two-structure two-fluid two-turbulence concept (2SFK), which consistently answers these requirements by identifying the large-scale transport structures in a statistical approach. An example of a 2SFK-based model is given and applied to the Rayleigh–Taylor case.

A perturbation method in which only the most secular terms are retained gives simple results for the weakly nonlinear growth of a single-mode shock-accelerated interface (Vandenboomgaerde et al., 2002). This result can be written as a series in integer powers of time. It can be considered as the Taylor expansion of an analytic function. We believe that an approximation of such a function has been identified; it described the evolution of the instability from linear to intermediate nonlinear regime. Furthermore, this function has no singularity. The relevance of this analytic formula is checked against two-dimensional simulations and experimental data.

The simplified perturbation method of Vandenboomgaerde et al. (2002) is applied to both the Richtmyer–Meshkov and the Rayleigh–Taylor instabilities. This theory is devoted to the calculus of the growth rate of the perturbation of the interface in the weakly nonlinear stage. In the standard approach, expansions appear to be series in time. We build accurate approximations by retaining only the terms with the highest power in time. This simplifies and accelerates the solution. High order expressions are then easily reachable. For the Richtmyer–Meshkov instability, multimode configurations become tractable and the selection mode process can be studied. Inferences for the intermediate nonlinear regime are also proposed. In particular, a class of homothetic configurations is inferred; its validity is verified with numerical simulations even as vortex structures appear at the interface. This kind of method can also be used for the Rayleigh–Taylor instability. Some examples are presented.

The three-dimensional (3D) turbulent mixing zone (TMZ) evolution under Rayleigh–Taylor and Richtmyer–Meshkov conditions was studied using two approaches. First, an extensive numerical study was made, investigating the growth of a random 3D perturbation in a wide range of density ratios. Following that, a new 3D statistical model was developed, similar to the previously developed two-dimensional (2D) statistical model, assuming binary interactions between bubbles that are growing at a 3D asymptotic velocity. Confirmation of the theoretical model was gained by detailed comparison of the bubble size distribution to the numerical simulations, enabled by a new analysis scheme that was applied to the 3D simulations. In addition, the results for the growth rate of the 3D bubble front obtained from the theoretical model show very good agreement with both the experimental and the 3D simulation results. A simple 3D drag–buoyancy model is also presented and compared with the results of the simulations and the experiments with good agreement. Its extension to the spike-front evolution, made by assuming the spikes' motion is governed by the single-mode evolution determined by the dominant bubbles, is in good agreement with the experiments and the 3D simulations. The good agreement between the 3D theoretical models, the 3D numerical simulations, and the experimental results, together with the clear differences between the 2D and the 3D results, suggest that the discrepancies between the experiments and the previously developed models are due to geometrical effects.

The passage of a shock wave through a spherical bubble results in the formation of a vortex ring. In the present study, simple dimensional analysis is used to show that the circulation is linearly dependent on the surrounding material speed of sound cs and the initial bubble radius R. In addition, it is shown that the velocities characterizing the flow field are linearly dependent on the speed of sound, and are independent of the initial bubble radius. The dependence of the circulation on the shock wave Mach number M is derived by Samtaney and Zabusky (1994) as (1 + 1/M + 2/M2) (M − 1). Experiments were performed for slow/fast (air-helium) and fast/slow (air-SF6) interactions. Full numerical simulations were conducted resulting in good agreement. From the results, it is seen that in both cases, according to the proposed scaling, the vortex ring velocity is bubble radius independent. The numerical results for the slow/fast interaction show that the proposed Mach scaling is valid for M < 2. Above M ≅ 2, the topology of the bubble changes due to a competition between the upstream surface of the bubble and the undisturbed shock wave.

The present article describes an experimental study that is a part of an integrated theoretical (Rikanati et al.2003) and experiential investigation of the Richtmyer–Meshkov (RM) hydrodynamic instability that develops on a perturbed contact surface by a shock wave. The Mach number and the high initial-amplitude effects on the evolution of the single-mode shock-wave-induced instability were studied. To distinguish between the above-mentioned effects, two sets of shock-tube experiments were conducted: high initial amplitudes with a low-Mach incident shock and small amplitude initial conditions with a moderate-Mach incident shock. In the high-amplitude experiments a reduction of the initial velocity with respect to the linear prediction was measured. The results were compared to those predicted by a vorticity deposition model and to previous experiments with moderate and high Mach numbers done by others and good agreement was found. The result suggested that the high initial-amplitude effect is the dominant one rather than the high Mach number effect as suggested by others. In the small amplitude–moderate Mach numbers experiments, a reduction from the impulsive theory was noted at late stages. It is concluded that while high Mach number effect can dramatically change the behavior of the flow at all stages, the high initial-amplitude effect is of minor importance at the late stages. That result is supported by a two-dimensional numerical simulation.

The growth of a single-mode perturbation is described by a buoyancy–drag equation, which describes all instability stages (linear, nonlinear and asymptotic) at time-dependent Atwood number and acceleration profile. The evolution of a multimode spectrum of perturbations from a short wavelength random noise is described using a single characteristic wavelength. The temporal evolution of this wavelength allows the description of both the linear stage and the late time self-similar behavior. Model results are compared to full two-dimensional numerical simulations and shock-tube experiments of random perturbations, studying the various stages of the evolution. Extensions to the model for more complicated flows are suggested.

Recent direct drive implosion experiments, performed on the OMEGA laser, have been analyzed by comparing full two-dimensional (2D) and one-dimensional (1D) numerical simulations. The 2D simulations result in a fusion yield higher than experimental results. A simple full-mixing model, leaving only the clean region, overestimates yield degradation. Fully turbulent mixing is expected to develop in most of the mixing region; however regions slightly beyond the radius of the most penetrating spike are expected to remain clean and to contribute to fusion yield. One can correct the mixing model by redefining the clean region. Accounting for this unmixed region results in improved agreement with experimental results. Differences in central pressure, density, temperature, and fusion rate in implosions dominated by low mode number perturbations imply that mix effects might not be limited to the mix region, and that 2D simulations are necessary to describe the large scale flow affecting the central region. The same analysis has been undertaken for implosions with different convergence ratios, but with similar initial perturbation spectra. These implosions should be compared to implosions dominated by high mode number perturbations, which might be described by models based on 1D simulations.

The late-time growth rate of the Richtmyer–Meshkov instability was experimentally studied at different Atwood numbers with two-dimensional (2D) and three-dimensional (3D) single-mode initial perturbations. The results of these experiments were found to be in good agreement with the results of the theoretical model and numerical simulations. In another set of experiments a bubble-competition phenomenon, which was observed in previous work for 2D initial perturbation (Sadot et al., 1998), was shown to exist also when the initial perturbation is of a 3D nature.

Experiments conducted on the EKAP facility at the Russian Federal Nuclear Center–VNIITF concerning the stabilization of Rayleigh–Taylor instability-induced mixing in miscible liquids by the formation of a molecular diffusion (or transitional) layer between the liquids initially were described. The experiments had an Atwood number of 1/3. The acceleration was 3500 times that of Earth's gravity, and several values of diffusion layer thickness were considered. The experiments showed that the growth of the turbulent mixing zone could be delayed by adjusting the amplitude of the initial perturbations and the characteristic thickness of the diffusion layer. This has been observed in experiments conducted with water and mercury. The mixing layer evolution was imaged using X-ray radiography.

Experiments conducted on the SOM facility at the Russian Federal Nuclear Center–VNIITF, concerning the turbulent mixing induced by the Rayleigh–Taylor instability in a three-layer system of immiscible liquids are described. The fluids are contained in a small tank 6.4 cm × 5.4 cm × 12 cm, which is accelerated vertically downward by a gas gun. The mixing layer evolution was imaged by seeding one of the fluids with particles and using a bidirectional light sheet method (refractive index matching was used to minimize measurement errors). Experiments were performed for two different accelerations (g = 350 g0 and g = 100 g0, where g0 = 980 cm/s2, and the acceleration decreases with distance traveled), and with aqueous solutions of glycerin and benzene (with density ratio 1.6). The lower, middle, and upper layers were a sodium hyposulfite–glycerin solution, a water–glycerin solution, and benzene, respectively. The glycerin solution was seeded with particles. The principal objective of the experiments was to obtain the distribution of fluid particle sizes arising from the mixing of the immiscible fluids.

The design, operation, and functionality of the multifunctional shock tube (MST) facility at the Russian Federal Nuclear Center–VNIITF are described. When complete, the versatile MST consists of three different driver sections that permit the execution of three different classes of experiments on the compressible turbulent mixing of gases induced by the (1) Richtmyer–Meshkov instability (generated by a stationary shock wave with shock Mach numbers <5), (2) Rayleigh–Taylor instability (generated by compression wave such that acceleration of the interface is <105g0, where g0 = 9.8 m/s2), and (3) combined Richtmyer–Meshkov and Rayleigh–Taylor instability (generated by a nonstationary shock wave with initial pressure at the front 5 × 106 Pa and acceleration of ≤106g0 of the interface). For each of these types of experiments, the density ratio of the gases is ρ2 /ρ1 ≤ 34. Perturbations are imposed on a thin membrane, embedded in a thin wire array of microconductors that is destroyed by an electric current. In addition, various limitations of experimental techniques used in the study of interfacial instability generated turbulent mixing are also briefly discussed.

Experiments on self-similar Rayleigh–Taylor instability-induced mixing in gases in the Earth's gravity conducted on the OSA facility at the Russian Federal Nuclear Center–VNIITF are described. These experiments are distinguished from other experiments, usually performed with immiscible liquids in a tank or with miscible liquids initially separated by a solid barrier that is retracted, in that a membrane (of ∼1 μm thickness) with liquid soap film embedded in a thin wire array (with microconductors of diameter 20 μm and with a spacing of 4 mm) initially separates the fluids. An electric current to initiate the fluid interpenetration and mixing destroys the membrane. Experiments performed for three different Atwood numbers are described: in SF6-Ar with A = 0.54, in SF6-He with A = 0.94, and in Kr-Ar with A = 0.35. Various parameters of the mixing were measured from Schlieren photographs. In particular, the dimensionless rate of mixing front growth is α = 0.078.

Experiments conducted at the OSA shock tube facility at the Russian Federal Nuclear Center–VNIITF to investigate the compressible turbulent mixing of argon and krypton gases induced by the Rayleigh–Taylor instability are described. A liquid soap film membrane of thickness ∼1 micrometer embedded in an array of microconductors is used, on which specified initial perturbations can be applied. The shock is piston driven by compressed gas. The gas interface was accelerated with an acceleration g′4 3104 m0s2. The membrane is disintegrated at the beginning of the experiment by a strong electric explosion. Imaging is performed using Schlieren photography. The dimensionless growth rate of the mixing zone was determined to be 0.04.

The interaction of the mixing zone between two gases of different densities with compression waves and shock waves has been investigated. The characteristics of the mixing zone in which the Rayleigh–Taylor instability is developing have been analyzed. The evolution of the mixing zone volume and mass during the accelerated motion has been defined. A qualitative distinction in the evolution of the mixing zone under the influence of a continuous deceleration resulting from the interaction with the reflected compression wave—shockless deceleration—is revealed as compared to deceleration that is accompanied by appearance of a shock wave moving through the mixing zone—shock-induced deceleration.

This article reports the first Richtmyer–Meshkov instability experiments using an improved version of the Atomic Weapons Establishment convergent shock tube. These investigate the shock-induced turbulent mixing across the interfaces of an air/dense gas/air region. Multipoint ignition of a detonatable gas mixture produces a cylindrically convergent shock that travels into a test cell containing the dense gas region. The mixing process is imaged with shadowgraphy. Sample results are presented from an unperturbed experiment and one with a notch perturbation imposed on one of the dense gas interfaces. The unperturbed experiment shows the mixing across the dense gas boundaries and the motion of the bulk dense gas region. Imposition of the notch perturbation produces a mushroom-shaped air void penetrating the dense gas region. Three-dimensional simulations performed using the AWE TURMOIL3D code are presented and compared with the sample experimental results. A very good agreement is demonstrated. Conducting these first turbulent mixing experiments has highlighted a number of areas for future development of the convergent shock-tube facility; these are also presented.

This article reports on the latest experiments in the series of Richtmyer–Meshkov instability (RMI) shock-tube experiments. Previous work described a double-bump experiment that evidenced some degree of unrepeatability. The present work features an enlarged perturbation introduced to improve repeatability. In common with the previous work, the experiments were conducted at shock Mach number 1.26 (70 kPa overpressure), using the Atomic Weapons Establishment 200 × 100 mm shock tube with a three-zone test cell arrangement of air/sulphur hexafluoride/air. The sulphur hexafluoride gas (SF6) was chosen for its high density (5.1 relative to air) providing an Atwood number of 0.67. Gas separation was by means of microfilm membranes, supported by fine wire meshes. A double-bump perturbation of two-dimensional geometry was superimposed on the downstream membrane representing a 0.6% addition to the dense gas volume. Visualization of the turbulent gas mixing was by laser sheet illumination of the seeded SF6 gas using a copper vapor laser pulsing at 12.5 kHz. Mie scattered light was recorded using a 35-mm rotating drum camera to capture a sequence of 50 images per experiment. Sample experimental results shown alongside corresponding three-dimensional hydrocode calculations highlight the problems in both analysis and comparison caused by multiple scattering arising from the necessary use of a high seeding concentration. Included is a demonstration of the effectiveness of introducing into the hydrocode a Monte Carlo-based simulation of the multiple scattering process. The results so derived yield greatly improved qualitative agreement with the experimental images. Quantitative analysis took the form of deriving relative intensity data from line-outs through experimental images and their code equivalents. A comparison revealed substantial agreement on major features.

This article investigates the molecular mixing caused by Rayleigh–Taylor (RT) instability of a gravitationally unstable density interface tilted at a small angle to the horizontal. The mixing is measured by the increase in background potential energy, and the mixing efficiency, or fraction of energy irreversibly lost to fluid motion doing work against gravity, is calculated. Laboratory experiments are carried out using saline and fresh water, and modeled with compressible numerical simulations, with a suitable choice of parameters and initial conditions. The experiments show that the high cumulative efficiency of mixing in RT instability at a horizontal interface is only slightly reduced by an interface tilt of up to 10°, despite the strong overturning that occurs. Instantaneous mixing efficiencies as high as 0.5–0.6 are measured, when RT instability is active, with lower values of about 0.35 during the subsequent overturning. The numerical simulations capture the most unstable scales and the overturning motion well, but generate more mixing than the experiments, with the instantaneous mixing efficiency remaining at 0.5 for most of the run. The difference may be due to restratification at small scales in the high Prandtl number experiments.