O. Sadot

Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions

(Received 6 October 2008 and in revised form 26 December 2008) An experimental and numerical systematic study of the growth of the Richtmyer– Meshkov instability-induced mixing following a re-shock is made, where the initial shock moves from the light fluid to the heavy one, over an incident Mach number range of 1.15–1.45. The evolution of the mixing zone following the re-shock is found to be independent of its amplitude at the time of the re-shock and to depend directly on the strength of the re-shock. A linear growth of the mixing zone with time following the passage of the re-shock and before the arrival of the reflected rarefaction wave is found. Moreover, when the mixing zone width is plotted as a function of the distance travelled, the growth slope is found to be independent of the re-shock strength. A comparison of the experimental results with direct numerical simulation calculations reveals that the linear growth rate of the mixing zone is the result of a bubble competition process.

Rayleigh-Taylor Growth Measurements of Three-Dimensional Modulations in a Nonlinear Regime

An understanding of the nonlinear evolution of Rayleigh-Taylor (RT) instability is essential in inertial confinement fusion and astrophysics. The nonlinear RT growth of three–dimensional (3-D) broadband nonuniformities was measured near saturation levels using x-ray radiography in planar foils accelerated by laser light. The initial 3-D target modulations were seeded by laser nonuniformities and subsequently amplified by the RT instability. The measured modulation Fourier spectra and nonlinear growth velocities are in excellent agreement with those predicted by Haans model [S. Haan, Phys. Rev. A 39, 5812 (1989)]. These spectra and growth velocities are insensitive to initial conditions. In a real-space analysis, the bubble merger was quantified by a self-similar evolution of bubble size distributions, in agreement with the Alon–Oron–Shvarts theoretical predictions [D. Oron et al. Phys. Plasmas 8, 2883 (2001)].

A general buoyancy-drag model for the evolution of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities

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.

Scaling laws of nonlinear Rayleigh-Taylor and Richtmyer-Meshkov instabilities in two and three dimensions

Abstract The late-time nonlinear evolution of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for random initial perturbations is investigated using a statistical mechanics model based on single-mode and bubble-competition physics at all Atwood numbers ( A ) and full numerical simulations in two and three dimensions. It is shown that the RT mixing zone bubble and spike fronts evolve as h ∼ α · A · gt 2 with different values of α for the bubble and spike fronts. The RM mixing zone fronts evolve as h ∼ t θ with different values of θ for bubbles and spikes. Similar analysis yields a linear growth with time of the Kelvin–Helmholtz mixing zone. The dependence of the RT and RM scaling parameters on A and the dimensionality will be discussed. The 3D predictions are found to be in good agreement with recent Linear Electric Motor (LEM) experiments.

Reshocked Richtmyer-Meshkov instability: Numerical study and modeling of random multi-mode experiments

The evolution of the three-dimensional planar Richtmyer-Meshkov (RM) instability during a two shock wave interaction (i.e., reshock) is investigated by means of comparing numerical simulations and analytical modelling with experimental results of low Mach numbers (M < 1.5) and fairly high Atwood numbers (A ∼ 0.7). The study discusses and analyses the differences in the evolution of the mixing zone for two different types of initial perturbations, namely, multi-mode random initial perturbation with a narrow or wide bubble size distribution. More specifically, the study is focused on the agreement between numerical simulations and experiments performed with an unknown random initial perturbation. Using a large set of experimental results with different reshock arrival times and Mach numbers, the numerical simulations results are compared to the experimental results for a variety of different scenarios. This methodology allows a constrained comparison, while requiring good agreement for all cases. A comprehe...

Late-time growth of the Richtmyer–Meshkov instability for different Atwood numbers and different dimensionalities

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.

Studies in the nonlinear evolution of the Rayleigh–Taylor and Richtmyer–Meshkov instabilities and their role in inertial confinement fusion

Hydrodynamic instabilities, such as the Rayleigh–Taylor and Richtmyer–Meshkov instabilities, play a central role when trying to achieve net thermonuclear fusion energy via the method of inertial confinement fusion (ICF). The development of hydrodynamic instabilities on both sides of the compressed shell may cause shell breakup and ignition failure. A newly developed statistical mechanics model describing the evolution of the turbulent mixing zone from an initial random perturbation is presented. The model will be shown to compare very well both with full numerical simulations and with experiments, performed using high power laser systems, and using shock tubes. Applying the model to typical ICF implosion conditions, an estimation of the maximum allowed target, in-flight aspect ratio as a function of equivalent surface roughness, will be derived.

Scaling in the shock–bubble interaction

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 c, 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/M 2 ) (M - 1). Experiments were performed for slow/fast (air-helium) and fast/slow (air-SF 6 ) 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.

Studies on the Nonlinear Evolution of the Richtmyer-Meshkov Instability

A statistical model predicting the evolution of turbulent mixing zone fronts was developed recently by Alon et al. It suggests that the three physical elements that govern the Rayleigh-Taylor and Richtmyer-Meshkov mixing zone evolution are the single-bubble evolution, the single-spike evolution, and the interaction between neighboring bubbles. In this paper we present an experimental investigation of these three elements in the Richtmyer-Meshkov case. The experiments were performed in a double-diaphragm shock tube. The interface evolution was studied both before and after the arrival of a secondary reflected shock. Experimental results for the single-bubble and two-bubble cases show distinct bubble and spike evolution. The results of the bubble competition, which determines the front evolution, were found to be in good agreement with both full numerical simulations and a simple potential flow model. These results strengthen the assumptions on which the statistical model is based.

Mitigation of exploding-wire-generated blast-waves by aqueous foam

In this work, we implement an exploding wire technique to generate small-scale cylindrical blast waves in aqueous foam. The exploding wire system offers an easy to operate and effective tool for studying blast-wave/foam interaction related phenomena in real explosion scenarios. The mitigation of blast waves as a function of the thickness of the foam barrier is discussed and quantified. A fluid mixture pseudo-gas based numerical approach with the aid of the point explosion theory is used to separate the mitigation mechanisms into the near- and the far-field related groups and to analyze the contribution of each group to the overall losses of the blast wave energy.