A. Yosef-Hai’s research while affiliated with Ben-Gurion University of the Negev and other places

The hydrodynamic instability, which develops on the contact surface between two fluids, has great importance in astrophysical phenomena such as the inhomogeneous density distribution following a supernova event. In this event acceleration waves pass across a material interface and initiate and enhance unstable conditions in which small perturbations grow dramatically. In the present study, an experimental technique aimed at investigating the above-mentioned hydrodynamic instability is presented. The experimental investigation is based on a shock-tube apparatus by which a shock wave is generated and initiates the instability that develops on the contact surface between two gases. The flexibility of the system enables one to vary the initial shape of the contact surface, the shock-wave Mach number, and the density ratio across the contact surface. Three selected sets of shock-tube experiments are presented in order to demonstrate the system capabilities: (1) large-initial amplitudes with low-Mach-number incident shockwaves; (2) small-initial amplitudes with moderate-Mach-number incident shock waves; and (3) shock bubble interaction. In the large-amplitude experiments a reduction of the initial velocity with respect to the linear growth prediction was measured. The results were compared to those predicted by a vorticity-deposition model and to previous experiments with moderate- and high-Mach number incident shock waves that were conducted by others. In this case, a reduction of the initial velocity was noted. However, at late times the growth rate had a 1/t behavior as in the small-amplitude low-Mach number case. In the small-amplitude moderate-Mach number shock experiments a reduction from the impulsive theory was noted at the late stages. The passage of a shock wave through a spherical bubble results in the formation of a vortex ring. Simple dimensional analysis shows that the circulation depends linearly on the speed of sound of the surrounding material and on the initial bubble radius.

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 · gt2 with different values of α for the bubble and spike fronts. The RM mixing zone fronts evolve as h ∼ tθ with different values of θ for bubbles and spikes. Similar analysis yields a linear growth with tune 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.

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.

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 [congruent with] 2, the topology of the bubble changes due to a competition between the upstream surface of the bubble and the undisturbed shock wave.

Using a statistical mechanics bubble competition model, Alon et al. (1994,1995) have shown that the two-dimensional Rayleigh-Taylor (RT) mixing zone bubble and spike fronts evolves as h=alpha (B/S).A.g.t(2) with alpha (B)similar to0.05 and alpha (S)similar to alpha (s). (1+A). The Richtmyer-Meshkov (RM) mixing zone fronts have been found to evolve as h=a(0).t(theta) with different theta's for bubble and spikes. The model predictions were theta (B)similar to0.4 and theta (S) similar to theta (B) at low A's and rises to 1.0 for A close to 1. Full 2D numerical simulations confirmed these scaling laws. Recent experimental results (Dimonte, 1999,2000) have indicated similar scaling laws of the mixing zone evolution, but there were some discrepancies in the values of the scaling parameters, mainly in the value of theta (B) and the similarity parameter, h/< lambda >. It will be shown, based on full 3D numerical simulations, a Layzer type model acid a 3D statistical-mechanics model that these discrepancies are mainly the effect of dimensionality. Accounting for the 3D nature of the problem results in scaling parameters that are very similar to the experimental values. The 3D single mode evolution, used in this model, was confirmed by shock tube experiments.

In order to verify the predictions of the 2D high Atwood number potential flow model for the evolution of the shock wave induced Richtmyer-Meshkov instability,(1) shock-tube experiments were performed with a single-mode perturbation and two competing bubbles as the initial conditions.(2) The experimental results were compared to theoretical model and to numerical simulation. In the present work the dependence of the instability on the Atwood number and the dimensionality of the instability were investigated in a shock tube apparatus. A high speed schlieren photography system were used to monitor the evolution of the unstable contact surface. Different Atwood numbers were achieved by using different gases. The results of those experiments were found to be in very good agreement with the predictions of theoretical model and numerical simulation. These results verify the key elements of the Atwood number scaling of the bubble-merger model used for the prediction of the multi-mode bubble and spike front evolution at all Atwood numbers. The dimensionality investigation of the instability evolution was done using a pyramid like initial perturbation. The results reveal the same two key elements of the bubble-merger model to describe the bubble and spike front evolution as in the 2D case(2) except for different scaling constants.

Recent high Mach number experiments of Aleshin et al. (1997) and Dimonte (1996, 2000) show a slower initial growth of the Richtmyer-Meshkov instability, compared with the Richtmyer impulsive model (1960). Holmes et al. (2000) suggest that the large reduction of the perturbation growth rate can be attributed to the high Mach number or to the large initial ratio of amplitude to wavelength. In the present work, shock tube experiments were performed at low Mach number to investigate this effect. A single mode initial perturbation with a relatively large ratio of amplitude to wavelength (0.25 to 0.4) was imposed on the interface between air and SF6. An M=1.2 shock wave initiated the instability at this interface. Our experiments belong to the irregular group, as defined by Aleshin et al., who considered three categories: soft, hard and irregular. We model the irregular case using a vortex description based on Samatane and Zabusky (1995). The results agree with the shock tube experiments. We use other models to describe the soft and the hard categories. The soft case model is described by the well known impulsive model with no velocity reduction. The hard case is explained by the ``wall effect'' according to the shock interface proximity (Rikanaty et al. 2000). These models, which agree with previous experimental results, assume potential flow and suggest that compressibility has a small effect on the instability development, even at early stages. Full 2D numerical simulations agree with these observations.

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·gt2 with different values of α for the bubble and spike fronts. The RM mixing zone fronts evolve as h∼tθ 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.RésuméL'évolution non linéaire, à long terme, des instabilités Rayleigh–Taylor (RT) et Richtmyer–Meskov (RM) à perturbations initiales aléatoires est étudiée au moyen d'un modèle de mécanique statistique basé sur la compétition de bulles ayant tous les nombres d'Atwood ( A ), et à l'aide de simulations numériques complètes à deux et trois dimensions. Les résultats montrent que les fronts de la zone de mélange RT de bulles et d'aiguilles varient comme h∼αA·gt2 avec différentes valeurs de α pour les fronts de bulles et d'aiguilles. Les fronts de la zone de mélange RM varient comme h∼tθ avec différentes valeurs de θ pour les bulles et pour les aiguilles. Une analyse similaire donne une croissance linéaire en fonction du temps pour la zone de mélange Kelvin–Helmholtz. La dépendance des paramètres d'échelle RT et RM en fonction de A et de la dimension est discutée. Les prédictions des simulations à trois dimensions sont en bon accord avec des expériences récentes.

In a recent theoretical [Phys. Rev. Lett. 74, 534 (1995)] and experimental work [Phys. Rev. Lett. 80, 1654 (1998)] it was shown that the evolution of shock wave induced 2D Richtmyer-Meshkov (RM) instability can be predicted by using bubble-merger statistical-mechanics models which is based on two fundamental features: the evolution of a single mode through the linear, non-linear and asymptotic stages and the non-linear interaction between two neighboring bubbles. In the present study this work was extended to describe the evolution of 3D RM instability. The dimensionality dependence was investigated in M ~1.2 shock tube apparatus. Single bubble and two competing bubble initial conditions were imposed on the contact surface using a very thin membrane. The amplitudes and wavelengths were chosen to match the ones used in the 2D experiments. The experimental results were compared with theoretical models and numerical simulations. The results reveal the same two key features of the bubble-merger model to describe the bubble and spike front evolution as in the 2D case except for different scaling constant, which depend on the dimensionality and give rise to differences in the scaling law parameters [D. Shvarts et al. IFSA conference 1999, France] ,[D. Shvarts et al.1999, present conference].