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 soundcsand the initial bubble radiusR. 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 numberMis 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 forM< 2. AboveM≅ 2, the topology of the bubble changes due to a competition between the upstream surface of the bubble and the undisturbed shock wave.

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 shock waves;(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.

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