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.