Effects of the Atwood number on three-dimensional azimuthal instability of a shock-accelerated spherical bubble

Abstract

The shock-driven evolution of a three-dimensional (3D) spherical gas bubble occurs frequently in natural phenomena and engineering applications. In the present study, the interaction between a planar shock wave and a spherical interface is investigated numerically by solving the 3D, compressible Euler equations using a fifth-order weighted essentially non-oscillatory scheme. A series of numerical cases spanning a wide range of Atwood (At) numbers is performed to examine the shock–bubble interaction (SBI), with emphasis on azimuthal instability. The results indicate that a primary vortex ring is consistently formed following shock acceleration of the spherical interface, whereas a leading vortex ring appears only in the case of heavy bubbles (At>0). As the distorted interface evolves, a pronounced At-dependent azimuthal instability emerges, exhibiting a clear modal distribution dominated by the m=4 mode: for heavy bubbles, the growth of azimuthal instability increases with increasing At number. Larger At numbers lead to stronger vortex ring formation; the accompanying shock wave reflections further reinforce the azimuthal disturbances, resulting in the growth of azimuthal modes over a broad range of scales. As the At number decreases, the azimuthal instability shifts toward the gradual amplification of small-scale perturbations. In contrast, for light bubbles (At<0), strong convective transport promotes a more pronounced development of azimuthal modes. These findings highlight the critical role of azimuthal instability in SBI beyond traditional streamwise analyses, with the dominant modal behavior consistently observed but its quantitative characteristics dependent on the adopted computational configuration.