Vorticity evolution in two- and three-dimensional simulations for shock–bubble interactions

Abstract

Representative results from a series of simulations for shock–bubble interactions are presented, which contrast the evolution of the simulated flow field under axisymmetry to the evolution when symmetry is relaxed and a non-axisymmetric perturbation is imposed. The evolution is simulated using a multifluid, adaptive Eulerian Godunov code, at a resolution of 128 grid points per bubble radius. For incident shock wave Mach numbers 1.1<M<5.0, the bubble deformation and vorticity evolution in two-dimensional (2D) axisymmetric (r–z) simulations differ visibly from those in 3D Cartesian simulations, but only for scenarios in which the bubble gas density is greater than ambient density, with Atwood numbers A>0.2. For A<0.2, stable vortices persist to late time regardless of the dimensionality of the simulation. For A>0.2, coherent vortical structures persist only in 2D treatment, while vorticity fields become highly disordered in 3D simulations. However, this distinction between low and high A is absent after integration, as trends in the circulation show 10% larger values of the circulation components in 2D than in 3D, regardless of the value of A.