Shock-accelerated dynamics of heavy rectangular bubbles: Influence of aspect ratio on Richtmyer–Meshkov instability

Physics of Fluids, vol. 37

Abstract

A systematic numerical investigation of the Richtmyer–Meshkov (RM) instability in shock-accelerated square and rectangular SF6 bubbles with varying aspect ratios is presented. Simulations are performed using a high-order discontinuous Galerkin method to resolve interface deformation, vorticity generation, and instability amplification. Building on our earlier study of shock-driven instabilities in square and rectangular light-gas bubbles [Singh and Torrilhon, Phys. Fluids 35, 012117 (2023)], the present work provides deeper physical insight into geometry-dependent mechanisms. The results demonstrate that bubble aspect ratio has a decisive influence on shock focusing, baroclinic vorticity deposition, and the onset of nonlinear structures. Horizontally elongated bubbles enhance confinement of transmitted shocks and circulation growth, while vertical elongation stabilizes the interface and delays nonlinear evolution. Quantitative diagnostics derived from the vorticity transport equation reveal that dilatation-induced and baroclinic contributions are amplified in horizontal configurations but suppressed in vertical ones. The evolution of enstrophy further indicates that horizontal elongation accelerates vortex roll-up, jet penetration, and transition toward turbulence-like dynamics, whereas vertical elongation promotes long-lived columnar vortices with reduced secondary instabilities. Interface-based measures of displacement, width, and height confirm these trends and establish clear links between geometry and instability growth.

Authors 2

1. Satyvir Singh Aachen Institute for Applied and Computational Mathematics

   RWTH Aachen University · Graphic Era University

   Affiliation as printed

   Department of Mathematics, Graphic Era Deemed to be University 2 , Dehradun,

   Institute for Applied and Computational Mathematics, RWTH Aachen University 1 , 52062 Aachen,

2. Manuel Torrilhon Aachen Institute for Applied and Computational Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute for Applied and Computational Mathematics, RWTH Aachen University 1 , 52062 Aachen,