  The Richtmyer-Meshkov (RM) instability has long been an interesting subject
due to its fundamental significance in scientific research, as well as its
crucial role in engineering applications. In this study, the contribution of
shock Mach number on the evolution of the RM instability induced by a
shock-accelerated square light bubble is investigated numerically. The square
bubble is composed of helium gas and the surrounding (ambient) gas is nitrogen.
Three cases of incident shock strength are considered: Ms = 1.21, 1.7, and 2.1.
An explicit mixed-type modal discontinuous Galerkin scheme with uniform meshes
is employed to numerically solve a two-dimensional system of unsteady
compressible Navier--Stokes--Fourier equations. The numerical results show that
the shock Mach number plays an important role during the interaction between a
planar shock wave and a square light bubble. The shock Mach number causes
significant changes in flow morphology, resulting in complex wave patterns,
vorticity generation, vortex formation, and bubble deformation. In contrast to
low Mach numbers, high Mach numbers produce the larger rolled-up vortex chains,
larger inward jet formation, and a stronger mixing zone with greater expansion.
The effects of Mach numbers are explored in detail through phenomena such as
the vorticity generation, and evolutions of enstrophy as well as dissipation
rate. Finally, the Mach number effects on the time-variations of the shock
trajectories and interface features are comprehensively analyzed.
