A numerical simulation of two-dimensional compressible Navier-Stokes equations using a high-order weighted essentially nonoscillatory finite difference shock capturing scheme is carried out in this paper, to study the effect of shock waves on the development of Rayleigh-Taylor instability. Shocks with different Mach numbers are introduced ahead or behind the Rayleigh-Taylor interface, and their effect on the transition to instability is demonstrated and compared. It is observed that shock waves can speed up the transition to instability for the Rayleigh-Taylor interface significantly. Stronger shocks are more effective in this speed-up process.

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