Two-dimensional Navier–Stokes simulations of gaseous mixtures induced by Richtmyer–Meshkov instability

Abstract

Two-dimensional numerical calculations of the fluid instability of shock-accelerated interfaces between a heavy fluid and a light one are carried out in order to simulate experiments performed by Poggi et al. [Phys. Fluids 10, 2698 (1998)]. In these experiments, the laser Doppler anemometry technique gives measurements of the fluctuating velocity. Experimental data show that a turbulent mixing zone is generated by the incident shock wave. This turbulent regime is reproduced by two-dimensional calculations. Before the first reshock, several quantities in the mixing zone, such as bubble and spike fronts, turbulent kinetic energy, enstrophy, adopt a quasi self-similar behavior versus time. In particular, we can see in numerical simulations the decay of the turbulent kinetic energy before the first reflected shock wave–mixing-zone interaction and its strong enhancement by reshocks. Furthermore, spectral analysis of the numerical results exhibit a k−3 energy spectrum. Experimental measurements also show that the turbulent boundary layers which develop on the shock-tube walls accelerate the fluid flow in the middle of the tube. Numerical simulations clearly reproduce both this acceleration and the lambda-shock structure observed in experiments.