Numerical simulation of the Richtmyer-Meshkov instability in initially nonuniform flows and mixing with reshock

Based on previous instability experiments of the double mode perturbed interface in initially nonuniform flows, we numerically investigate the effect of the nonuniformity of flows on the evolution of instability in a nonlinear regime after reshock by adopting two different nonuniform coefficients (δ_{1} = 0.6162 and δ_{2} = 0.4961) in the Gaussian distribution of the initial nonuniform density. We obtain the evolution of the mixing zone width and vortex structure of the air-SF_{6} interface and compare the circulation discrepancies of the nonuniform and uniform flows before and after reshock. These results indicate that the nonuniformity of the initial flow has great effect on the evolution of instability in the linear regime and the weak nonlinear regime prior to reshock. However, the mixing layer has little dependence on the nonuniformity of the initial flow in the nonlinear regime after reshock; namely, the effect of the nonuniformity is reduced significantly as the instability enters the strongly nonlinear regime after reshock. Although the growth rate of the perturbations has a significant increase, the characteristics of the flow like the mixing width, vorticity, and circulation are close to those of a uniform flow.