Multicomponent Reynolds-Averaged Navier--Stokes Simulations of Reshocked Richtmyer--Meshkov Instability and Turbulent Mixing: Reshock Time and Atwood Number Effects*

Reshocked Richtmyer--Meshkov turbulent mixing of gases with various Atwood numbers and shock Mach numbers is simulated using a third-order weighted essentially nonoscillatory implementation of a $K$--$\epsilon$ multicomponent Reynolds-averaged Navier--Stokes model. First, mixing layer widths from simulations with Mach number $Ma = 1.20$, Atwood number $At = 0.67$ (air/SF$_6$), and different times of reshock are shown to be in very good agreement with the experimental data of Leinov et al. [J. Fluid Mech. \textbf{626}, 449 (2009)]. Second, widths from simulations with $Ma = 1.50$ and $At = \pm 0.21$, $\pm 0.67$ and $\pm 0.87$ (corresponding to air/CO$_2$, air/SF$_6$ and H$_2$/air) are compared to the large-eddy simulation data of Lombardini et al. [J. Fluid Mech. \textbf{670}, 439 (2011)] and discussed. Budgets of the turbulent transport equations are considered to elucidate the mechanisms contributing to turbulent mixing in reshocked Richtmyer--Meshkov instability. Convergence of the mixing layer widths, mean fields, and turbulent fields under grid refinement is also assessed.