The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability

We investigate the late-time Richtmyer–Meshkov instability (RMI) growth of sinuous perturbations on an air/sulphur hexafluoride interface (Atwood number, $A \sim 0.67$) subjected to a Mach 1.2 planar shock wave at Los Alamos National Laboratory's vertical shock tube facility. Interface perturbations are established using a novel membraneless technique where cross-flowing air and SF$_6$ separated by an oscillating splitter plate create a perturbed density interface. The interface formed has multi-modal features and residual small perturbations, however, a dominant mode is still noticeable. The late-time perturbation growths scale with $ka_0$ initial conditions (where $k$ is the wavenumber and $a_0$ is the initial amplitude of the dominant mode) as measured at the pre-shock interface. Past nonlinear models based on potential-flow theory, heuristic/interpolation approaches, Padé approximants and numerical simulations are evaluated against present experimental results. Accounting for an explicit $ka_0$ dependence in Sadot et al.'s (Phys. Rev. Lett., vol. 80, issue 8, 1998, pp. 1654–1657) model, we propose an empirical rational function that captures the asymptotic behaviour of perturbation growth for a broad range of initial conditions ($0.30 \leq ka_0 \leq 0.86$). The onset of mixing transition and its initial condition dependence are investigated with respect to the minimum state criterion ($Re = 1.6 \times 10^5$) for unsteady flows by Zhou (Phys. Plasmas, vol. 14, 2007, 082701). Earlier mixing transitions for higher $ka_0$ initial conditions are noted from local and global Reynolds number estimates which are corroborated by the existence of an inertial sub-range and formation of mixing regions indicating the physical significance of the minimum state criterion in RMI flows. The transition is accompanied by the increasing teapot-like appearance of joint probability density functions of $p$–$q$ (invariants of the reduced velocity gradient tensor), establishing the technique as a useful tool for turbulence detection in two-dimensional diagnostics.