Time-resolved particle image velocimetry measurements of the turbulent Richtmyer–Meshkov instability

Abstract

Abstract Experiments are presented on the Richtmyer–Meshkov instability (RMI) with a three-dimensional, multi-mode initial perturbation. The experiments use a vertical shock tube, where a stably stratified interface is formed between air and sulphur hexafluoride (SF$_6$) via counterflow. A perturbation is imposed at the interface by vertical oscillation of the gas column, forming Faraday waves. The interface is accelerated by a Mach 1.17 (in air) shock wave, and the development of the mixing region between the gases is investigated using particle image velocimetry. Following shock acceleration, a reflected shock wave from the bottom of the shock tube interacts with the mixing layer a second time (reshock). The experiment is initialized with both high and low amplitude perturbations to examine the effect of the perturbation amplitude on measured quantities. The instability growth exponent ($\\theta$) is determined from the kinetic energy field using the width of the mixing layer and the decay of kinetic energy, which are found to be in agreement when the flow is most strongly excited. A growth exponent of $\\theta \\approx 0.5$ is found for all cases except the high-amplitude reshocked regime (where $\\theta \\approx 0.33$). High-amplitude experiments exhibit the transitional outer Reynolds number $(Re \\equiv {h \\dot {h}}/{\\nu } > 10^4)$ required for mixing transition following the incident shock, and both experiments are elevated well above this threshold following reshock. However, neither set of experiments meet the more stringent requirements proposed by Zhou et al. (Phys. Rev. E, vol. 67, issue 5, 2003) which include the time dependent aspect of the RMI, an observation which is also made when examining the spectra.