The late-time development of Richtmyer–Meshkov instability is studied in shock tube experiments. This investigation makes use of the experimental apparatus and visualization methods utilized in the earlier study of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)] but employs stronger shocks and initial perturbations with shorter wavelengths to obtain much later-time (in the dimensionless sense) images of the single-mode instability. These modifications produce a very detailed look at the evolution of the late-time single-mode instability, revealing the transition and development of turbulence in the vortex cores that eventually results in the disintegration of the laminar vortex structures into small scale features. Amplitude measurements taken from these images are shown to be effectively collapsed when plotted in dimensionless variables defined using the wave number and the initial growth rate. The amplitude measurements are compared with several late-time nonlinear models and solutions. The best agreement is obtained with the model of Sadot et al. [Phys. Rev. Lett. 80, 1654 (1998)] which can be slightly improved by modifying the expression for the late-time asymptotic growth rate.

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Abstract

A vertical shock tube is used to perform experiments in which an interface is formed using opposed flows of air and SF 6 . A three-dimensional single-mode perturbation is created by the periodic vertical motion of the gases within the shock tube. Richtmyer-Meshkov instability is produced by an impulsive acceleration by a weak shock wave ͑M s = 1.2͒. Planar laser induced fluorescence produces still images, and planar Mie scattering produces movies of the experiment. A three-dimensional numerical simulation of this experiment utilizing the Eulerian adaptive mesh refinement code, RAPTOR, was also conducted. Good agreement is obtained between experiments and the simulations. However, existing late time models, which have a 1 / t dependence, disagree with measurements of the late time instability development. In contrast, both the experiments and simulation suggest a t −0.54 late time dependence for the overall growth rate. Comparisons with individual bubble and spike velocities show the bubbles appear to decay approximately at 1 / t and the spikes to decay at a much slower rate of t −0.38 .

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