The study of compressible turbulent mixing associated with Richtmyer-Meshkov (RM), Rayleigh-Taylor (RT), and Kelvin-Helmholtz (KH) instabilities is motivated by diverse applications in science and engineering, including supersonic combustion, detonation, instability of collapsing gas bubbles, stratified flows in geophysical applications, chemical engineering, inertial confinement fusion (ICF), supernovae, and molecular clouds. Further, the interaction of shock waves with materials is also of interest in biomedical applications, such as fragmentation of cancer cells during shockwave chemotherapy and cavitation damage to human tissues during lithotripsy. In many of these applications, the Reynolds number is very high and the instabilities rapidly lead to turbulent mixing. In the case of ICF, which is regarded as a promising approach to controlled thermonuclear fusion: (1) these instabilities lead to the growth of perturbations on the interfaces within the capsules; (2) perturbations grow into the nonlinear regime by mode coupling and eventually cause mixing...

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