Experiments on the Richtmyer-Meshkov instability of incompressible fluids

Abstract

Richtmyer-Meshkov (R-M) instability occurs when two different density fluids are impulsively accelerated in the direction normal to their nearly planar interface. The instability causes perturbations on the interface to grow and to possibly become turbulent. R-M instability is a fundamental fluid instability that is important to fields ranging from astrophysics to high-speed combustion. For example, R-M instability is currently one of the limiting factors in achieving a positive net yield in laser driven inertial confinement fusion experiments. This experimental study investigates the instability of an interface between incompressible, miscible liquids with an initial sinusoidal perturbation. After undergoing a nearly impulsive acceleration, the initial perturbation quickly inverts and then grows in amplitude. The vorticity on the interface eventually coalesces into a series of alternating signed vortices. Disturbance amplitudes are measured and compared to theoretical predictions. Linear stability theory gives excellent agreement with the measured initial perturbation growth rates, while the predicted amplitudes differ by less than 10% from experimental measurements up to a nondimensional time kȧ₀t = 0.7. Fourth order, single-mode perturbation theory extends the 1.0% amplitude agreement up to a nondimensional time kȧ₀t = 1.3. A discrete vortex model and a combined model equation are within 10% of the experimental amplitude measurements up to the maximum experimental nondimensional time kȧ₀t = 30. The effects of Reynolds number (based on circulation) on the vortex core evolution and overall growth rate of the interface are also investigated. In addition, an instability in the vortex cores is observed for the first time and criteria established for its occurrence.