Experimental study of the Richtmyer–Meshkov instability of incompressible fluids

Abstract

The Richtmyer–Meshkov instability of a low-Atwood-number miscible two-liquid system is investigated experimentally. The initially stratified fluids are contained within a rectangular tank mounted on a sled that rides on a vertical set of rails. The instability is generated by dropping the sled onto a coil spring, producing a nearly impulsive upward acceleration. The subsequent free-fall that occurs as the container travels upward and then downward on the rails allows the instability to evolve in the absence of gravity. The interface separating the two liquids initially has a well-defined sinusoidal perturbation that quickly inverts and then grows in amplitude after undergoing the impulsive acceleration. Disturbance amplitudes are measured and compared to theoretical predictions. Linear stability theory gives excellent agreement with the measured initial growth rate, $\dot{a}_0$, for single-mode perturbations with the predicted amplitudes differing by less than 10% from experimental measurements up to a non-dimensional time $k\dot {a}_0 t = 0.7$, where $k$ is the wavenumber. Linear stability theory also provides excellent agreement for the individual mode amplitudes of multi-mode initial perturbations until the interface becomes multi-valued. Comparison with previously published weakly nonlinear single-mode models shows good agreement up to $k\dot{a}_0 t = 3$, whereas published nonlinear single-mode models provide good agreement up to $k\dot{a}_0 t = 30$. The effects of Reynolds number on the vortex core evolution and overall growth rate of the interface are also investigated. Measurements of the overall amplitude are found to be unaffected by the Reynolds number for the range of values studied here. However, experiments carried out at lower values of Reynolds numbers were found to have decreased vortex core rotation rates. In addition, an instability in the vortex cores is observed. The time of appearance of this instability was found to increase when the Reynolds number is decreased.