Oscillatory Kelvin–Helmholtz instability. Part 2. An experiment in fluids with a large viscosity contrast

Abstract

The stability of two-layer oscillatory flows was studied experimentally in a cylindrical container with a vertical axis. Two superposed immiscible liquids, differing greatly in viscosity, were set in relative oscillatory motion by alternating container rotation. Waves arising beyond a threshold were observed in detail for small oscillation frequencies ranging from 0.1 to 6 Hz. Measurements were performed on the growth rate and the wavenumber of these waves. The instability threshold was determined from the growth rate data. It was found that the threshold and the wavenumber varied with the frequency. In particular, significantly lower thresholds and longer waves were found than those predicted by the inviscid theory of the oscillatory Kelvin–Helmholtz instability. Favourable agreement with the predictions of an existing viscous theory for small oscillation amplitude flows indicates the important role of viscosity, even at the highest frequency, and suggests a similar mechanism behind the instability as that for the short wave instability in steady Couette flows. A semi-numerical stability determination for finite amplitude flows was also performed to improve the prediction in experiments with a frequency lower than 1 Hz.