Oscillatory transverse instability of interfacial waves in horizontally oscillating flows

We present the results of an experimental investigation into the stability of steep interfacial waves in two immiscible liquid layers subject to horizontal oscillations. Two-dimensional waves, which arise beyond a critical forcing speed V c (product of forcing frequency and amplitude), can in turn lose stability to oscillatory transverse amplitude modulations with a near sub-harmonic response at a critical value of the forcing speed, V cs > V c. We characterize the resulting transverse waves and study the effect of viscosity on the onset of this secondary instability. Our experiments show that V cs increases with the ratio of the viscosities of the two liquids, N ≥ 1, which is in contrast to the decreasing trend of V c. The thresholds converge with decreasing N but appear to remain distinct even as N → 1. However, our results suggest a change of behavior for N ≤ 39, which also coincides with the first observations of interface breakup. © 2012 American Institute of Physics.