Secondary instabilities of interfacial waves due to coupling with a long wave mode in a two-layer Couette flow

We report experiments on the stability of interfacial waves in a two-layer Couette flow. As the shear rate is increased, the periodic wave train arising from the primary instability undergoes a secondary instability which results in wave coalescence or nucleation, after a long transient. This secondary instability crucially involves the coupling with a long wave mode, which corresponds to variations of the mean interface level. These observations are favourably compared to stability results on travelling wave solutions for a set of two coupled equations, one fur the envelope of a weakly unstable wave packet, and the other for the marginal long wave mode with zero wave number. A physical mechanism for this instability is proposed, as well as an interpretation for the onset of chaos. (C)1999 Elsevier Science B.V. All rights reserved.