Institut de Mecanique des Fluides

Abstract:

The coupling between long and short wave instabilities is a privileged situation for the emergence of striking wave patterns. We present experimental results on secondary instabilities of interfacial waves in a two-layer Couette flow, showing the destabilization of a supercritical short wave through the interaction with a neutral (or slightly damped) mean flow long wave mode. The interaction leads to wave coalescence or nucleation and eventually results in either a uniform wave train with shorter or longer wavelength, or a chaotic state. As the shear stress is increased and then decreased, the cycle of coalescence and nucleation can be understood of a set of two coupled amplitude equation, which leads to a generalization of the Eckhaus-Benjamin-Feir criterion. A physical mechanism for this instability is proposed.