Secondary instabilities of interfacial waves due to coupling with a long wave mode in a two-layer Couette flow |
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| Institution: | 1. Dpto. Matemática Aplicada a la Ingeniería Aeroespacial, E.T.S.I. Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Spain;2. Dpto. Aeronaves y Vehículos Espaciales, E.T.S.I. Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Spain;1. Department of Mechanical Engineering, Yazd University, Yazd, Iran;2. Division of Fluid Dynamics, Department of Applied Mechanics, Chalmers University of Technology, Gothenburg, Sweden;3. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran;4. TetraPak, Lund, Sweden |
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| Abstract: | 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 for 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. |
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