On the stability of multi-layered fluids. Part I: analysis |
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| Authors: | H Knoester and J van der Zanden |
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| Institution: | (1) Department of Mechanical Engineering and Marine Technology, Research Group for Fluid Dynamics, Delft University of Technology, Rotterdamseweg 145, 2628 AL Delft, The Netherlands;(2) Present address: AKZO Research Laboratory, Arnhem, The Netherlands |
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| Abstract: | The linear stability of the Poiseuille flow of multi-layered different fluids, described mathematically by a system of Orr-Somerfeld differential equations, is investigated. A spectral method is used to rewrite this system into a generalized eigenvalue problem, which can be solved with the QZ-algorithm. Special attention is paid to the tractibility of the interfacial conditions of the stability problem. Since we will limit ourselves to a linear stability analysis, the analytical treatment of the interfacial conditions is simplified. Some results related to simple flow configurations are presented. The origin of certain regions of interfacial instability is explained by simple analytical reasoning. |
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| Keywords: | stability linear-stability analysis multi-layered flow Orr-Sommerfeld equations interfacial conditions generalized eigenvalue problem air-water flow |
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