Nonlinear inertial effects on the instability of a single long wave of finite amplitude at the interface of two viscous fluids |
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Authors: | Henry Power Miguel Villegas Carlos Carmona |
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Affiliation: | (1) Instituto de Mecánica de Fluídos, Facultad de Ingeniería, Universidad Central de Venezuela, Venezuela;(2) Dep. de Física Aplicada, Facultad de Ingeniería, Universidad Central de Venezuela, Caracas;(3) Dep. de Matemática y Física, Universidad Francisco de Miranda, Venezuela |
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Abstract: | The evolution of a single long wave of finite amplitude at the interface of two immiscible fluids of different viscosities and densities, between two horizontal plates is solved, using a boundary layer flow approximation for the equation of motion in each fluid layer. It is found that when the nonlinear inertial effects are taken into account in a moderate manner, at least in the frame of the boundary layer approximation, the initial unperturbed flow with smooth interface is stable to a single wave perturbation at the interface, even in the presence of adverse density and viscosity stratifications. However, when the nonlinear effects are increased in a specific way, and the magnitudes of the parameters involved are kept within the order of magnitude established for the present theory, an unstable flow configuration can be obtained. |
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