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29 March 2024
 
  » arxiv » physics/9908007

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Stability of Plane-Parallel Vibrational Flow In a Two-Layer System
Mikhail V. Khenner ; Dmitrii V. Lyubimov ; Tatyana S. Belozerova ; Bernard Roux ;
Date 4 Aug 1999
Subject Fluid Dynamics; Computational Physics | physics.flu-dyn physics.comp-ph
Affiliation Comp. Sci. Dept., Tel Aviv University, Theor. Phys. Dept., Perm State University, Russia, IRPHE, Technopole de Chateau-Gombert, Marseille, France
AbstractThe stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillation. There exists a simple basic state which corresponds to the unperturbed interface and plane-parallel unsteady counter flows; the properties of this state are examined. A linear stability problem for the interface is formulated and solved a) for both inviscid and b) for both viscous fluids. A transformation is found which reduces the linear stability problem under inviscid approximation to the Mathieu equation. The parametric resonant regions of instability associated with the intensification of capillary-gravity waves at the interface are examined and the results are compared to those found in the viscous case in a fully numerical investigation.
Source arXiv, physics/9908007
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