Stability of Plane-Parallel Vibrational Flow In a Two-Layer System

Abstract

The 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.

15 pages, 6 figures; soon to appear in European Journal of Fluid Mechanics

Cited by in corpus (5)

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• Hydrodynamic instabilities in miscible fluids
• Running interfacial waves in two-layer fluid system subject to longitudinal vibrations
• Comparison of the effect of horizontal vibrations on interfacial waves in a two-layer system of inviscid liquids to effective gravity inversion
• Elastic and inelastic collisions of interfacial solitons and integrability of two-layer fluid system subject to horizontal vibrations