Stability of plane-parallel vibrational flow in a two-layer system

The stability of the interface separating two immiscible incompressible flu ids of different densities and viscosities is considered in the case of flu ids filling a cavity which performs horizontal harmonic oscillations. There exists a simple basic state which corresponds to the unperturbed interface and plane-parallel unsteady counter flows; the properties of this state ar e examined. A linear stability problem for the interface is formulated and solved for both (a) inviscid and (b) viscous fluids. A transformation is fo und which reduces the linear stability problem under the inviscid approxima tion to the Mathieu equation. The parametric resonant regions of instabilit y associated with the intensification of capillary-gravity waves at the int erface are examined and the results are compared to those found in the visc ous case in a fully numerical investigation. (C) 1999 Editions scientifique s et medicales Elsevier SAS.