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.