Instability of a nearly inextensible thin layer in a shear flow

The stability of a nearly inextensible thin layer in a shear flow is investigated using an adjoint-based approach of the perturbed Stokes flow, i.e., for small inertia effects. The thin layer may be a very viscous fluid or an elastic sheet. We show that long waves are unstable, and that short waves are also unstable when the effect of inertia dominates that of surface tension. In contrast with the two-layer flow with a clean interface, the instability persists even when the fluids on either side of the thin layer have the same viscosity. (C) 2003 Editions scientifiques et medicales Elsevier SAS. All rights reserved.