Interfacial instability of density-stratified two-layer systems under initial stress

Abstract

of interfacial instability in two coherent semi-infinite layers of different properties and the corresponding critical wavelength are found by solving a static bifurcation problem in finite plane strain. Subsequently, the stability of perturbations of any wavelength is determined from the appropriate linearized equations of motion. For gravitationally stable or unstable density stratifications, the critical stress at which the interface is destabilized is shown to depend on the wavelength of a perturbation ; it is also determined in a complex manner by initial stress gradients perpendicular to the layer interface and by layer stiffness, as is illustrated here in detail for the examples of a hyperelastic solid and an elastoplastic solid, both resting on an inviscid fluid of different density. The very large wavelength that is predicted for the gravitational instability of a semi-infinite elastic solid on a buoyant fluid substratum brings forward the essential role of pre-stress and associated stiffness reduction as well as that of a finite layer thickness in destabilizing geological and geophysical two-layer systems.