A shock wave instability induced on a periodically disturbed interface

Abstract

The shock wave instability induced when interacting with a small waviness on an interface was investigated analytically and numerically. The perturbation to the shock was phenomenologically treated assuming this as the consequence of the shock refraction. The instability develops in the form of wave-like stretchings into the lower density medium followed with the loss of stability in the flow behind it, and eventually evolving into an intense vortex structure. The instability mode is aperiodical and unconditional, and either a transition to another stable state or continuous development as a secondary flow is possible. Among other interesting features are: a similarity law in the spatial and temporal evolution of the perturbations with respect to the interface curvature; the instability locus independence of the gas density distribution thus identifying the interface conditions as the sole triggering factor; the role of the density gradient in the instability evolution discriminating between qualitatively different outcomes; and the possibility of decay via non-viscous dumping mechanisms. The phenomenological connection between the shock and the interface stability is discussed.