Anomalous reflection of a shock wave at a fluid interface

Abstract

Several wave patterns can be produced by the interaction of a shock wave with a fluid interface. Regular wave patterns have previously been explained by a shock-polar analysis. We focus on an irregular wave pattern that typically occurs when a shock passes from a medium of high to low acoustic impedance. Curvature of either the shock front or contact causes the flow to bifurcate from a locally self-similar quasi-stationary shock diffraction, to an unsteady anomalous reflection. We show that the anomalous reflection wave pattern can be explained with a modified shock-polar analysis in which the geometric node velocity is replaced by a downstream boundary condition. Anomalous reflection is analogous to the transition from a regular to a Mach reflection when the reflected wave is a rarefaction instead of a shock. These bifurcations have been incorporated into a front-tracking code that provides an accurate description of wave interactions. Numerical results for two illustrative cases are described: a planar shock passing over a bubble, and an expanding shock impacting a planar contact.