Interaction of a Plane Shock and Oblique Plane Disturbances With Special Reference to Entropy Waves

Abstract

The problem of the interaction between a plane entropy wave of arbitrary orientation and a plane oblique shock of infinite extent is investigated. As a result of the interaction, it is found that, in the perturbed flow field downstream of the shock, three kinds of disturbances are present—namety, an entropy mode, a vorticity mode, and a sound mode. The nature of the sound wave generated depends on the orientation of the upstream disturbance. Within certain orientations of the upstream disturbance, the sound waves generated downstream attenuate. Beyond these orientations, the sound waves generated have constant amplitudes. When the downstream sound waves are not attenuated, there is no phase shift in the entropy disturbance across the shock; when the downstream sound waves are attenuated, a phase shift occurs in the entropy disturbance across the shock. An illustrative example is given for the interaction between a plane normal shock and a sinusoidal entropy wave. At a given shock strength the amplitudes of the shock displacement and the downstream disturbances generated are plotted as functions of the orientation of the upstream disturbance.