SOUND DIFFRACTION AND DISSIPATION AT A SHARP TRAILING EDGE IN A SUPERSONIC-FLOW

This paper is concerned with the process of energy conversion between acoustic waves and vorticity when plane sound waves impinge upon a sharp trailing edge of a semi-infinite plate positioned in a supersonic mean flow. It is shown that the diffracted field, confined to the Mach cone emanating from the trailing edge, is everywhere bounded and vanishes at the edge so that the issue of satisfying the Kutta condition at the sharp edge does not arise, which would require, in subsonic mean flows, a circulation to be imposed to the plate in order to remove the singularity at the edge, consequently resulting in vortex shedding from the plate. In the case of supersonic mean flows, no such circulation is needed because there is no singularity at the trailing edge, and the vorticity shed from the plate is entirely due to the discontinuity across the plate which is produced by the incident waves independently on the trailing edge conditions, and is swept downstream of the plate by the mean flow, forming a vortical wake behind it. The incident waves in this case completely determined the strength of the vortical wake as if the trailing edge did not exist, which is fundamentally different from the case of subsonic mean flows. It is shown, however, that energy exchange between sound and vorticity still occurs because, similarly to the case of subsonic mean flows, the vorticity, once shed into the sound field, experiences a lift force that does work as it is swept downstream by the mean flow. This process may either dissipate or produce acoustic energy, depending on the angle of the incident waves and the Mach number of the supersonic mean flow. © 1991.