The multiple source feedback of supersonic jet screech. IV. Space–time diagrams and the fast/slow waves of transitory wave theory

Abstract

In Part II [J. Acoust. Soc. Am. 108, 2588 (2000)] the space–time wave diagrams of multiple (point) source screech were elucidated, showing the condition for perfect, or nearly so, reinforcement of the feedback sound at the nozzle. In the transitory wave theory [J. Acoust. Soc. Am. 106, 2194 (1999)] the velocity modulation of a transitory instability wave as it traverses the periodic cell structure results in a continuous phased array which was resolved into fast (approx. sonic) upstream and slow downstream source waves (of constant sinuous amplitude, apart from the envelope factor), only the former radiating strongly, in the upstream direction. The two points of view are reconciled by constructing fast and slow waves in the space–time diagrams by: (a) introducing intermediate negative sources: (b) taking the sources at half strength and adding virtual sources at the zero positions on the fast wave traces, of the same sign as adjacent sources: (c) taking the other half-strength sources and adding virtual sources of opposite sign, the sources then being of the same sign along the slow wave traces. The implications of the need to introduce negative sources in the point source array are discussed.