On the inviscid acoustic-mode instability of supersonic shear flows

The same methods used previously to study acoustic-mode instability in supersonic boundary layers are applied to free shear layers, and new calculations are made for boundary layers with cooling and suction. The objective is to obtain additional information about acoustic-mode instability, and to find what features of the instability are common to boundary layers and free shear flows. Acoustic modes exist whenever there is an embedded region of locally supersonic flow relative to the phase speed of the instability wave. Consequently, they can be found in boundary layers, wakes, and jets, but not in mixing layers unless the flow is confined. In this first part of a two-part paper, attention is directed principally to two-dimensional waves. The linear, inviscid stability theory is used to calculate spatial amplification rates at Mach number 3 for the sinuous and varicose modes of a single wake flow and a single jet flow, each made up of the same mixing-layer profile plus a central region of uniform flow. Along with sequences of sinuous and varicose unstable modes clearly identifiable as acoustic modes, both of these flows, unlike the boundary layer, have a lowest sinuous mode that is the most unstable. The unstable modes include both subsonic and radiating disturbances with large amplification rates. The latter phenomenon is also found for highly cooled boundary layers with suction. In these boundary layers, suction is generally stabilizing for nonradiating acoustic disturbances, but destabilizing for radiating disturbances.The work described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA). Support from the Aerodynamics Division of the Office of Aeronautics and Exploration Technology is gratefully acknowledged. A preliminary version of this paper was presented at the Fourth Symposium on Numerical and Physical Aspects of Aerodynamic Flows, California State University, Long Beach, CA, 16–19 January 1989.