The long-time impulse response of compressible swept-wing boundary layers

Following the investigation of the long-time limit of the impulse response of an incompressible swept boundary layer (Taylor & Peake 1998), we now con sider the corresponding behaviour of two representative sets of compressibl e swept-wing profiles, one set in subsonic flow and the other in supersonic flow. The key feature of the incompressible analysis was the occurrence of modal pinch points in the cross-flow wavenumber plane, and in this paper t he existence of such pinches over a wide portion of space in high-speed flo w is confirmed. We also show that close to the attachment line, no unstable pinches in the chordwise wavenumber plane can be found for these realistic wing profiles, contrary to predictions made previously for incompressible flow with simple Falker-Skan-Cooke profiles (Lingwood 1997). A method for s earching for absolute instabilities is described and applied to the compres sible boundary layers, and we are able to confirm that these profiles are n ot absolutely unstable. The pinch point property of the compressible bounda ry layers is used here to predict the maximum local growth rate achieved by waves in a wavepacket in any given direction. By determining the direction of maximum amplification, we are able to derive upper bounds on the amplif ication rate of the wavepacket over the wing, and initial comparison with e xperimental data shows that the resulting N-factors are more consistent tha n might be expected from existing conventional methods.