Following the investigation of the long-time limit of the impulse
response of an
incompressible swept boundary layer (Taylor & Peake 1998), we now consider
the
corresponding behaviour of two representative sets of compressible 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 the existence of such pinches over
a wide
portion of space in high-speed flow 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 searching for absolute instabilities is described and applied to the
compressible
boundary layers, and we are able to confirm that these profiles are not
absolutely
unstable. The pinch point property of the compressible boundary 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 amplification rate of the wavepacket
over
the wing, and initial comparison with experimental data shows that the
resulting
N-factors are more consistent than might be expected from existing conventional
methods.
Nonlinear Stability of Nonstationary Cross-Flow Vortices in Compressible Boundary Layers
