To examine possible links between a global instability and laminar–turbulent breakdown
in a three-dimensional boundary layer, the spatio-temporal stability of primary
and secondary crossflow vortices has been investigated for the DLR swept-plate
experiment. In the absence of any available procedure for the direct verification of
pinching for three-dimensional wave packets the alternative saddle-point continuation
method has been applied. This procedure is known to give reliable results only in a
certain vicinity of the most unstable ray. Therefore, finding no absolute instability
by this method does not prove that the flow is absolutely stable. Accordingly, our
results obtained this way need to be confirmed experimentally or by numerical simulations.
A geometric interpretation of the time-asymptotic saddle-point result explains
certain convergence and continuation problems encountered in the numerical wave
packet analysis. Similar to previous results, all our three-dimensional wave packets
for primary crossflow vortices were found to be convectively unstable.Due to prohibitive CPU time requirements the existing procedure for the verification
of pinching for two-dimensional wave packets of secondary high-frequency instabilities
could not be implemented. Again saddle-point continuation was used. Surprisingly, all
two-dimensional wave packets of high-frequency secondary instabilities investigated
were also found to be convectively unstable. This finding was corroborated by
recent spatial direct numerical simulations of Wassermann & Kloker (2001) for a
similar problem. This suggests that laminar–turbulent breakdown occurs after the
high-frequency secondary instabilities enter the nonlinear stage, and spatial marching
techniques, such as the parabolized stability equation method, should be applicable
for the computation of these nonlinear states.