The simplest receptivity problem of linear disturbances artificially
excited in a
three-dimensional boundary layer adjacent to a solid surface is studied
in the framework
of the generalized triple-deck theory. In order to provide a mathematical
model to
be compared with experimental data from wind-tunnel tests we consider the
base
flow over a swept flat plate. Then crossflow in the near-wall region originates
owing
to an almost constant pressure gradient induced from outside with a displacement
body on top. A pulsed or vibrating ribbon installed on the solid surface
serves as
an external agency provoking initially weak pulsations. A periodic dependence
of
the ribbon shape on a coordinate normal to the streamwise direction makes
the
receptivity problem effectively two-dimensional, thereby allowing a rigorous
analysis
to be carried out without additional assumptions.
The most striking result from the asymptotic theory is the discovery
of streamwise
absolute instability intrinsic to a three-dimensional boundary layer at
high Reynolds
numbers. However, due to limitations imposed on the receptivity problem
no definite
conclusions can be made with regard to possible continued convection of
disturbances
in the crossflow direction. An investigation of the dispersion-relation
roots points to
the fact that wave packets of different kinds can be generated by an external
source
operating in the pulse mode. Rapidly growing wave packets sweep downstream,
weaker wave packets move against the oncoming stream. Insofar as the amplitude
of
all of the modulated signals increases exponentially in time and space,
the excitation
process gives rise to absolutely unstable disturbances in the streamwise
direction.
The computation confirms the theoretical prediction about the existence
of
upstream-advancing wave packets. They can be prevented from being persistently
amplified
only in a region ahead of the ribbon where nearly critical values of the
Reynolds
number are attained.
The results achieved are shown to be broadly consistent with wind-tunnel
measurements.
Hence a conjecture is made that the onset of transition is probably associated,
under some environmental conditions, with the mechanism of streamwise absolute
instability in the supercritical range of the Reynolds numbers.