The long-time limit of the response of incompressible
three-dimensional boundary
layer flows on infinite swept wedges and infinite swept wings to
impulsive forcing is
examined using causal linear stability theory. Following
the discovery by Lingwood
(1995) of the presence of absolute instabilities caused by
pinch points occurring in
the radial direction in the boundary layer flow of a
rotating disk, we search for
pinch points in the cross flow direction for both the
model Falkner–Skan–Cooke
profile of a swept wedge and for a genuine swept-wing
configuration. It is shown
in both cases that, within a particular range of the
parameter space, the boundary
layer does indeed support pinch points in the wavenumber
plane corresponding to
the crossflow direction. These crossflow-induced pinch
points do not constitute an
absolute instability, as there is no simultaneous pinch
occurring in the streamwise
wavenumber plane, but nevertheless we show here how they
can be used to find
the maximum local growth rate contained in a wavepacket
travelling in any given
direction. Lingwood (1997) also found pinch points in the
chordwise wavenumber
plane in the boundary layer of the leading-edge region of
a swept wing (i.e. at
very high flow angles). The results presented in this paper,
however, demonstrate the
presence of pinch points for a much larger range of flow
angles and pressure gradients
than was found by Lingwood, and indeed describe the flow
over a much greater, and
practically significant, portion of the wing.
Modeling Three Dimensional Effects on Cross Flow Instability from Leading Edge Dimples
