Receptivity and sensitivity of the leading-edge boundary layer of a swept wing
Abstract
A global stability analysis of the boundary layer in the leading edge of a swept wing
is performed in the incompressible flow regime. It is demonstrated that the global
eigenfunctions display the features characterizing the local instability of the attachment
line, as in swept Hiemenz flow, and those of local cross-flow instabilities further
downstream along the wing. A continuous connection along the chordwise direction
is established between the two local eigenfunctions. An adjoint-based receptivity
analysis reveals that the global eigenfunction is most responsive to forcing applied
in the immediate vicinity of the attachment line. Furthermore, a sensitivity analysis
identifies the wavemaker at a location that is also very close to the attachment
line where the corresponding local instability analysis holds: the local cross-flow
instability further along the wing is merely fed by its attachment-line counterpart. As
a consequence, global mode calculations for the entire leading-edge region only need
to include attachment-line structures. The result additionally implies that effective
open-loop control strategies should focus on base-flow modifications in the region where the local attachment-line instability prevails.