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Attachment-Line Instability
Primary attachment lines exist at the windward side of a flight vehicle with sufficiently flat lower side. At large angles of attack secondary and tertiary attachment lines can be present at the leeward side of the vehicle, Sub-Section
3.3.2, see also [28]. The canonical attachment line situation in aerodynamics corresponds to an attachment line along the leading edge of a swept wing with in the span-wise direction constant symmetric profile at zero angle of attack, or at the windward symmetry line of a circular cylinder at angle of attack or yaw.
At such attachment lines both inviscid and boundary-layer flow diverge symmetrically with respect to the upper and the lower side of the wing, respectively to the left and the right hand side of the cylinder at angle of attack [28]. The infinitely extended attachment line is a useful approximation of reality, which can be helpful for basic considerations and for estimations of flow properties. We have discussed flow properties of such cases in Section
7.2. We have noted that finite flow and hence a boundary layer exists in the direction of the attachment line.[136] This boundary layer can be laminar, transitional or turbulent. On the infinitely extended attachment line only one of these three flow states can exist.
The simplest presentation of an infinite swept attachment-line flow is the swept Hiemenz boundary-layer flow, which is an exact solution of the incompressible continuity equation and the Navier-Stokes equations [44]. The (linear) stability model for this flow is the Gortler-Hammerlin model, which in its extended form gives insight into the stability behavior of attachment-line flow, see, e. g., [45]. Attachment-line flow is the “initial condition” for the, however only initially, highly three-dimensional boundary-layer flow away from the attachment line to the upper and the lower side of the wing or cylinder (see above). The there observed cross-flow instability, see below, has recently been connected by F. P. Bertolotti to the instability of the swept Hiemenz flow [46].
An extension of these concepts to general supersonic and hypersonic attachment-line boundary layers would give the basis needed to understand instability and transition phenomena of these flows, including the attachment-line contamination phenomenon which we comment on in the following sub-section. We mention in this regard the recent investigations [47]-[49].
