The long-time behaviour of incompressible swept-wing boundary layers subject to impulsive forcing

Abstract

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.