This paper presents the Adjoint Parabolized Stability Equations (APSE) which are used to predict the receptivity of shear layers to a variety of disturbances. Results from the APSE are first carefully validated against solutions of the Adjoint Navier-Stokes (ANS) equations which demonstrates that APSE is an accurate and effecient means of predicting receptivity. Then APSE is used to document the nonparallel receptivity characteristics of both Blasius and Falkner-Skan boundary layers for two-dimensional and oblique Tollmein-Schlichting (TS) instabilities. These results are compared to receptivity predictions based on local parallel theory in order to establish the effects of mean boundary layer growth on receptivity. In general, the inclusion of nonparallel effects for the receptivity prediction of TS instabilities is found to be small under all conditions. Comparing results from Blasius and Falkner-Skan base flows shows that adverse pressure gradients tend to reduce receptivity while favorable pressure gradients lead to an increase in receptivity. This is in contrast to the well known effects of pressure gradient on TS instability growth rates. Likewise, our investigations for three-dimensional disturbances also show that oblique modes have greater receptivity than two dimensional waves, again in contrast to the effects of obliquity on instability growth rates. In general there is a trade-off between receptivity and instability -the stronger the instability the weaker the receptivity.
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