Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry

By using the triple-deck scaling of Stewartson (1969) and Messiter (1970) we show that small but relatively sudden surface geometry variations that produce only very weak static pressure variations can nevertheless produce strong, i.e. 0(1), coupling between an externally imposed acoustic disturbance and a spatially growing Tollmien- Schlichting wave. The analysis provides a qualitative explanation of the Leehey & Shapiro (1979) boundary-layer receptivity measurements and is in good quantitative agreement with the Aizin & Polyakov (1979) experiment. It may also explain why small ‘trip wires’ can promote early transition.