An oncoming two-dimensional laminar boundary layer that develops an un
stable inflection point and becomes three-dimensional is described by
the Hall-Smith (1991) vortex/wave interaction equations. These equatio
ns are now examined in the neighbourhood of the position where the cri
tical surface starts to form. A consistent structure is established in
which an inviscid core flow is matched to a viscous buffer-layer solu
tion where the appropriate jump condition on the transverse shear stre
ss is satisfied. The final result is a bifurcation equation for the (c
onstant) amplitude of the wave pressure. A representative classical ve
locity profile is considered to illustrate solutions of this equation
for a range of values of the wave-numbers.