Ft. Smith et al., INITIATION OF 3-DIMENSIONAL NONLINEAR TRANSITION PATHS FROM AN INFECTIONAL PROFILE, European journal of mechanics. B, Fluids, 12(4), 1993, pp. 447-473
Strongly nonlinear vortex/wave interaction in a laminar boundary layer
as described by Hall & Smith [1991] and Brown et al. [1993] features
an algebraic bifurcation, from a zero value of the wave-pressure ampli
tude to a non-zero constant value at the initial station of the three-
dimensional interaction. In the present study this discontinuity is re
moved on a shorter streamwise length scale. On this new scale the wave
-pressure amplitude satisfies an integro-differential equation which,
depending on the relative signs of the coefficients, possesses a solut
ion that matches downstream with the previously-determined constant va
lue. There are, however, in addition, further solutions that are of in
terest in their own right and which, in conjunction with proposed exte
nsions to the equation, indicate the possibility of alternative short
or long-scale vortex developments within the boundary layer. These alt
ernatives are found more likely to occur than is the strong interactio
n described at the start.