Three-dimensional effects in boundary-layer transition - A high Reynolds number weakly-nonlinear theory

The present treatment of TS waves in an incompressible flat-plate boundary layer is dedicated to the neighborhood of the lower branch, assuming that the local Reynolds number is asymptotically large. In a quasi-two-dimensional TS wave of short wavelength, whose amplitude is modulated over a longer length-scale in the Z direction, nonlinear effects generate a streamwise vortex that in turn modifies the TS wave. The streamwise-vortex flow structure obtained agrees qualitatively with the experimental observations of Klebanoff et al (1962). Attention is given to the subharmonic secondary instability.