Streamlines:
As the picture shows, the boundary-layer streamlines do *not* follow the thickened wall shape; they cross it! It are only the potential flow streamlines immediately *above* the boundary layer that follow this shape. Note in particular the top green line.
Also note that there are still deviations at small x. At small x, the Reynolds number Re_x = U x/nu is NOT large, and boundary layer theory is inaccurate. In fact, the boundary layer solution predicts an unphysical square-root singularity at the start of the plate, while the true flow is smooth. (Note that the "true" flow as plotted is still not accurate right at the apex of the plate. But by using optimal coordinates, it should be OK everywhere else, including at x=0 for non zero y.)
Shear stress against x:
The stress becoes infinite at x=0.
Just the potential flow streamlines:
Early times "Stokes' second problem" boundary layer:
The Stokes-second-problem term only spreads out the streamlines, by reducing the flow velocity, which makes the flow between a typical boundary-layer streamline and the wall require more area to flow through.
Later time boundary layer with flow reversal, but no Van Dommelen & Shen separation yet:
Note that the second term provides the front/rear antisymmetry of the streamlines, including the formation of the initial recirculating wake.
Vorticity field:
The vorticity layer is much thicker at the rear than at the front of the cylinder.
For large times, the vorticity layer at the front approaches a finite, thin, thickness, while the one at the rear keeps groing in thickness.
See also: