Free-stream coherent structures in the unsteady Rayleigh boundary layer

Results are presented for nonlinear equilibrium solutions of the Navier-Stokes equations in the boundary layer set up by a flat plate started impulsively from rest. The solutions take the form of a wave-roll-streak interaction, which takes place in a layer located at the edge of the boundary layer. This extends previous results for similar nonlinear equilibrium solutions in steady 2D boundary layers. The results are derived asymptotically and then compared to numerical results obtained by marching the reduced boundary-region disturbance equations forward in time. It is concluded that the previously found canonical free-stream coherent structures in steady boundary layers can be embedded in unbounded, unsteady shear flows.