Distributed excitation of Tollmien–Schlichting waves by vortical free-stream disturbances

Nonlocalized receptivity to vortical free-stream disturbances is analyzed for a Blasius boundary layer over a wavy surface. Vortical disturbances are rescaled through an interaction with steady disturbances generated by the surface waviness. The rescaled disturbances provide a distributed energy transfer to the natural eigenmodes when conditions are close to resonance; this occurs in the neighborhood of the lower branch of neutral stability. Downstream of the energy transfer, the traveling wave solution is dominated by the natural eigenmode. Forcing from the vortical disturbances is concentrated in the outer region of the boundary layer. This leads to a relatively weak receptivity as compared to the acoustic problem. Total receptivity amplitudes are approximately ten times larger than for localized vortical receptivity, but approximately fifty times smaller than for nonlocalized acoustic receptivity.