NONLOCALIZED RECEPTIVITY OF BOUNDARY-LAYERS

A perturbation scheme is developed to analyse the disturbance field produced by acoustic forcing over a flat plate with non-localized surface irregularities. Both the amplitude of the forcing and the height of the irregularity are assumed to be small. At first order, two modes are calculated: a Stokes mode resulting from the acoustic forcing, and a wall mode resulting from the surface irregularity. These modes interact at second order to produce a forced travelling wave with the frequency of the acoustic wave and a wavenumber associated with the surface irregularity. Streamwise variations in the mean flow mediate a distributed energy transfer between the forced mode and the eigenmode. Sufficiently far downstream, the forced-mode amplitude becomes small and the total disturbance is dominated by the resulting eigenmode. Receptivity amplitudes, expressed in terms of effective branch I values, are O(10) for a broad range of surface wavenumbers.