Localized receptivity of boundary layers

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Abstract
The boundary‐layer receptivity resulting from acoustic forcing over a flat plate with a localized surface irregularity is analyzed using perturbation methods. The length‐scale reduction, essential to acoustic receptivity, is captured within the framework of the classical stability theory. At first order, two disturbances are calculated: an unsteady disturbance resulting from the acoustic forcing and a steady disturbance resulting from the surface irregularity. These disturbance fields interact at second order to produce a traveling‐wave field bearing the frequency of the acoustic wave and wave numbers associated with Fourier components of the surface irregularity. Components of the traveling‐wave field scale linearly with both the acoustic forcing and the height of the surface irregularity. Receptivity occurs when the frequency and wave number of a traveling‐wave component perfectly match the local eigenmode. Results are in general agreement with asymptotic analyses for irregularities in the neighborhood of branch I. Downstream of branch I, the current results show significant deviations from the asymptotic theory. Comparisons to experiments show good agreement for receptivity amplitudes when the height of the surface irregularity is small.