Receptivity of inviscid modes in supersonic boundary layers due to scattering of free-stream sound by localised wall roughness

The present paper investigates the receptivity of inviscid first and second modes in super/hypersonic boundary layers due to the interaction between a weak free-stream acoustic wave and a small isolated surface roughness element. The large-Reynolds-number asymptotic analysis reveals the detailed processes of the excitation. The distortion of the acoustic signature by the curved wall contributes to the leading-order receptivity, producing an eigenmode of viscous correction by the Stokes layer. With this modification, the accuracy of the receptivity calculation at moderate Reynolds numbers (approximately a few thousands) is improved remarkably.