Leading-Edge Receptivity of Moderately Supersonic Boundary Layers to Free-Stream Disturbances

We study the receptivity and resulting global instability of boundary layers due to free-stream vortical and acoustic disturbances at moderately supersonic Mach numbers. The vortical disturbances produce an unsteady boundary layer flow that develops into oblique instability waves with a viscous triple-deck structure in the downstream region. The boundary layer fluctuations produced by the acoustic disturbances evolve into oblique normal modes in a region that lies downstream of the viscous triple-deck region but will still be fairly close to the leading edge when the phase speed of these disturbances is small compared to the free-stream velocity. We use asymptotic analysis to show that both the vortically and small phase speed acoustically-generated disturbances ultimately develop into modified Rayleigh modes that can exhibit spatial growth or decay depending on the nature of the receptivity process.