Boundary-layer receptivity to external disturbances using multiple scales

Non-homogeneous multiple scales are introduced to solve the resonant problem of non-parallel boundary-layer receptivity originating from the quadratic mixing of environmental disturbances. The resulting algorithm is computationally inexpensive and can be efficiently included in industrial codes for transition prediction. The mutual interactions between acoustic wave, vorticity wave, wall vibration and wall roughness are discussed in detail and the receptivity coefficient, which relates the amplitude of the excited wave to the amplitude of the exciting sources, is computed. The largest effect is found for the interaction between acoustic waves and wall roughness perturbations. Other coupling mechanisms are less effective. By comparing parallel and non-parallel results, it is found that flow non-parallelism can play a non-negligible role even in Blasius’ boundary layer, although the largest effects are evident for the three-dimensional boundary layer over and infinite swept wing. For the particular case of wall roughness – wall vibration mixing, the velocity disturbance is shown to be exactly equal to the velocity perturbation induced by the wall roughness alone on a wall vibrating in the normal direction.