Triadic Resonance Analysis of Distributed Roughness Effects on Crossflow Instability in Swept-Wing Boundary Layers

Abstract

It is known that crossflow instability and transition can be influenced significantly by micron-sized surface roughness. He, Butler and Wu sought to explain such a sensitive effect from the standpoint of a generalized resonant triad interactions between crossflow instability modes and distributed roughness-induced perturbations. The mechanism was demonstrated for Falkner-Skan-Cooke similarity velocity profiles. In the present paper, we examine its role in destabilising stationary and travelling crossflow vortices in the boundary layers over the NLF(2)-0415 swept wing, for which Reibert & Saric’s experiment found that micron-sized roughness caused much earlier transition. Our analysis shows that the generalized resonance mechanism operates in a swept-wing boundary layer and the resulting corrections to the growth rates of crossflow eigenmodes are proportional to the height of distributed surface roughness. The mechanism is highly effective when the roughness is near the leading edge. Importantly, it is found that the wavenumbers of the roughness spectra participating in the most effective resonant interactions with stationary and travelling-wave crossflow vortices are very close to the wavenumbers of the right-branch neutral stationary eigenmode. As a result, micron-sized distributed roughness generates a perturbation of much larger amplitude, which alters, through the resonant triad interactions, the growth rates of the crossflow vortices by an O(1) amount.