Surface-Roughness Effects on Crossflow Instability of Swept-Wing Boundary Layers Through Generalized Resonances

Abstract

It is known that crossflow instability and transition can be influenced significantly by micrometer-sized surface roughness. A recent study sought to explain such a sensitive effect from the standpoint of a generalized resonant-triad interaction 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 destabilizing stationary and travelling crossflow vortices in the boundary layers over the NLF(2)-0415 swept wing, for which experiments found that micrometer-sized roughness caused earlier transition. Our analysis shows that the generalized resonance mechanism operates in a swept-wing boundary layer. Under the assumption that roughness consists of all spectral components, a crossflow mode with a fixed-dimensional frequency and wavelength resonates at each chordwise location with one or more other modes. We derive the amplitude equations for the interacting modes. The calculations show that the resonance is highly effective, especially when the roughness elements are near the leading edge. Importantly, it is found that the wave numbers of the roughness spectra participating in the most effective resonant interactions are very close to those of the right-branch neutral stationary eigenmode. As a result, micrometer-sized distributed roughness generates a perturbation of much larger amplitude, which alters, through the resonant interactions, the local growth rates of the crossflow vortices by an amount for both stationary and travelling vortices. We also traced the chordwise development of crossflow vortices with fixed-dimensional frequencies and spanwise wave numbers by integrating the local growth rate, or by solving the initial-value problem of the amplitude equations, for roughness without and with chordwise modulation. For roughness with a height of , the accumulated effect of the dominant resonances, whether acting alone or simultaneously, leads to a significant correction to the amplification factor of stationary and travelling vortices.