Effects of freestream turbulence on the secondary instability of the roughness-induced crossflow vortex in swept flat plate boundary layers

In a three-dimensional boundary layer with spanwise constant flow and chordwise acceleration, which is unique to the vicinity of the leading edge of a swept wing, an inviscid instability induces the crossflow vortex (CFV), around which a secondary instability further occurs to yield a turbulent transition. It is well known that surface roughness induces stationary CFVs and that CFVs are receptive to freestream turbulence (FST), but the interference of both effects remains unclear. To determine the transition mechanisms in mixed roughness and FST environments, we performed direct numerical simulations of a Falkner–Skan–Cooke boundary layer under various conditions considering the presence of cylindrical roughness and the peak FST wavelength. Without roughness, the FST with a long wavelength comparable to the most unstable mode promotes CFV induction, resulting in an earlier transition. Conversely, the short-wavelength FST interacts with a wake vortex induced by the presence of roughness, yielding a hairpin vortex as a secondary instability. We discuss the main production terms of the disturbance energy associated with each of the type-1 and -2 secondary instabilities, which are accompanied by finger and hairpin vortices, respectively. The rapid turbulent transition via the type-1 secondary instability is due to the spanwise velocity gradient of the developed CFV, whereas that via the type-2 is due to a wall-normal gradient and is similar to the fully developed wall turbulence. The wavelength of FST played a key role in inducing a high-frequency secondary instability on the CFV or the CFV itself, and the receptivity to FST differed between the CFV and wake vortex.