Numerical study of the effect of freestream turbulence on by-pass transition in a boundary layer

We use direct numerical simulations in the presence of free-stream turbulence having different values of intensity, Tu, and integral length scale, L, in order to determine which kind of structures are involved in the path to transition of a boundary-layer flow. The main aim is to determine under which conditions the path to transition involves structures similar to the linear or non-linear optimal perturbations. For high values of Tu and L, we observe a large-amplitude path to transition characterized by localized vortical structures and patches of high- and low-momentum fluctuations. Such a scenario is found to correlate well with the Λ and hairpin structures resulting from the time evolution of non-linear optimal perturbations, whereas, for lower Tu and L, a larger correlation is found with respect to linear optimal disturbances. This indicates that a large-amplitude path to transition exists, different from the one characterized by elongated streaks undergoing secondary instability. To distinguish between the two transition scenarios, a simple parameter linked to the streamwise localisation of high- and low-momentum zones is introduced. Finally, an accurate law to predict the transition location is provided, taking into account both Tu and L, valid for both the transition scenarios.