Transition to turbulence by mode interaction

Transition to turbulence in a boundary layer can be achieved by the so-called natural route, which is characterized by the growth of Tollmien-Schlichting waves. In practical flows, the natural route is often bypassed: Under the influence of free-stream turbulence, elongated boundary layer streaks, which are also called Klebanoff modes, often develop. Klebanoff modes can breakdown due to the interaction with the turbulent free stream or with Tollmien-Schlichting waves. It is the latter mechanism that forms the focus of this work.; The role of this interaction has been controversial, partly because previous experiments and numerical simulations were giving seemingly contradictory results. Direct numerical simulations (DNS) were performed, and successfully reproduced some of those seeming contradictory results by changing the perturbation parameters. Our results indicate that boundary layer streaks may stabilize or destabilize the flow depending on the amplitude and spanwise wave number of the streaks.; A seemingly paradoxical result from our DNS is that, on one hand, the presence of boundary layer streaks always reduces the growth rate of Tollmien-Schlichting waves; on the other hand, the interaction of non-transitional streaks and Tollmien-Schlichting waves may result in transition to turbulence. The transition location shows complicated dependence on flow parameters. The DNS reveals that the majority of this type of transition is achieved through developing lambda-structures. This finding indicates that these transitions can be related to the secondary instabilities of Tollmien-Schlichting waves.; A Floquet analysis is performed in order to explain the DNS results and provides insight into the transition mechanism. We find that boundary layer streaks affect the transition process from three aspects: First, streaks reduce the instability of Tollmien-Schlichting waves and stronger streaks are more stabilizing. Second, streaks introduce three-dimensional perturbations that can develop into secondary instability modes. Third, the amplitude and spanwise wave number of boundary layer streaks together with the amplitude of Tollmien-Schlichting waves affect the growth rate of secondary instability modes of the primary Tollmien-Schlichting waves. Combined effects of the induced perturbation and the modified growth rate of secondary modes determine the transition pattern.