On the breakdown of boundary layer streaks

A scenario of transition to turbulence likely to occur during the developme nt of natural disturbances in a flat-plate boundary layer is studied. The p erturbations at the leading edge of the flat plate that show the highest po tential for transient energy amplification consist of streamwise aligned vo rtices. Due to the lift-up mechanism these optimal disturbances lead to elo ngated streamwise streaks downstream, with significant spanwise modulation, Direct numerical simulations are used to follow the nonlinear evolution of these streaks and to verify secondary instability calculations. The theory is based on a linear Floquet expansion and focuses on the temporal, invisc id instability of these flow structures. The procedure requires integration in the complex plane, in the coordinate direction normal to the wall, to p roperly identify neutral modes belonging to the discrete spectrum. The stre ak critical amplitude, beyond which streamwise travelling waves are excited , is about 26% of the free-stream velocity. The sinuous instability mode (e ither the fundamental or the subharmonic, depending on the streak amplitude ) represents the most dangerous disturbance. Varicose waves are more stable , and are characterized by a critical amplitude of about 37%. Stability cal culations of streamwise streaks employing the shape assumption, carried out in a parallel investigation, are compared to the results obtained here usi ng the nonlinearly modified mean fields; the need to consider a base flow w hich includes mean flow modification and harmonics of the fundamental strea k is clearly demonstrated.