Boundary-layer transition by interaction of discrete and continuous modes

The natural and bypass routes to boundary-layer turbulence have traditionally been studied independently. In certain flow regimes, both transition mechanisms might coexist, and, if so, can interact. A nonlinear interaction of discrete and continuous Orr-Sommerfeld modes, which are at the origin of orderly and bypass transition, respectively, is found. It causes breakdown to turbulence, even though neither mode alone is sufficient. Direct numerical simulations of the interaction shows that breakdown occurs through a pattern of A-structures, similar to the secondary instability of Tollmien-Schlichting waves. However, the streaks produced by the Orr-Sommerfcld continuous mode set the spanwise length scale, which is much smaller than that of the secondary instability of Tollmien-Schlichting waves. Floquet analysis explains some of the features seen in the simulations as a competition between destabilizing and stabilizing interactions between finite-amplitude distortions.