In this talk several aspects of transition to turbulence in wall-bounded shear flows are addressed. One aspect discusses the formation and evolution of coherent structures, such as counter-rotating vortex pairs (CVPs) and hairpins, observed in various transitional as well as turbulent flows. The vortex dynamics is followed using a novel analytical-based numerical method for the evolution of localized disturbances in homogenous shear base-flows. Using insights gained from the evolution of localized disturbances, a minimal element model, capable of following the evolution of packets of hairpins, is developed. The model is compared successfully with experiments and the excellent agreement in all cases demonstrates the universality and robustness of the model.
The other aspect discusses transition from an instability point of view. An analytical model for subcritical transition via the transient growth mechanism is developed. The linear transient growth mechanism is represented analytically by four decaying normal modes and their nonlinear interactions. The model utilizes separation of scales between the slowly evolving base flow and the rapidly evolving secondary disturbance to capture most transition stages using the multiple time scales method. The model predictions are verified by comparison with direct numerical simulations. It is shown that the most dangerous secondary disturbances are associated with spanwise wavenumbers, which generate the strongest inflection points, i.e. those having maximal shear, rather than with those maximizing the energy gain during the transient growth phase.