Published online by Cambridge University Press: 20 January 2017
The secondary instability of linear transient growth (TG) in Couette flow is explored theoretically, utilizing an analytical representation of the TG based on four modes and their nonlinear interactions. The evolution of the secondary disturbance is derived using the multiple time scales method. The theoretical predictions are compared with direct numerical simulations and very good agreement with respect to the growth of the disturbance energy and associated vortical structures is observed, up to the final stage just before the breakdown to turbulence. The theoretical model enables us to perform a full parametric study, including TG symmetry type, various wavenumbers, initial energy, TG nonlinearity and Reynolds number, to find all possible routes to transition and the optimal parameters for each type of the secondary disturbance. It is found 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 TG phase.