Transient growth on streaky unbounded shear flow: the symbiosis of Orr and `push-over' mechanisms

Recent work by Lozano-Duran et al. (2021) has revisited the ability of streaky shear flows to produce energy growth of small perturbations in order to examine which of the many linear processes available are important to sustain wall-bounded turbulence. Of the three mechanisms available - the Orr and lift-up mechanisms well-known from treating U(y) profiles plus the less familiar `push-over' mechanism which arises due to the spanwise shear of the streaks, they find that Orr and push over are important but lift up is not (at least for their computations at Re<sub>τ</sub>=180 in a minimal channel). In this talk, we will explain how Orr, a `fast' (inertial) mechanism, and `slow' push over (in analogy with lift up) can seemingly interact constructively using Kelvin's (1887) now-textbook unbounded shear model augmented by (spatially) periodic spanwise shear to represent the streaks.