Transient Growth on Streaky Shear flows

Abstract: 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 $Re_\tau=180$ in a minimal channel). I’ll discuss 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. I’ll also show how this model can be used to study stratified flows and, time-permitting, flows with oscillatory shear where a new form of self-sustaining mechanism has been found. Bio: Rich Kerswell is a professor in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge. His research focuses on fluid dynamics, particularly in the transition to turbulence, geophysical fluid flows, and nonlinear dynamics. Kerswell is known for studying how simple fluid systems can exhibit complex, chaotic behavior and has contributed to understanding turbulence's onset and sustainment in various contexts, including pipes and planetary atmospheres. His work integrates mathematical modeling, theoretical analysis, and computational simulations to explore instabilities and the fundamental mechanisms governing fluid behavior in nature and industry.