Transition delay using control theory

This review gives an account of recent research efforts to use feedback control for the delay of laminar-turbulent transition in wall-bounded shear flows. The emphasis is on reducing the growth of small-amplitude disturbances in the boundary layer using numerical simulations and a linear control approach. Starting with the application of classical control theory to two-dimensional perturbations developing in spatially invariant flows, flow control based on control theory has progressed towards more realistic three-dimensional, spatially inhomogeneous flow configurations with localized sensing/actuation. The development of low-dimensional models of the Navier-Stokes equations has played a key role in this progress. Moreover, shortcomings and future challenges, as well as recent experimental advances in this multi-disciplinary field, are discussed.