Spatially-localized optimal control of transition to turbulence

For the problem of controlling the onset of turbulence in a channel flow, we study the design of localized optimal state-feedback controllers. The actuation is generated by blowing and suction at the walls and we assume that the actuators are placed along a two-dimensional lattice of equally spaced points, and that each actuator uses information from only a limited number of nearby neighbors. We utilize recently developed tools for designing structured optimal feedback gains to reduce variance amplification of velocity fluctuations in the presence of flow disturbances. Our high-fidelity simulations of nonlinear flow dynamics, conducted at low Reynolds numbers, show that this approach can indeed maintain the laminar flow. This is in contrast to the localized strategies obtained by spatial truncation of optimal centralized controllers, which may introduce instability and promote transition even in the situations where the uncontrolled flow stays laminar.