Model-based control of transitional and turbulent wall-bounded shear flows

Turbulent flows are ubiquitous in nature and engineering. Dissipation of kinetic energy by turbulent flow around airplanes, ships, and submarines increases resistance to their motion (drag). In this dissertation, we have designed flow control strategies for enhancing performance of vehicles and other systems involving turbulent flows. While traditional flow control techniques combine physical intuition with costly numerical simulations and experiments, we have developed control-oriented models of wall-bounded shear flows that enable simulation-free and computationally-efficient design of flow controllers.;Model-based approach to flow control design has been motivated by the realization that progressive loss of robustness and consequential noise amplification initiate the departure from the laminar flow. In view of this, we have used the Navier-Stokes equations with uncertainty linearized around the laminar flow as a control-oriented model for transitional flows and we have shown that reducing the sensitivity of fluctuations to external disturbances represents a powerful paradigm for preventing transition. In addition, we have established that turbulence modeling in conjunction with judiciously selected linearization of the flow with control can be used as a powerful control-oriented model for turbulent flows.;We have illustrated the predictive power of our model-based control design in three concrete problems: preventing transition by (i) a sensorless strategy based on traveling waves and (ii) an optimal state-feedback controller based on local flow information; and (iii) skin-friction drag reduction in turbulent flows by transverse wall oscillations. We have developed analytical and computational tools based on perturbation analysis (in the control amplitude) for control design by means of spatially- and temporally- periodic flow manipulation in problems (i) and (iii), respectively. In problem (ii), we have utilized tools for designing structured optimal state-feedback gains. Our theoretical results supported by full-scale numerical simulations have revealed that the theory developed in this dissertation for the linearized flow equations with uncertainty has considerable ability to capture full-scale phenomena.