Abstract

Flow estimation and control provide a path forward toward achieving many important engineering objectives, such as decreasing drag, delaying flow separation and transition, and reducing flow-generated noise. While state estimation and control are classical topics in dynamical systems and control theory, standard methods have several disadvantages when applied to turbulent flows, including high cost and restrictions in their ability to incorporate key physics. In this presentation, I will describe an alternative framework for optimal flow estimation and control formulated in terms of resolvent operators obtained from the Navier-Stokes equations, which have been shown to efficiently describe organized motions within turbulent flows. The resolvent-based framework provides a hierarchy of methods for different tasks, including space-time statistical modeling, flow-field reconstruction in the time domain, real-time causal estimation, and control. When equivalent assumptions are made, the causal resolvent-based estimator and controller reproduce the Kalman filter and LQG controller, respectively, but at substantially lower computational cost. Unlike these methods, the resolvent-based approach can naturally accommodate forcing terms (nonlinear terms from Navier-Stokes) with colored-in-time statistics, which significantly improves the accuracy of the estimates. Moreover, the use of the resolvent framework facilitates physical interpretation of the mechanisms involved in the estimation and control procedure in terms of coherent flow structures. The performance of the resolvent-based methods is demonstrated using the flow over a backward-facing step and a turbulent channel flow.