Data-Driven Modeling and Control of Oscillatory Instabilities in a Kolmogorov-like Flow

Modeling and control of transitional flows remains an important problem of engineering interest. However, the high-dimensional and nonlinear nature of fluid dynamics is not amenable to control design.  Recently data-driven methods have shown potential for creating reduced-order models, which facilitate the design of controllers. In this work, we apply data-driven techniques to develop a reduced-order model from direct numerical simulations of a canonical transitioning flow, Kolmogorov flow, under experimentally realizable parameters. We use Proper Orthogonal Decomposition (POD) in conjunction with a system identification technique, Sparse Identification of Nonlinear Dynamics (SINDy), for reduced-order model construction. Optimal and robust controllers are synthesized to suppress unsteady flow via body forcing actuation. The controllers successfully attenuate the targeted instabilities and reduced-order model predictions show quantitative agreement with full-order simulations. Our results highlight the utility of modern data-driven methods in flow control applications and pave the way for future experimental studies of thin layer flows.