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Abstract In this work, we consider the problem of learning a reduced-order model of a high-dimensional stochastic nonlinear system with control inputs from noisy data. In particular, we develop a hybrid parametric/nonparametric model that learns the “average” linear dynamics in the data using dynamic mode decomposition with control (DMDc) and the nonlinearities and model uncertainties using Gaussian process (GP) regression and compare it with total least-squares dynamic mode decomposition (tlsDMD), extended here to systems with control inputs (tlsDMDc). The proposed approach is also compared with existing methods, such as DMDc-only and GP-only models, in two tasks: controlling the stochastic nonlinear Stuart–Landau equation and predicting the flowfield induced by a jet-like body force field in a turbulent boundary layer using data from large-scale numerical simulations. 

In this work, we consider the problem of learning a reduced-order model of a high-dimensional stochastic nonlinear system with control inputs from noisy data. In particular, we develop a hybrid parametric/nonparametric model that learns the “average” linear dynamics in the data using dynamic mode decomposition with control (DMDc) and the nonlinearities and model uncertainties using Gaussian process (GP) regression and compare it with total least-squares dynamic mode decomposition (tlsDMD), extended here to systems with control inputs (tlsDMDc). The proposed approach is also compared with existing methods, such as DMDconly and GP-only models, in two tasks: controlling the stochastic nonlinear Stuart–Landau equation and predicting the flowfield induced by a jet-like body force field in a turbulent boundary layer using data from large-scale numerical simulations. 

Turbulent boundary layers are largely influenced by spatiotemporally developing coherent structures known as Large-Scale Motions (LSMs). This work examines the idea of creating synthetic hairpin trains, a model for LSMs, generated in a nominal zero pressure gradient laminar boundary layer. The study investigates the agreement between the experimentally measured flow field and the hairpin vortices and its simulated counterpart with a hybrid 2D inlet region. This approach uses time-varying unsteady spatially discrete velocity data obtained through experiments as an inflow boundary condition to the direct numerical simulation (DNS). A pre-processing divergence correction and interpolation scheme is employed to convert experimental data into a format better suited for the DNS. The matching is done by recreating a downstream flow using this hybrid physio-cyber approach. This method demonstrates the capability to produce a sequence of hairpins even with a simple 2D planar coarse dataset. A satisfactory qualitative and quantitative agreement was evident when comparing Q-criterion iso-surfaces of instantaneous DNS and phase-locked experimental data. The results of this study not only demonstrate the efficacy of the proposed approach in recreating LSMs but also suggest its applicability to future hybrid experimental-DNS flow control studies. 

Turbulent boundary layers are dominated by large-scale motions (LSMs) of streamwise momentum surplus and deficit that contribute significantly to the statistics of the flow. In particular, the high-momentum LSMs residing in the outer region of the boundary layer have the potential to re-energize the flow and delay separation if brought closer to the wall. This work explores the effect of selectively manipulating LSMs in a moderate Reynolds number turbulent boundary layer for separation delay via well-resolved large-eddy simulations. Toward that goal, a model predictive control scheme is developed based on a reduced-order model of the flow that directs LSMs of interest closer to the wall in an optimal way via a body force-induced downwash. The performance improvement achieved by targeting LSMs for separation delay, compared to a naive actuation scheme that does not account for the presence of LSMs, is demonstrated.