Advanced measurement techniques and high-performance computing have made large data sets available for a broad range of turbulent flows in engineering applications. Drawing on this abundance of data, dynamical models that reproduce structural and statistical features of turbulent flows enable effective model-based flow control strategies. We describe a framework for completing second-order statistics of turbulent flows using models based on the linearized Navier-Stokes equations. Dynamical couplings between states of the linearized model dictate structural constraints on the statistics of flow fluctuations. Colored-in-time stochastic forcing that drives the linearized model is then sought to account for and reconcile dynamics with available data (that is, partially known statistics). The number of dynamical degrees of freedom that are directly affected by stochastic excitation is minimized as a measure of model parsimony. We show that the effect of colored-in-time excitation is equivalent to white-in-time excitation together with a low-rank structural perturbation of the linearized dynamical generator, pointing to suitable dynamical corrections that may account for the absence of the nonlinear interactions in the linearized model. Building on this equivalence we formulate a class of closely related minimum-control-energy covariance completion problems for statistical modeling. Our approach provides a data-driven refinement of control-oriented models and it captures complex dynamics of turbulent flows in a way that is tractable for analysis, optimization, and control design.
Armin Zare is an Assistant Professor in the Department of Mechanical Engineering at the University of Texas at Dallas, Richardson, TX. Prior to joining the University of Texas at Dallas, he was a Post-doctoral Research Associate in the Ming Hsieh Department of Electrical and Computer Engineering at the University of Southern California, Los Angeles, CA. He received the BSc in Electrical Engineering from Sharif University of Technology, Tehran, Iran, in 2010 and the MSEE and PhD degree in Electrical Engineering from the University of Minnesota, Minneapolis, MN, in 2016 under the supervision of Mihailo Jovanovic. His research interests are broadly in the modeling, dynamics, and control of large-scale and distributed systems with a focus on applications in fluid mechanics and renewable energy generation. His primary focus is on the modeling and control of complex fluid flows using tools from systems theory and optimization. He was a recipient of the Doctoral Dissertation Fellowship from the University of Minnesota in 2015 and a finalist for the Best Student Paper Award at the American Control Conference in 2014.