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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. The spectral content of the resulting colored-in-time stochastic contribution can alternatively arise from 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. <\/jats:p>","DOI":"10.1146\/annurev-control-053018-023843","type":"journal-article","created":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T18:18:33Z","timestamp":1572373113000},"page":"195-219","source":"Crossref","is-referenced-by-count":45,"title":["Stochastic Dynamical Modeling of Turbulent Flows"],"prefix":"10.1146","volume":"3","author":[{"given":"A.","family":"Zare","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Texas at Dallas, Richardson, Texas 75080, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T.T.","family":"Georgiou","sequence":"additional","affiliation":[{"name":"Department of Mechanical 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