Skip to content Skip to navigation

Color of Turbulence: Low-complexity stochastic dynamical modeling of turbulent flows

Event Type: 
Date and Time: 
Friday, October 5, 2018 - 16:30
CTR Conference Room 103
Event Sponsor: 
Parviz Moin, Director of Center for Turbulence Research
Dr. Armin Zare

This talk describes how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier-Stokes (NS) equations. The complexity is quantified by the number of degrees of freedom in the linearized evolution model that are directly influenced by stochastic excitation sources. For the case where only a subset of correlations are known, we develop a framework to complete unavailable second-order statistics in a way that is consistent with linearization around turbulent mean velocity. In general, white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics. We develop models for colored-in-time forcing using a maximum entropy formulation together with a regularization that serves as a proxy for rank minimization. We show that colored-in-time excitation of the NS equations can also be interpreted as a low-rank modification to the generator of the linearized dynamics. Our method provides a data-driven refinement of models that originate from first principles and it captures complex dynamics of turbulent flows in a way that is tractable for analysis, optimization, and control design.

Dr. Armin Zare received his B.Sc. degree in Electrical Engineering from Sharif University of Technology, Tehran, Iran, in 2010, and his Ph.D. degree in Electrical Engineering from the University of Minnesota, Minneapolis, in 2016, under the supervision of Mihailo Jovanovic. Zare is currently a Postdoctoral Research Associate in the Ming Hsieh Department of Electrical Engineering at the University of Southern California, Los Angeles. He is broadly interested in the modeling and control of distributed systems in addition to large-scale and distributed optimization. His primary research interests are in the modeling and control of wall-bounded shear flows using tools from optimization and systems theory. Zare was the recipient of the Doctoral Dissertation Fellowship from the University of Minnesota in 2015 and a finalist for the Best Student Paper Award at the 2014 American Control Conference.