Past Event: Oden Institute Seminar

Color of Turbulence: Low-complexity stochastic dynamical modeling of turbulent flows **Different Room, Time**

Armin Zare, Post-doctoral Research Associate, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles.

Abstract

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. Bio Armin Zare received the B.Sc. degree in Electrical Engineering from Sharif University of Technology, Tehran, Iran, in 2010, and the Ph.D. degree in Electrical Engineering from the University of Minnesota, Minneapolis, in 2016. He is currently a Post-doctoral 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. He 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.