Reduced-order models for flow control: balanced models and Koopman modes

C. W. Rowley, I. Mezic, S. Bagheri, P. Schlatter, and D. S. Henningson

Seventh IUTAM Symposium on Laminar-Turbulent Transition , June 2009.

Abstract:

This paper addresses recent developments in model-reduction techniques applicable to fluid flows. The main goal is to obtain low-order models tractable enough to be used for analysis and design of feedback laws for flow control, while retaining the essential physics. We first give a brief overview of several model reduction techniques, including Proper Orthogonal Decomposition, balanced truncation, and the related Eigensystem Realization Algorithm, and discuss strengths and weaknesses of each approach. We then describe a new method for analyzing nonlinear flows based on spectral analysis of the Koopman operator, a linear operator defined for any nonlinear dynamical system. We show that, for an example of a jet in crossflow, the resulting Koopman modes decouple the dynamics at different timescales more effectively than POD modes, and capture the relevant frequencies more accurately than linear stability analysis.

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