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.
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.
Full text: pdf