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

Clarence W. Rowley, Igor Mezić, Shervin Bagheri, Philipp Schlatter, Dan S. Henningson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Scopus citations


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 [3], balanced truncation [8, 9], and the related Eigensystem Realization Algorithm [5, 6], 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.

Original languageEnglish (US)
Title of host publication7th IUTAM Symposium on Laminar-Turbulent Transition - Proceedings of the 7th IUTAM Symposium on Laminar-Turbulent Transition
PublisherSpringer Verlag
Number of pages8
ISBN (Print)9789048137220
StatePublished - 2010
Event7th IUTAM Symposium on Laminar-Turbulent Transition - Stockholm, Sweden
Duration: Jun 23 2009Jun 26 2009

Publication series

NameIUTAM Bookseries
ISSN (Print)1875-3507


Other7th IUTAM Symposium on Laminar-Turbulent Transition

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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