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 [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.
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Rowley, C.W., Mezić, I., Bagheri, S., Schlatter, P., Henningson, D.S. (2010). Reduced-order models for flow control: balanced models and Koopman modes. In: Schlatter, P., Henningson, D. (eds) Seventh IUTAM Symposium on Laminar-Turbulent Transition. IUTAM Bookseries, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3723-7_6
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DOI: https://doi.org/10.1007/978-90-481-3723-7_6
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