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Main Title: On long-term boundedness of Galerkin models
Author(s): Schlegel, Michael
Noack, Bernd R.
Type: Article
Language Code: en
Abstract: We investigate linear–quadratic dynamical systems with energy-preserving quadratic terms. These systems arise for instance as Galerkin systems of incompressible flows. A criterion is presented to ensure long-term boundedness of the system dynamics. If the criterion is violated, a globally stable attractor cannot exist for an effective nonlinearity. Thus, the criterion can be considered a minimum requirement for control-oriented Galerkin models of viscous fluid flows. The criterion is exemplified, for example, for Galerkin systems of two-dimensional cylinder wake flow models in the transient and the post-transient regime, for the Lorenz system and for wall-bounded shear flows. There are numerous potential applications of the criterion, for instance, system reduction and control of strongly nonlinear dynamical systems.
Issue Date: 2015
Date Available: 27-Oct-2017
DDC Class: 530 Physik
Subject(s): flow control
low-dimensional models
nonlinear dynamical systems
Usage rights: Terms of German Copyright Law
Journal Title: Journal of fluid mechanics
Publisher: Cambridge University Press
Publisher Place: Cambridge
Volume: 765
Publisher DOI: 10.1017/jfm.2014.736
Page Start: 325
Page End: 352
EISSN: 1469-7645
ISSN: 0022-1120
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:Institut für Strömungsmechanik und Technische Akustik (ISTA) » Publications

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