Journal
JOURNAL OF FLUID MECHANICS
Volume 765, Issue -, Pages -Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2014.736
Keywords
flow control; low-dimensional models; nonlinear dynamical systems
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Funding
- Deutsche Forschungsgemeinschaft (DFG) [SCHL 586/2-1, SCHL 586/1-1, NO 258/2-3, NO 258/1-1]
- French Angence Nationale de la Recherche (ANR)
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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.
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