Thumbnail Image

On long-term boundedness of Galerkin models

Schlegel, Michael; Noack, Bernd R.

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.
Published in: Journal of fluid mechanics, 10.1017/jfm.2014.736, Cambridge University Press
  • 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.