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A hierarchy of low-dimensional models for the transient and post-transient cylinder wake

Published online by Cambridge University Press:  29 December 2003

BERND R. NOACK
Affiliation:
Hermann-Föttinger-Institut für Strömungsmechanik, Technische Universität Berlin HF1, Straße des 17. Juni 135, D-10623 Berlin, Germany
KONSTANTIN AFANASIEV
Affiliation:
Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Division Scientific Computing, Department Scientific Software, Takustr. 7, D-14195 Berlin-Dahlem, Germany
MAREK MORZYŃSKI
Affiliation:
Institute of Combustion Engines and Basics of Machine Design, Poznań University of Technology, ul. Piotrowo 3, PL 60-965 Poznań, Poland
GILEAD TADMOR
Affiliation:
Department of Electrical and Computer Engineering, Northeastern University, 440 Dana Research Building, Boston, MA 02115, USA
FRANK THIELE
Affiliation:
Hermann-Föttinger-Institut für Strömungsmechanik, Technische Universität Berlin HF1, Straße des 17. Juni 135, D-10623 Berlin, Germany

Abstract

A hierarchy of low-dimensional Galerkin models is proposed for the viscous, incompressible flow around a circular cylinder building on the pioneering works of Stuart (1958), Deane et al. (1991), and Ma & Karniadakis (2002). The empirical Galerkin model is based on an eight-dimensional Karhunen–Loève decomposition of a numerical simulation and incorporates a new ‘shift-mode’ representing the mean-field correction. The inclusion of the shift-mode significantly improves the resolution of the transient dynamics from the onset of vortex shedding to the periodic von Kármán vortex street. In addition, the Reynolds-number dependence of the flow can be described with good accuracy. The inclusion of stability eigenmodes further enhances the accuracy of fluctuation dynamics. Mathematical and physical system reduction approaches lead to invariant-manifold and to mean-field models, respectively. The corresponding two-dimensional dynamical systems are further reduced to the Landau amplitude equation.

Type
Papers
Copyright
© 2003 Cambridge University Press

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