Journal of Fluid Mechanics



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


BERND R. NOACK a1c1, KONSTANTIN AFANASIEV a2, MAREK MORZYNSKI a3, GILEAD TADMOR a4 and FRANK THIELE a1
a1 Hermann-Föttinger-Institut für Strömungsmechanik, Technische Universität Berlin HF1, Straße des 17. Juni 135, D-10623 Berlin, Germany
a2 Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Division Scientific Computing, Department Scientific Software, Takustr. 7, D-14195 Berlin-Dahlem, Germany
a3 Institute of Combustion Engines and Basics of Machine Design, Poznan University of Technology, ul. Piotrowo 3, PL 60-965 Poznan, Poland
a4 Department of Electrical and Computer Engineering, Northeastern University, 440 Dana Research Building, Boston, MA 02115, USA

Article author query
noack b   [Google Scholar] 
afanasiev k   [Google Scholar] 
morzynski m   [Google Scholar] 
tadmor g   [Google Scholar] 
thiele f   [Google Scholar] 
 

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.

(Received February 20 2003)
(Revised July 23 2003)


Correspondence:
c1 Author to whom correspondence should be addressed: NoackBR@pi.tu-berlin.de


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