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

• Published in: Journal of fluid mechanics Vol. 497; pp. 335 - 363
• Main Authors: NOACK, BERND R., AFANASIEV, KONSTANTIN, MORZYŃSKI, MAREK, TADMOR, GILEAD, THIELE, FRANK
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.12.2003
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Jets; Physics; Rotational flow and vorticity; Separated flows; Turbulent flows, convection, and heat transfer; Wakes; Vortex shedding; Digital simulation; Unsteady state; Wakes; Circular cylinder; Modelling; Karhunen-Loeve transforms; Vortex flow; Incompressible fluid; Viscous fluids
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112003006694

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.