Low Order Model Dynamics of the Forced Cylinder Wake

The periodically forced cylinder wake exhibits complex but highly symmetrical patterns. In recent work, the authors have exploited symmetry-group equivariant bifurcation theory to derive low order equations describing, approximately, the dominant nonlinear dynamics of wake mode interactions. The models have been shown to qualitatively predict the observed bifurcations suggesting that the Karman wake remains, dynamically, a fairly simple system at least when viewed in 2D. Preliminary experimental data are presented supporting the feasibility of using 2D simulation results for the derivation of the low order model parameters. A POD analysis of the wake PIV velocity field yields flow modes closely similarly to those obtained via 2D CFD computations for Re in the 1000 range. The paper presents new results of simulations for Re = 200. For this low Reynolds number, the forced Karman wake exhibits rich dynamics dominated by quasi-periodicity, mode locking, torus doubling and chaos. The low Re torus breakdown may be explained by the Afraimovich-Shilnikov theorem. Interestingly, in a previous analysis for the higher Re number, Re = 1000, transition to a period-doubled flow state was found to occur via a route akin to the Takens-Bogdanov bifurcation scenario.