Dynamics of Reduced Order Models of the Forced Karman Cylinder Wake

Mureithi, Njuki and Baranyi, László and Huynh, Kenny (2012) Dynamics of Reduced Order Models of the Forced Karman Cylinder Wake. In: Conference on Modelling Fluid Flow (CMFF’12) : The 15th International Conference on Fluid Flow Technologies. Budapest University of Technology and Economics, Budapest, pp. 1004-1011. ISBN 9789630845885

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Abstract

Employing symmetry-group equivariant bifurcation theory discrete reduced order models for the dynamics of the forced Karman wake have been developed. It turns out that the bifurcation behaviour of the complex forced wake flow can be approximately described by these simple models. Although the symmetry approach is highly convenient when deriving the reduced order models, the general form of the resulting model requires the extra step of determination of the model coefficients for a given physical flow. In addition, an important assumption of the approach above is that symmetry holds exactly over the complete flow domain (and to infinity). In reality this is not the case – particularly for flow assumed to have translational symmetry. The present paper addresses these two concerns. In a first attempt to obtain a physical interpretation of the reduced order model coefficients, the POD modes are employed in a Galerkin reduction of the complex Ginzburg- Landau (CGL) equation. The latter equation is a well known approximate model for spatio-temporal flow dynamics. To account for imperfect flow field symmetry, POD modes are derived directly from experimental PIV measurements. An analysis of the CGL-based reduced order model yields the key bifurcations of the symmetrically forced Karman wake. Most importantly the model confirms the saddle-node bifurcation, supporting the findings based on the symmetry-based approach.

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