Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

O(2) symmetry constrained mode interactions in 2D cylinder wake flow

N.W. Mureithi*
Department of Mechanical Engineering, École Polytechnique, Box 6079, Station Centre-ville, Montréal, QC, H3C 3A7, Canada

  Full Text
A fundamental symmetry group theoretic analysis of the periodically forced cylinder wake dynamics problem is presented. The analysis yields a clear and concise explanation of experimentally observed cylinder wake dynamics.

First it is shown that the underlying problem can be posed as a mode interaction problem subject to O(2) symmetry constraints. An analysis of the amplitude equations for S/K mode interactions predicts the experimentally observed period-doubling instabilities when λsk = 1/1. For 2/1 wavelength ratio, it is shown that traveling wave solutions are to be expected. Furthermore, the apparent lack of interactions for 3/1 ratio is shown to be due to the fact that important nonlinear coupling terms appear only at 7th order.

For asymmetrical K1/K mode interactions, the symmetry 'compatibility', via common subgroups, explains the strong resonances observed experimentally for 1/1 and 1/3 frequency ratios. For a frequency ratio 1/2, it is shown that K1 and K mode symmetries are incompatible. Consequently, traveling wave solutions most likely underlie the organized wake topology observed in experiments.

Keywords:  Karman wake; Mode interactions; Bifurcations; Symmetry group; Normal forms

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