Symmetry breaking and mode-interaction in vortex-structure interaction

This paper presents some results of experiments and numerical computations on various aspects of vortex-structure interaction. Experimental tests were conducted in a small wind tunnel to investigate the effect of mechanical cylinder oscillation in the flow direction on the wake vortex structure. Depending on the excitation to Karman shedding frequency ratio, mode locked states, in the form of spatio-temporally repeatable patterns, could be observed. Symmetrical excitation leads to breaking of the Karman mode spatial-temporal symmetry. Depending on the excitation to Karman frequency ratio, modes lacking the usual Karman symmetry is observed. The existence of a stable spatio-temporal structure appears to be strongly dependent on the interaction (lock-in) between the near wake symmetrical shedding and the 'established' far wake Karman pattern. Preliminary work based on symmetry (group) theory is presented to support the foregoing experimental observations. By considering two oscillators having the D-m(kappa,2pi/m) inline shedding symmetry and the Karman wake having the spatio-temporal symmetry Z(2)(K, pi), the possible symmetries of subsequent flow perturbations resulting from the modal interaction are determined. A mode having the reduced symmetry. Z(2) (kappa, pi(2)) was theoretically predicted and confirmed in the experiments. Finally, experimental tests show strong subharmonic lockin for forcing at rational ratios the vortex shedding frequency in the range 1 < m / n < 2. This phenomenon was also predicted theoretically.