The transition from two-dimensional to three-dimensional flows in a finite circular
cylinder driven by an axially oscillating sidewall is explored in detail. The complete
symmetry group of this flow, including a spatio-temporal symmetry related to the
oscillating sidewall, is Z2xO(2). Previous studies in flows with the same symmetries,
such as symmetric bluff-body wakes and periodically forced rectangular cavities,
were unable to obtain the theoretically predicted bifurcation to modulated travelling
waves. In the simpler cylindrical geometry, where the azimuthal direction is physically
periodic, we have found these predicted modulated travelling waves as stable fully
saturated nonlinear solutions for the first time. A careful analysis of the base states and their linear stability identifies different parameter regimes where three-dimensional states are either synchronous with the forcing or quasi-periodic, corresponding to different symmetry-breaking processes. These results are in good agreement with theoretical predictions and previous results in similar flows. These different regimes are separated by three codimension-two bifurcation points that are yet to be fully analysed theoretically. Finally, the saturated nonlinear states and their properties in different parameter regimes are analysed.
CitationPanades, C.; Marques, F.; Lopez, J. M. Transitions to three-dimensional flows in a cylinder driven by oscillations of the sidewall. "Journal of fluid mechanics", Agost 2011, vol. 681, p. 515-536.
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