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The transition from two-dimensional to three-dimensional flows in a finitecircular cylinder driven by an axially oscillating sidewall is explored indetail. The complete symmetry group of this flow, including a spatio-temporalsymmetry related to the oscillating sidewall, is $Z_2\times O(2)$. Previousstudies in flows with the same symmetries, such as symmetric bluff-body wakesand periodically forced rectangular cavities, were unable to obtain thetheoretically predicted bifurcation to modulated traveling waves. In thesimpler cylindrical geometry, where the azimuthal direction is physicallyperiodic, we have found these predicted modulated traveling waves as stablefully saturated nonlinear solutions for the first time. A careful analysis ofthe base states and their linear stability identifies different parameterregimes where three-dimensional states that are either synchronous with theforcing or quasiperiodic, corresponding to different symmetry-breakingprocesses. These results are in good agreement with theoretical predictions andprevious results in similar flows. These different regimes are separated bythree codimension-two bifurcation points that are yet to be fully analyzedtheoretically. Finally, the saturated nonlinear states and their properties indifferent parameter regimes are analyzed.

Transitions to three-dimensional flows in a cylinder driven by oscillations of the sidewall