TY - JOUR
T1 - Transitions to three-dimensional flows in a cylinder driven by oscillations of the sidewall
AU - Panades, C.
AU - Marques, F.
AU - Lopez, Juan
N1 - Funding Information:
This work was supported by the National Science Foundation grants DMS-05052705 and DMS-0922864, the Spanish Government grant FIS2009-08821 and the Korean Science and Engineering Foundation WCU grant R32-2009-000-20021-0.
PY - 2011/8/25
Y1 - 2011/8/25
N2 - 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 Z2 ×-O(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.
AB - 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 Z2 ×-O(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.
KW - bifurcation
KW - nonlinear instability
KW - parametric instability
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U2 - 10.1017/jfm.2011.215
DO - 10.1017/jfm.2011.215
M3 - Article
AN - SCOPUS:80052166609
SN - 0022-1120
VL - 681
SP - 515
EP - 536
JO - journal of fluid mechanics
JF - journal of fluid mechanics
ER -