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

TL;DR

This study investigates the transition from 2D to 3D flows in a cylinder with an oscillating sidewall, discovering stable modulated traveling waves and symmetry-breaking bifurcations, advancing understanding of flow dynamics in symmetric geometries.

Contribution

First experimental identification of stable modulated traveling waves in a cylindrical geometry with oscillating sidewall, confirming theoretical predictions and analyzing symmetry-breaking bifurcations.

Findings

Stable modulated traveling waves were observed in the flow.

Multiple parameter regimes exhibit different symmetry-breaking states.

Flow states include synchronous and quasiperiodic behaviors.

Abstract

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 $Z_2\times O(2)$. 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 traveling waves. In the simpler cylindrical geometry, where the azimuthal direction is physically periodic, we have found these predicted modulated traveling 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 that are either synchronous with the forcing or quasiperiodic, 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 analyzed theoretically. Finally, the saturated nonlinear states and their properties in different parameter regimes are analyzed.