Influence of three-dimensionality on wake synchronization of oscillatory cylinder

TL;DR

This study explores how three-dimensional wake structures behind oscillating cylinders affect flow synchronization, using phase-reduction analysis to quantify and compare the effects with two-dimensional flows.

Contribution

It introduces an ensemble-based phase-reduction framework for three-dimensional wakes and demonstrates its effectiveness in predicting synchronization conditions.

Findings

Three-dimensional wakes have lower phase-sensitivity functions than two-dimensional wakes.

Cylinder motion influences wake three-dimensionality and vortex shedding phase.

Predicted synchronization conditions match direct numerical simulation results.

Abstract

We investigate the effect of three-dimensionality on the synchronization characteristics of the wake behind an oscillating circular cylinder at Re = 300. Cylinder oscillations in rotation, transverse translation, and streamwise translation are considered. We utilize phase-reduction analysis, which quantifies the phase-sensitivity function of periodic flows, to examine the synchronization properties. Here, we present an ensemble-based framework for phase-reduction analysis to handle three-dimensional wakes that are not perfectly time-periodic. Based on the phase-sensitivity functions, synchronizability to three types of cylinder oscillations is evaluated. In spite of similar trends, we find that phase-sensitivity functions involving three-dimensional wakes are lower in magnitude compared to those of two-dimensional wakes, which leads to narrower conditions for synchronization to weak cylinder oscillations. We unveil that the difference between the phase-sensitivity functions of two- and three-dimensional flows is strongly correlated to the amplitude variation of the three-dimensional flow by the cylinder motions. This finding reveals that the cylinder motion modifies the three-dimensionality of the wake as well as the phase of vortex shedding, which leads to reduced phase modulation. The synchronization conditions of three-dimensional wakes, predicted by phase-reduction analysis, agree with the identification by parametric studies using direct numerical simulations for forced oscillations with small amplitudes. This study presents the potential capability of phase-reduction to study synchronization characteristics of complex flows.