Phase-response analysis of synchronization for periodic flows

TL;DR

This paper uses phase-reduction analysis to study how periodic fluid flows, like cylinder wakes, synchronize with external forces, providing insights into conditions and optimal directions for synchronization.

Contribution

It introduces a phase-based method to analyze synchronization in unsteady flows, linking phase response to external forcing and validating with numerical simulations.

Findings

Identifies conditions for flow synchronization with external forcing

Determines optimal forcing directions for synchronization

Shows close agreement between phase analysis and numerical simulations

Abstract

We apply the phase-reduction analysis to examine synchronization properties of periodic fluid flows. The dynamics of unsteady flows are described in terms of the phase dynamics reducing the high-dimensional fluid flow to its single scalar phase variable. We characterize the phase response to impulse perturbations, which can in turn quantify the influence of periodic perturbations on the unsteady flow. These insights from the phase-based analysis uncover the condition for synchronization. In the present work, we study as an example the influence of periodic external forcing on unsteady cylinder wake. The condition for synchronization is identified and agrees closely with results from direct numerical simulations. Moreover, the analysis reveals the optimal forcing direction for synchronization. The phase-response analysis holds potential to uncover lock-on characteristics for a range of periodic flows.