Phase-locking of laminar wake to periodic vibrations of a circular cylinder

TL;DR

This paper develops a phase-reduction model to analyze and control the synchronization between vortex shedding and cylinder vibrations, offering insights into wake stabilization and drag reduction.

Contribution

It introduces a novel phase-based linear model for wake dynamics that predicts phase-locking conditions and enables control of vortex-induced vibrations.

Findings

The model accurately predicts phase-locking conditions.

Synchronization can be used to stabilize the wake and reduce drag.

Different vibrational modes can promote or inhibit synchronization.

Abstract

Phase synchronization between the vortex shedding behind a two-dimensional circular cylinder and its vibrations is investigated using the phase-reduction analysis. Leveraging this approach enables the development of a one-dimensional, linear model with respect to the limit-cycle attractor of the laminar wake, which accurately describes the phase dynamics of the high-dimensional, nonlinear fluid flow and its response to rotational, transverse and longitudinal vibrations of the cylinder. This phase-based model is derived by assessing the phase-response and sensitivity of the wake dynamics to impulse perturbations of the cylinder, which can be performed in simulations and experiments. The resulting model in turn yields the theoretical conditions required for phase-locking between the cylinder vibrations and the wake. We furthermore show that this synchronization mechanism can be employed to stabilize the wake and subsequently reduce drag. We also uncover the circumstances under which the concurrent occurrence of different vibrational motions can be used to promote or impede synchronization. These findings provide valuable insights for the study of vortex-induced body oscillations, the enhancement of aerodynamic performance of flyers, or the mitigation of structural vibrations by synchronizing or desynchronizing the oscillatory motions of body to the periodic wake.