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Phase-response analysis of synchronization for periodic flows

Published online by Cambridge University Press:  03 May 2018

Kunihiko Taira Open the ORCID record for Kunihiko Taira [Opens in a new window]  and
Hiroya Nakao
Kunihiko Taira*
Affiliation:
Department of Mechanical Engineering, Florida State University, Tallahassee, FL 32310, USA
Hiroya Nakao
Affiliation:
Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
*
†Email address for correspondence: ktaira@fsu.edu
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Abstract

We apply phase-reduction analysis to examine synchronization properties of periodic fluid flows. The dynamics of unsteady flows is 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 phase-based analysis uncover the condition for synchronization. In the present work, we study as an example the influence of periodic external forcing on an 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. Phase-response analysis holds potential to uncover lock-on characteristics for a range of periodic flows.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Wakes/Jets: Wakes
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , R2
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Copyright
© 2018 Cambridge University Press 

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