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Physics > Fluid Dynamics

arXiv:1804.01274 (physics)
[Submitted on 4 Apr 2018]

Title:Phase-response analysis of synchronization for periodic flows

Authors:Kunihiko Taira, Hiroya Nakao
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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.
Comments: 11 pages, 6 figures
Subjects: Fluid Dynamics (physics.flu-dyn); Adaptation and Self-Organizing Systems (nlin.AO)
Cite as: arXiv:1804.01274 [physics.flu-dyn]
  (or arXiv:1804.01274v1 [physics.flu-dyn] for this version)
  https://doi.org/10.48550/arXiv.1804.01274
Related DOI: https://doi.org/10.1017/jfm.2018.327

Submission history

From: Kunihiko Taira [view email]
[v1] Wed, 4 Apr 2018 07:38:55 UTC (1,684 KB)
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