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Hydrodynamic synchronization of nonlinear oscillators at low Reynolds number

M. Leoni and T. B. Liverpool
Phys. Rev. E 85, 040901(R) – Published 5 April 2012

Abstract

We introduce a generic model of a weakly nonlinear self-sustained oscillator as a simplified tool to study synchronization in a fluid at low Reynolds number. By averaging over the fast degrees of freedom, we examine the effect of hydrodynamic interactions on the slow dynamics of two oscillators and show that they can lead to synchronization. Furthermore, we find that synchronization is strongly enhanced when the oscillators are nonisochronous, which on the limit cycle means the oscillations have an amplitude-dependent frequency. Nonisochronity is determined by a nonlinear coupling α being nonzero. We find that its (α) sign determines if they synchronize in phase or antiphase. We then study an infinite array of oscillators in the long-wavelength limit, in the presence of noise. For α>0, hydrodynamic interactions can lead to a homogeneous synchronized state. Numerical simulations for a finite number of oscillators confirm this and, when α<0, show the propagation of waves, reminiscent of metachronal coordination.

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  • Received 29 August 2011

DOI:https://doi.org/10.1103/PhysRevE.85.040901

©2012 American Physical Society

Authors & Affiliations

M. Leoni1 and T. B. Liverpool1,2

  • 1Department of Mathematics, University of Bristol, Clifton, Bristol BS8 1TW, United Kingdom
  • 2The Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA

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Issue

Vol. 85, Iss. 4 — April 2012

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