Hydrodynamic synchronisation of non-linear oscillators at low Reynolds number

Abstract

We introduce a generic model of weakly non-linear self-sustained oscillator as a simplified tool to study synchronisation 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 synchronisation. Furthermore, we find that synchronisation is strongly enhanced when the oscillators are non-isochronous, which on the limit cycle means the oscillations have an amplitude-dependent frequency. Non-isochronity is determined by a nonlinear coupling $\alpha$ being non-zero. We find that its ($\alpha$) sign determines if they synchronise in- or anti-phase. We then study an infinite array of oscillators in the long wavelength limit, in presence of noise. For $\alpha >0$, hydrodynamic interactions can lead to a homogeneous synchronised state. Numerical simulations for a finite number of oscillators confirm this and, when $\alpha <0$, show the propagation of waves, reminiscent of metachronal coordination.

4 pages, 2 figures

References in corpus (5)

• Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia
• Generic Conditions for Hydrodynamic Synchronization
• Synchronization of rotating helices by hydrodynamic interactions
• Swimmers in thin films: from swarming to hydrodynamic instabilities
• Many-Body Theory of Synchronization by Long-Range Interactions

Cited by in corpus (6)

• Green Algae as Model Organisms for Biological Fluid Dynamics
• Active phase and amplitude fluctuations of flagellar beating
• Antiphase Synchronization in a Flagellar-Dominance Mutant of Chlamydomonas
• Synchronisation and liquid crystalline order in soft active fluids
• The Phase Synchronized State of Oriented Active Fluids
• Polarisation of cells and soft objects driven by mechanical interactions: Consequences for migration and chemotaxis