1202.3865 (M. Leoni et al.)

Hydrodynamic synchronisation of non-linear oscillators at low Reynolds
number    [PDF]

M. Leoni, T. B. Liverpool

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.

View original: http://arxiv.org/abs/1202.3865