  A density oscillator is a fluid system in which oscillatory flow occurs
between different density fluids through the pore connecting them. We
investigate the synchronization in coupled density oscillators using
two-dimensional hydrodynamic simulation and analyze the stability of the
synchronous state based on the phase reduction theory. Our results show that
the anti-phase, three-phase, and 2-2 partial-in-phase synchronization modes
spontaneously appear as stable states in two, three, and four coupled
oscillators, respectively. The phase dynamics of coupled density oscillators is
interpreted with their sufficiently large first Fourier components of the phase
coupling function.
