  A density oscillator exhibits limit-cycle oscillations driven by the density
difference of the two fluids. We performed two-dimensional hydrodynamic
simulations with a simple model, and reproduced the oscillatory flow observed
in experiments. As the density difference is increased as a bifurcation
parameter, a damped oscillation changes to a limit-cycle oscillation through a
supercritical Hopf bifurcation. We estimated the critical density difference at
the bifurcation point and confirmed that the period of the oscillation remains
finite even around the bifurcation point.
