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A density oscillator exhibits limit-cycle oscillations driven by the densitydifference of the two fluids. We performed two-dimensional hydrodynamicsimulations with a simple model, and reproduced the oscillatory flow observedin experiments. As the density difference is increased as a bifurcationparameter, a damped oscillation changes to a limit-cycle oscillation through asupercritical Hopf bifurcation. We estimated the critical density difference atthe bifurcation point and confirmed that the period of the oscillation remainsfinite even around the bifurcation point.

Bifurcation analysis of a density oscillator using two-dimensional hydrodynamic simulation