Hydrodynamic instabilities often cause spatio-temporal pattern formations and transitions between them. We investigate a model experimental system, a density oscillator, where the bifurcation from a resting state to an oscillatory state is triggered by the increase in the density difference of the two fluids. Our results show that the oscillation amplitude increases from zero and the period decreases above a critical density difference. The detailed data close to the bifurcation point provide a critical exponent consistent with the supercritical Hopf bifurcation.

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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.