Experimental study on the bifurcation of a density oscillator depending on density difference

TL;DR

This study experimentally investigates how a density oscillator transitions from rest to oscillation as the density difference increases, revealing a supercritical Hopf bifurcation with specific amplitude and period changes.

Contribution

It provides detailed experimental data on the bifurcation behavior of a density oscillator, confirming the supercritical Hopf bifurcation nature.

Findings

Oscillation amplitude increases from zero at bifurcation

Oscillation period decreases above critical density difference

Critical exponent aligns with supercritical Hopf bifurcation

Abstract

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.