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

TL;DR

This study uses two-dimensional hydrodynamic simulations to analyze a density oscillator, revealing a supercritical Hopf bifurcation where oscillations emerge as the density difference increases.

Contribution

It demonstrates the bifurcation behavior of a density oscillator through simulations, providing insights into the transition from damped to sustained oscillations.

Findings

Oscillations are reproduced in simulations matching experiments.

A supercritical Hopf bifurcation occurs at a critical density difference.

Oscillation period remains finite at the bifurcation point.

Abstract

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.