Oscillatory instability in a Bénard problem of two fluids

Abstract

A linear stability analysis for a Bénard problem with two layers is considered. The equations are not self-adjoint. The system can lose stability to time-periodic disturbances. For example, it is shown numerically that when the viscosities and coefficients of cubical expansion of the fluids are different, a Hopf bifurcation can occur, resulting in a pair of traveling waves or a standing wave. This may have application in the modeling of convection in the Earth’s mantle.