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 selfadjoint. The system can lose stability to timeperiodic 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.
 Publication:

Physics of Fluids
 Pub Date:
 March 1985
 DOI:
 10.1063/1.865046
 Bibcode:
 1985PhFl...28..788R
 Keywords:

 Benard Cells;
 Boundary Layer Flow;
 Computational Fluid Dynamics;
 Flow Stability;
 LiquidLiquid Interfaces;
 Asymptotic Methods;
 Boussinesq Approximation;
 Convective Flow;
 Earth Mantle;
 Eigenvalues;
 Periodic Variations;
 Standing Waves;
 Traveling Waves;
 Fluid Mechanics and Heat Transfer