Time-dependent pattern formation for convection in two layers of immiscible liquids

A linear and weakly nonlinear stability analysis is performed for specific two-layer systems which have been examined experimentally in the past for purely buoyancy driven convection. Time-dependent oscillations arise at the first onset of instability. For the water/silicone oil system, oscillations are predicted for a range of wavelengths and depth fractions. For the Fluorinert/silicone oil system, oscillations are theoretically predicted in a very narrow parameter range. A 3D Hopf bifurcation on a hexagonal lattice is investigated for time-periodic patterns that arise at onset in extended domains. In both fluid systems, travelling rolls, wavy rolls of type 1, and oscillating triangles are stable for most regimes, (C) 2000 Elsevier Science Ltd. All rights reserved.