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.