These papers concern the onset of thermal convection in a two-fluid system filling the space between two horizontal plates; the lower plate is kept at a higher temperature than the upper plate. The study of thermal convection in two-layer flows is important in the understanding of processes that involve free surfaces.
In the first two papers, a situation is examined where a pair of Hopf modes with wavenumber A and a steady mode at wavenumber 2A are simultaneously at criticality. This is a resonant mode interaction in the presence of O(2) symmetry. The amplitude evolution equations were examined numerically, and a new solution, the asymmetric mixed mode, was found.
The remaining works concern the specific two-layer system with silicone oil 47v10 over Fluorinert. Here, the interface remains flat and the first instability is a Hopf mode due to the competition between the bulk modes of each fluid. The pattern formation problem in three dimensions is addressed for the case of doubly periodic solutions on a hexagonal lattice. Of the solutions with maximal symmetry, the traveling rolls are found to be stable. This is in contrast with past results of the qualitatively different mechanism of interfacial instability, where the solutions with maximal symmetry were found to be unstable.