PATTERN-FORMATION FOR OSCILLATORY BULK-MODE COMPETITION IN A 2-LAYER BENARD-PROBLEM

Two immiscible liquids lie between parallel plates and are heated from below. The focus is on the case where the interfacial mode is strongl y stabilized by surface tension and a suitable density stratification. A mechanism for a Hopf bifurcation is the competition between the lea st stable of the bulk modes in each fluid. The well known criterion fo r balancing the effective Rayleigh numbers in both fluids is augmented with a criterion for non-self-adjointness of the system, yielding a h euristic method for picking suitable fluids when Hopf modes are desire d. The pattern formation problem in three dimensions is addressed for the case of doubly periodic solutions on a hexagonal lattice. Of the s olutions with maximal symmetry, the travelling rolls are found to be s table.