BENARD-MARANGONI CONVECTION IN SQUARE CONTAINERS

Convection in a square container of small aspect ratio is studied taki ng into account thermocapillarity as well as gravity effects. In addit ion to the geometrical symmetry (D-4), the existence of hidden transla tional symmetries, due to boundary conditions, allows us to explain th e qualitative features of the patterns found in recently reported expe riments [T. Ondarzuhu et al., Phys. Rev. Leu. 70, 3892 (1993)]. The no nlinear interaction between mixed modes and pure modes is shown to giv e rise to a sequence of bifurcations that leads to the onset of oscill ations, as observed experimentally.