Bénard-Marangoni convection in square containers

Abstract

Convection in a square container of small aspect ratio is studied taking into account thermocapillarity as well as gravity effects. In addition to the geometrical symmetry (D4), the existence of hidden translational symmetries, due to boundary conditions, allows us to explain the qualitative features of the patterns found in recently reported experiments @T. Ondarzuhu et al., Phys. Rev. Lett. 70, 3892 ~1993!#. The nonlinear interaction between mixed modes and pure modes is shown to give rise to a sequence of bifurcations that leads to the onset of oscillations, as observed experimentally.