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 ([Formula Presented]), 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. © 1996 The American Physical Society.