Time-independent square patterns in surface-tension-driven Benard convection

The transition between hexagonal and square patterns is investigated in laboratory experiments on surface-tension-driven Benard (Marangoni) convection in a fluid of Prandtl number 81. As the Marangoni number M is increased, an ideal hexagonal pattern is supplanted by a defect-free square pattern; the transition occurs gradually with patterns of mixed hexagonal, pentagonal, and square symmetry arising at intermediate values of M. An elementary topological process associated with two-dimensional patterns governs local changes in morphology; the dynamics are relaxational with all patterns becoming stationary with M fixed for a sufficiently long time. The transition is hysteretic and depends strongly on the pattern wave number. (C) 1999 American Institute of Physics. [S1070-6631(99)00209-3].