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

Michael F. Schatz, Stephen J. VanHook, W. D. McCormick, J. B. Swift, Harry L. Swinney
1999 Physics of Fluids  
The transition between hexagonal and square patterns is investigated in laboratory experiments on surface-tension-driven Bénard ͑Marangoni͒ 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
more » ... atterns 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.
doi:10.1063/1.870120 fatcat:wiv6jo6atzei7kothn45f5gquy