BENARD-MARANGONI CONVECTIVE PATTERNS IN SMALL CYLINDRICAL LAYERS

A study of Benard-Marangoni convection in containers of small aspect r ation (defined as the ratio of the diameter of the container to The de pth of the liquid) is presented. In this situation, sidewall constrain ts have an important role in selecting the pattern at the onset of con vection. In many situations, this pattern is axisymmetric with well-di stributed azimuthal modal lines (simple model. When increasing an exte rnal parameter (supercritical heating), more complex dynamics can appe ar due lo secondary instabilities. The experimental results presented here show that patterns beyond threshold can be just simple modes, a l inear combination of simple modes, or more complicated structures that cannot be described just by superposition of a few modes. These exper imental results are compared with some theoretical models, based on am plitude -equations, and on a generalized Swift-Hohenberg equation. Whe reas the former approach provides a simple and straightforward descrip tion for certain patterns near threshold, simulations of the latter gi ve many of the patterns observed in the experiments.