Bénard-Marangoni convective patterns in small cylindrical layers

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Abstract
A study of Bénard-Marangoni convection in containers of small aspect ratio (defined as the ratio of the diameter of the container to the depth of the liquid) is presented. In this situation, sidewall constraints have an important role in selecting the pattern at the onset of convection. In many situations, this pattern is axisymmetric with well-distributed azimuthal nodal lines (simple mode). When increasing an external parameter (supercritical heating), more complex dynamics can appear due to secondary instabilities. The experimental results presented here show that patterns beyond threshold can be just simple modes, a linear combination of simple modes, or more complicated structures that cannot be described just by superposition of a few modes. These experimental results are compared with some theoretical models, based on amplitude equations, and on a generalized Swift-Hohenberg equation. Whereas the former approach provides a simple and straightforward description for certain patterns near threshold, simulations of the latter give many of the patterns observed in the experiments.