Pattern selection in single-component systems coupling Bénard convection and solidification

A horizontal layer is heated from below and cooled from above so that the enclosed single-component liquid is frozen in the upper part of the layer. When the imposed temperature difference is such that the Rayleigh number across the liquid is supercritical, there is Bénard convection coupled with the dynamics of the solidification interface. An experiment is presented which shows that the interfacial corrugations that result are two-dimensional when this solid is thin but hexagonal when the solid is thick. A weakly nonlinear convective instability theory is presented which explains this behaviour, and isolates this ‘purely thermal’ mechanism of pattern selection. Jump behaviour is seen in the liquid-layer thickness at the onset of hexagonal convection.