Three-dimensional bifurcations of a two-phase Rayleigh–Benard problem in a cylinder

Three-dimensional (3D) bifurcations of a partially melted or solidified material in a cylinder heated from below are studied numerically. Through nonlinear calculations, bifurcation diagrams are constructed for a melt of a Prandtl number of one. As the interface is fixed, our calculated results agree reasonably well with previous calculations, but some discrepancies exist, which are further discussed through their dynamic evolutions and imperfect bifurcations of 5° tilt. As the interface is allowed to deform, the bifurcation behavior changes significantly, both for the onset of convection and its convection mode. For the initial melt aspect ratio of one, the primary bifurcation changes from supercritical to subcritical with the increasing solid amount, and the onset mode from an axisymmetric (m0) mode to a 3D (m1) mode. Although the free interface destabilizes the conductive mode and leads to an earlier onset of convection, it may stabilize some flow modes through its confinement. Imperfect bifurcations due to a 5° tilt are further illustrated.