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

Three-dimensional (3D) bifurcations of a partially melted or solidified mat erial in a cylinder heated from below are studied numerically. Through nonl inear calculations, bifurcation diagrams are constructed fur a melt of a Pr andtl number of one. As the interface is fixed, our calculated results agre e reasonably well with previous calculations, but some discrepancies exist, which are further discussed, through their dynamic evolutions and imperfec t bifurcations of 5 degrees tilt. As the interface is allowed to deform, th e bifurcation behavior changes significantly. both for the onset of convect ion and its convection mode. For the initial melt aspect ratio of one, the primary bifurcation changes from supercritical to subcritical with the incr easing solid amount, and the onset mode from an axisymmetric (m0) mode to a 3D (ml) mode. Although the free interface destabilizes the conductive mode and leads to an earlier onset of convection, it may stabilize some flow mo des through its confinement. Imperfect bifurcations due to a 5 degrees tilt al-e further illustrated. (C) 2001 Elsevier Science Ltd. All rights reserv ed.