PATTERN STUDY IN THE 2-D SOLUTAL CONVECTION ABOVE A BRIDGMAN-TYPE SOLIDIFICATION FRONT

We numerically investigate the two-dimensional (2-D) convective flow d eveloping in the liquid phase above an alloy growing in the upward Bri dgman configuration of directional solidification. Using a time-depend ent approach, we are able to describe the various cycles of hysteresis that connect the different branches of stable steady solutions. The m ain trends of the present results show that the bifurcation diagram, c omposed of the branches, found in previous works for the partition coe fficient k = 0.3, remains qualitatively valid for k = 1.1: for a small frontal width the leading primary bifurcation is subcritical, while a transcritical bifurcation occurs for larger front. We bring the new c omplementary feature that the subcritical bifurcation becomes supercri tical when the front width tends to zero. Furthermore, for an intermed iate frontal width, we address the question of the nature of upper sta bility limits on various stable steady branches. We show that the limi t occurs via either a steady secondary bifurcation or a Hopf bifurcati on that initiates an unsteady solution branch which is followed up to chaos. The related route is a subharmonic cascade. When following this chaotic branch, a striking relaminarization process towards a steady secondary branch occurs. Finally we shortly investigate the case of a twice larger frontal width, for which several cycles of hysteresis are equally reported. (C) 1997 American Institute of Physics.