Linear and nonlinear convection in solidifying ternary alloys

In this paper we consider buoyancy-driven flow and directional solidification of a ternary alloy in two dimensions. A steady flow can be established by forcing liquid downward at an average rate V through a temperature gradient that is fixed in the laboratory frame of reference and spans both the eutectic and liquidus temperature of the material being solidified. Our results include both a linear stability analysis and numerical solution of the governing equations for finite-amplitude steady states. The ternary system is characterized by two distinct mushy zones – a primary layer with dendrites composed of a single species and, beneath the primary layer, a secondary layer with a dendritic region composed of two species. The two layers have independent effective Rayleigh numbers, which allows for a variety of convection scenarios.