A new oscillatory instability in a

We consider the solidi cation of a binary alloy in a mushy layer and analyse the linear stability of a quiescent state with speci c interest in identifying an oscillatory convective instability. We employ a near-eutectic approximation and consider the limit of large fareld temperature. These asymptotic limits allow us to examine the dynamics of the mushy layer in the form of small deviations from the classical case of convection in a horizontal porous layer of uniform permeability. We consider also the limit of large Stefan number, which incorporates a key balance necessary for the existence of the oscillatory instability. The model we consider here contains no double-di usive e ects and no region in which a statically stable density gradient exists. The mechanism underlying the oscillatory instability we discover is instead associated with a complex interaction between heat transfer, convection and solidi cation.