Ca. Chung et F. Chen, Morphological instability in a directionally solidifying binary solution with an imposed shear flow, J FLUID MEC, 436, 2001, pp. 85-106
The effect of an imposed shear flow on the stability of directionally solid
ifying binary alloys is investigated. It is shown that without the imposed
shear flow the system is dominated by stationary boundary-layer-mode convec
tion, a convection of salt-finger type confined to the solute boundary laye
r above the melt/mush interface. When the shear flow (no matter how small)
is imposed, the boundary-layer mode becomes a longitudinal mode (roll-axis
parallel to the imposed flow) propagating in the direction perpendicular to
the shear flow, while the modes containing a transverse component are inhi
bited. As the shear flow becomes large enough, a transverse mode (roll-axis
perpendicular to the imposed flow) of very unstable characteristics is ind
uced. This mode, called the morphological mode, can exist even without buoy
ancy. It is triggered by the flow induced in the mushy layer through the Be
rnoulli force, a pressure variation resulting from the imposed flow passing
along the corrugated melt/mush interface. It, nonetheless, has no relation
to the boundary layer instability of the shear flow. The effect of imposed
shear flow is so significant that the stability characteristics can be ent
irely different when the intensity of the imposed flow is larger than a cri
tical value, which is calculated in the present paper.