  We study the effects of externally imposed shear and buoyancy driven flows on
the stability of a solid-liquid interface. By reanalyzing the data of Gilpin
\emph{et al.} [\emph{J. Fluid Mech.}, {\bf 99}(3), 619 (1980)] we show that the
instability of the ice-water interface observed in their experiments was
affected by buoyancy effects, and that their velocity measurements are more
accurately described by Monin-Obukhov theory. A linear stability analysis of
shear and buoyancy driven flow of melt over its solid phase shows that buoyancy
is the only destabilizing factor and that the regime of shear flow here, by
inhibiting vertical motions and hence the upward heat flux, stabilizes the
system. It is also shown that all perturbations to the solid-liquid interface
decay at a very modest strength of the shear flow. However, at much larger
shear, where flow instabilities coupled with buoyancy might enhance vertical
motions, a re-entrant instability may arise.
