We study the convective instability of the melt during the initial transient
in a directional solidification experiment in a vertical configuration. We
obtain analytically the dispersion relation, and perform an additional
asymptotic expansion for large Rayleigh number that permits a simpler
analytical analysis and a better numerical behavior. We find a transient
instability, i.e. a regime in which the system destabilizes during the
transient whereas the final unperturbed steady state is stable. This could be
relevant to growth mode predictions in solidification.Comment: 28 pages, 5 figures. The following article has been accepted for
publication in Physics of Fluids. After it is published, it will be found at
http://pof.aip.or
