Transient convective instabilities in directional solidification
arXiv:1005.5261 · doi:10.1063/1.3511520
Abstract
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.
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.org