Abstract
Nonlinear solutal convection in the melt under a planar solidifying surface is investigated in the limit of small segregation k and for cases where the amplitude of motion is not restricted to be small. In contrast to the small-amplitude case, it is found that there is no subcritical instability and that squares can be the only stable flow pattern for a significant range of amplitudes that widens as k decreases or as Péclet number z∞ increases. All the other flow structures are unstable with the exception of down-hexagons, which can be stable only in a narrow range of small amplitudes. This later range of amplitudes is independent of k, but it reduces in size as z∞ increases.
Published Version
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