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Flow-induced patterns in directional solidification: localized morphologies in three-dimensional flows

Published online by Cambridge University Press:  02 November 2000

Y.-J. CHEN  and
S. H. DAVIS
Y.-J. CHEN
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
S. H. DAVIS
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
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Abstract

We consider the effect of steady, three-dimensional cellular convective fields impressed upon the moving front of a dilute binary alloy in directional solidification. The flows have length scales longer than the characteristic lengths of the morphological instability. A Floquet problem with multiple degrees of freedom in space governs the interfacial dynamics and determines the morphological patterns and marginal stability boundaries. In the cases of weak flows the induced patterns are superpositions of rolls modulated by the forced flows. When the flows are strong, the instability becomes spatially localized and confined at inward flow-stagnation regions on the front. Numerical computations and the WKB method are used to solve the eigenvalue problems, showing various localized states depending on the structures of the imposed flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 421 , 25 October 2000 , pp. 369 - 380
Copyright
© 2000 Cambridge University Press

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