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Localisation of convection in mushy layers by weak background flow

Published online by Cambridge University Press:  11 May 2011

S. M. ROPER ,
S. H. DAVIS  and
P. W. VOORHEES
S. M. ROPER*
Affiliation:
School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, UK
S. H. DAVIS
Affiliation:
Engineering Sciences and Applied Math, Northwestern University, Evanston, IL 60208-3125, USA
P. W. VOORHEES
Affiliation:
Materials Science and Engineering, Northwestern University, Evanston, IL 60208-3108, USA
*
†Email address for correspondence: Steven.Roper@glasgow.ac.uk
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Abstract

It is known that freckles form at the sidewalls of directionally solidified materials. We present a weakly nonlinear analysis of the effects of a weak and slowly varying background flow formed by non-axial thermal gradients on convection near onset in a mushy layer. We find that in the two-dimensional case, the onset of mush convection occurs away from the walls. However if three-dimensional disturbances are allowed, the onset occurs near the walls of the container confining the mush. We derive amplitude equations governing this behaviour and simulate their evolution numerically.

JFM classification

Convection: Convection in porous media Nonlinear Dynamical Systems: Low-dimensional models Phase change: Solidification/melting

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 675 , 25 May 2011 , pp. 518 - 528
Copyright
Copyright © Cambridge University Press 2011

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References

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